Section 2: Physics of Ultrasound
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<strong>Section</strong> 2: <strong>Physics</strong> <strong>of</strong> <strong>Ultrasound</strong>
Content: <strong>Section</strong> 2: <strong>Physics</strong> <strong>of</strong> <strong>Ultrasound</strong><br />
2.0: <strong>Ultrasound</strong> Formula<br />
2.1: Wave Propagation<br />
2.2: Modes <strong>of</strong> Sound Wave Propagation<br />
2.3: Sound Propagation in Elastic Materials<br />
2.4: Properties <strong>of</strong> Acoustic Plane Wave<br />
2.5: Wavelength and Defect Detection<br />
2.6: Attenuation <strong>of</strong> Sound Waves<br />
2.7: Acoustic Impedance<br />
2.8: Reflection and Transmission Coefficients (Pressure)<br />
2.9: Refraction and Snell's Law<br />
2.10: Mode Conversion<br />
2.11: Signal-to-Noise Ratio<br />
2.12: The Sound Fields- Dead / Fresnel & Fraunh<strong>of</strong>er Zones<br />
2.13: Inverse Square Rule/ Inverse Rule<br />
2.14: Resonance<br />
2.15 Measurement <strong>of</strong> Sound<br />
2.16 Practice Makes Perfect
2.0: <strong>Ultrasound</strong> Formula<br />
http://www.ndt-ed.org/GeneralResources/Calculator/calculator.htm
Ultrasonic Formula
Ultrasonic Formula
Parameters <strong>of</strong> Ultrasonic Waves
2.1: Wave Propagation<br />
Ultrasonic testing is based on time-varying deformations or vibrations in<br />
materials, which is generally referred to as acoustics. All material substances<br />
are comprised <strong>of</strong> atoms, which may be forced into vibration motion about their<br />
equilibrium positions. Many different patterns <strong>of</strong> vibration motion exist at the<br />
atomic level, however, most are irrelevant to acoustics and ultrasonic testing.<br />
Acoustics is focused on particles that contain many atoms that move in<br />
unison to produce a mechanical wave. When a material is not stressed in<br />
tension or compression beyond its elastic limit, its individual particles perform<br />
elastic oscillations. When the particles <strong>of</strong> a medium are displaced from their<br />
equilibrium positions, internal (electrostatic) restoration forces arise. It is these<br />
elastic restoring forces between particles, combined with inertia <strong>of</strong> the<br />
particles, that leads to the oscillatory motions <strong>of</strong> the medium.<br />
Keywords:<br />
■ internal (electrostatic) restoration forces<br />
■ inertia <strong>of</strong> the particles
Acoustic Spectrum
Acoustic Spectrum
Acoustic Spectrum
Acoustic Wave – Node and Anti-Node<br />
The points where the two waves constantly cancel each other are called<br />
nodes, and the points <strong>of</strong> maximum amplitude between them, antinodes.<br />
http://www.physicsclassroom.com/Class/waves/u10l4c.cfm<br />
http://www.physicsclassroom.com/Class/waves/h4.gif
Acoustic Wave – Node and Anti-Node<br />
Formation <strong>of</strong> a standing wave by two waves from opposite directions
http://hyperphysics.phy-astr.gsu.edu/hbase/waves/standw.html
Q151 A point, line or surface <strong>of</strong> a vibration body marked by absolute or<br />
relative freedom from vibratory motion (momentarily?) is referred to as:<br />
a) a node<br />
b) an antinode<br />
c) rarefaction<br />
d) compression
2.2: Modes <strong>of</strong> Sound Wave Propagation<br />
2.2.1 Modes <strong>of</strong> <strong>Ultrasound</strong><br />
In solids, sound waves can propagate in four principle modes that are based<br />
on the way the particles oscillate. Sound can propagate as;<br />
• longitudinal waves,<br />
• shear waves,<br />
• surface waves,<br />
• and in thin materials as plate waves.<br />
Longitudinal and shear waves are the two modes <strong>of</strong> propagation most widely<br />
used in ultrasonic testing. The particle movement responsible for the<br />
propagation <strong>of</strong> longitudinal and shear waves is illustrated below.
2.2.2 Propagation & Polarization Vectors<br />
• Propagation Vector- The direction <strong>of</strong> wave propagation<br />
• Polarization Vector- The direction <strong>of</strong> particle motion
Longitudinal and shear waves
Longitudinal and shear waves- Defined the Vectors
Longitudinal and shear waves
Longitudinal and shear waves
2.2.3 Longitudinal Wave<br />
Also Knows as:<br />
• longitudinal waves,<br />
• pressure wave<br />
• compressional waves.<br />
• density waves<br />
can be generated in (1) liquids, as well as (2) solids<br />
http://www.ndt-ed.org/EducationResources/CommunityCollege/Ultrasonics/Graphics/Flash/longitudinal.swf
In longitudinal waves, the oscillations occur in the longitudinal direction or the<br />
direction <strong>of</strong> wave propagation. Since compressional and dilational forces are<br />
active in these waves, they are also called pressure or compressional waves.<br />
They are also sometimes called density waves because their particle density<br />
fluctuates as they move. Compression waves can be generated in liquids, as<br />
well as solids because the energy travels through the atomic structure by a<br />
series <strong>of</strong> compressions and expansion (rarefaction) movements.
Longitudinal wave: Longitudinal waves (L-Waves) compress and decompress<br />
the material in the direction <strong>of</strong> motion, much like sound waves in air.
Longitudinal Wave
2.2.4 Shear waves (S-Waves)<br />
In air, sound travels by the compression and rarefaction <strong>of</strong> air molecules in<br />
the direction <strong>of</strong> travel. However, in solids, molecules can support vibrations in<br />
other directions, hence, a number <strong>of</strong> different types <strong>of</strong> sound waves are<br />
possible. Waves can be characterized in space by oscillatory patterns that<br />
are capable <strong>of</strong> maintaining their shape and propagating in a stable<br />
manner. The propagation <strong>of</strong> waves is <strong>of</strong>ten described in terms <strong>of</strong> what are<br />
called “wave modes.”<br />
As mentioned previously, longitudinal and transverse (shear) waves are most<br />
<strong>of</strong>ten used in ultrasonic inspection. However, at surfaces and interfaces,<br />
various types <strong>of</strong> elliptical or complex vibrations <strong>of</strong> the particles make other<br />
waves possible. Some <strong>of</strong> these wave modes such as (1) Rayleigh and (2)<br />
Lamb waves are also useful for ultrasonic inspection.<br />
Keywords:<br />
Compression<br />
Rarefaction
Shear waves vibrate particles at right angles compared to the motion <strong>of</strong> the<br />
ultrasonic wave. The velocity <strong>of</strong> shear waves through a material is<br />
approximately half that <strong>of</strong> the longitudinal waves. The angle in which the<br />
ultrasonic wave enters the material determines whether longitudinal, shear, or<br />
both waves are produced.
Shear waves
In the transverse or shear wave, the particles oscillate at a right angle or<br />
transverse to the direction <strong>of</strong> propagation. Shear waves require an<br />
acoustically solid material for effective propagation, and therefore, are not<br />
effectively propagated in materials such as liquids or gasses. Shear waves<br />
are relatively weak when compared to longitudinal waves. In fact, shear<br />
waves are usually generated in materials using some <strong>of</strong> the energy from<br />
longitudinal waves.<br />
http://www.ndt-ed.org/EducationResources/CommunityCollege/Ultrasonics/Graphics/Flash/transverse.swf
Q10: For a shear wave travelling from steel to water incident on the boundary<br />
at 10 degrees will give a refracted shear wave in water with an angle <strong>of</strong>:<br />
A. 0 degrees<br />
B. 5 degrees<br />
C. 20 degrees<br />
D. none <strong>of</strong> the above
2.2.5 Rayleigh Characteristics<br />
Rayleigh waves are a type <strong>of</strong> surface wave that travel near the surface <strong>of</strong><br />
solids. Rayleigh waves include both longitudinal and transverse motions that<br />
decrease exponentially in amplitude as distance from the surface increases.<br />
There is a phase difference between these component motions. In isotropic<br />
solids these waves cause the surface particles to move in ellipses in planes<br />
normal to the surface and parallel to the direction <strong>of</strong> propagation – the major<br />
axis <strong>of</strong> the ellipse is vertical. At the surface and at shallow depths this motion<br />
is retrograde 逆 行 , that is the in-plane motion <strong>of</strong> a particle is counterclockwise<br />
when the wave travels from left to right.<br />
http://en.wikipedia.org/wiki/Rayleigh_wave
Rayleigh waves are a type <strong>of</strong> surface acoustic wave that travel on solids.<br />
They can be produced in materials in many ways, such as by a localized<br />
impact or by piezo-electric transduction, and are frequently used in nondestructive<br />
testing for detecting defects. They are part <strong>of</strong> the seismic waves<br />
that are produced on the Earth by earthquakes. When guided in layers they<br />
are referred to as Lamb waves, Rayleigh–Lamb waves, or generalized<br />
Rayleigh waves.
Rayleigh waves
Q29: The longitudinal wave incident angle which results in formation <strong>of</strong> a<br />
Rayleigh wave is called:<br />
A. Normal incidence<br />
B. The first critical angle<br />
C. The second critical angle<br />
D. Any angle above the first critical angle
Surface (or Rayleigh) waves travel the surface <strong>of</strong> a relatively thick solid<br />
material penetrating to a depth <strong>of</strong> one wavelength.<br />
Surface waves combine both (1) a longitudinal and (2) transverse motion to<br />
create an elliptic orbit motion as shown in the image and animation below.<br />
http://www.ndt-ed.org/EducationResources/CommunityCollege/Ultrasonics/Graphics/Flash/rayleigh.swf
The major axis <strong>of</strong> the ellipse is perpendicular to the surface <strong>of</strong> the solid. As<br />
the depth <strong>of</strong> an individual atom from the surface increases the width <strong>of</strong> its<br />
elliptical motion decreases. Surface waves are generated when a<br />
longitudinal wave intersects a surface near the second critical angle and<br />
they travel at a velocity between .87 and .95 <strong>of</strong> a shear wave. Rayleigh<br />
waves are useful because they are very sensitive to surface defects (and<br />
other surface features) and they follow the surface around curves.<br />
Because <strong>of</strong> this, Rayleigh waves can be used to inspect areas that other<br />
waves might have difficulty reaching.<br />
Wave velocity:<br />
• Longitudinal wave velocity =1v,<br />
• The velocity <strong>of</strong> shear waves through a material is approximately half that<br />
<strong>of</strong> the longitudinal waves, (≈0.5v)<br />
• Surface waves are generated when a longitudinal wave intersects a<br />
surface near the second critical angle and they travel at a velocity<br />
between .87 and .95 <strong>of</strong> a shear wave. ≈(0.87~0.95)x0.5v
The major axis <strong>of</strong> the ellipse is perpendicular to the surface <strong>of</strong> the solid.
Surface wave
Surface wave or Rayleigh wave are formed when shear waves refract to 90.<br />
The whip-like particle vibration <strong>of</strong> the shear wave is converted into elliptical<br />
motion by the particle changing direction at the interface with the surface. The<br />
wave are not <strong>of</strong>ten used in industrial NDT although they do have some<br />
application in aerospace industry. Their mode <strong>of</strong> propagation is elliptical along<br />
the surface <strong>of</strong> material, penetrating to a depth <strong>of</strong> one wavelength. They will<br />
follow the contour <strong>of</strong> the surface and they travel at approximately 90% <strong>of</strong> the<br />
velocity <strong>of</strong> the shear waves.<br />
Depth <strong>of</strong> penetration <strong>of</strong><br />
about one wavelength<br />
Direction <strong>of</strong> wave propagation
Surface wave has the ability to follow surface contour, until it meet a sharp<br />
change i.e. a surface crack/seam/lap. However the surface waves could be<br />
easily completely absorbed by excess couplant <strong>of</strong> simply touching the part<br />
ahead <strong>of</strong> the waves.<br />
Transducer<br />
Wedge<br />
Surface discontinuity<br />
Specimen
Surface wave - Following Contour<br />
Surface wave
Surface wave – One wavelength deep<br />
λ<br />
λ
Rayleigh Wave<br />
http://web.ics.purdue.edu/~braile/edumod/waves/Rwave_files/image001.gif
Love Wave<br />
http://web.ics.purdue.edu/~braile/edumod/waves/Lwave_files/image001.gif
Love Wave
Other Reading: Rayleigh Waves<br />
Surface waves (Rayleigh waves) are another type <strong>of</strong> ultrasonic wave used in<br />
the inspection <strong>of</strong> materials. These waves travel along the flat or curved<br />
surface <strong>of</strong> relatively thick solid parts. For the propagation <strong>of</strong> waves <strong>of</strong> this type,<br />
the waves must be traveling along an interface bounded on one side by the<br />
strong elastic forces <strong>of</strong> a solid and on the other side by the practically<br />
negligible elastic forces between gas molecules. Surface waves leak energy<br />
into liquid couplants and do not exist for any significant distance along the<br />
surface <strong>of</strong> a solid immersed in a liquid, unless the liquid covers the solid<br />
surface only as a very thin film. Surface waves are subject to attenuation in a<br />
given material, as are longitudinal or transverse waves. They have a velocity<br />
approximately 90% <strong>of</strong> the transverse wave velocity in the same material. The<br />
region within which these waves propagate with effective energy is not much<br />
thicker than about one wavelength beneath the surface <strong>of</strong> the metal.
At this depth, wave energy is about 4% <strong>of</strong> the wave energy at the surface,<br />
and the amplitude <strong>of</strong> oscillation decreases sharply to a negligible value at<br />
greater depths. Surface waves follow contoured surfaces. For example,<br />
surface waves traveling on the top surface <strong>of</strong> a metal block are reflected from<br />
a sharp edge, but if the edge is rounded <strong>of</strong>f, the waves continue down the<br />
side face and are reflected at the lower edge, returning to the sending point.<br />
Surface waves will travel completely around a cube if all edges <strong>of</strong> the cube<br />
are rounded <strong>of</strong>f. Surface waves can be used to inspect parts that have<br />
complex contours.
Q110: What kind <strong>of</strong> wave mode travel at a velocity slightly below the shear<br />
wave and their modes <strong>of</strong> propagation are both longitudinal and transverse<br />
with respect to the surface?<br />
a) Rayleigh wave<br />
b) Transverse wave<br />
c) L-wave<br />
d) Longitudinal wave
Q: Which <strong>of</strong> the following modes <strong>of</strong> vibration exhibits the shortest wavelength<br />
at a given frequency and in a given material?<br />
A. longitudinal wave<br />
B. compression wave<br />
C. shear wave<br />
D. surface wave
2.2.6 Lamb Wave:<br />
Lamb waves propagate in solid plates. They are elastic waves whose<br />
particle motion lies in the plane that contains the direction <strong>of</strong> wave<br />
propagation and the plate normal (the direction perpendicular to the plate). In<br />
1917, the english mathematician horace lamb published his classic analysis<br />
and description <strong>of</strong> acoustic waves <strong>of</strong> this type. Their properties turned out to<br />
be quite complex. An infinite medium supports just two wave modes traveling<br />
at unique velocities; but plates support two infinite sets <strong>of</strong> lamb wave modes,<br />
whose velocities depend on the relationship between wavelength and plate<br />
thickness.
Since the 1990s, the understanding and utilization <strong>of</strong> lamb waves has<br />
advanced greatly, thanks to the rapid increase in the availability <strong>of</strong> computing<br />
power. Lamb's theoretical formulations have found substantial practical<br />
application, especially in the field <strong>of</strong> nondestructive testing.<br />
The term rayleigh–lamb waves embraces the rayleigh wave, a type <strong>of</strong> wave<br />
that propagates along a single surface. Both rayleigh and lamb waves are<br />
constrained by the elastic properties <strong>of</strong> the surface(s) that guide them.<br />
http://en.wikipedia.org/wiki/Lamb_wave<br />
http://pediaview.com/openpedia/Lamb_waves
Types <strong>of</strong> Wave<br />
New!<br />
• Plate wave- Love<br />
• Stoneley wave<br />
• Sezawa
Plate or Lamb waves are the most commonly used plate waves in<br />
NDT. Lamb waves are complex vibrational waves that propagate parallel to<br />
the test surface throughout the thickness <strong>of</strong> the material. Propagation <strong>of</strong> Lamb<br />
waves depends on the density and the elastic material properties <strong>of</strong> a<br />
component. They are also influenced a great deal by the test frequency and<br />
material thickness. Lamb waves are generated at an incident angle in which<br />
the parallel component <strong>of</strong> the velocity <strong>of</strong> the wave in the source is equal to the<br />
velocity <strong>of</strong> the wave in the test material. Lamb waves will travel several<br />
meters in steel and so are useful to scan plate, wire, and tubes.<br />
Lamb wave influenced by: (Dispersive Wave)<br />
■<br />
■<br />
■<br />
■<br />
Density<br />
Elastic material properties<br />
Frequencies<br />
Material thickness
Plate or Lamb waves are similar to surface waves except they can only be<br />
generated in materials a few wavelengths thick.<br />
http://www.ndt.net/ndtaz/files/lamb_a.gif
Plate wave or Lamb wave are formed by the introduction <strong>of</strong> surface wave<br />
into a thin material. They are a combination <strong>of</strong> (1) compression and surface or<br />
(2) shear and surface waves causing the plate material to flex by totally<br />
saturating the material. The two types <strong>of</strong> plate waves:
With Lamb waves, a number <strong>of</strong> modes <strong>of</strong> particle vibration are possible, but<br />
the two most common are symmetrical and asymmetrical. The complex<br />
motion <strong>of</strong> the particles is similar to the elliptical orbits for surface<br />
waves. Symmetrical Lamb waves move in a symmetrical fashion about the<br />
median plane <strong>of</strong> the plate. This is sometimes called the extensional mode<br />
because the wave is “stretching and compressing” the plate in the wave<br />
motion direction. Wave motion in the symmetrical mode is most efficiently<br />
produced when the exciting force is parallel to the plate. The asymmetrical<br />
Lamb wave mode is <strong>of</strong>ten called the “flexural mode” because a large portion<br />
<strong>of</strong> the motion moves in a normal direction to the plate, and a little motion<br />
occurs in the direction parallel to the plate. In this mode, the body <strong>of</strong> the plate<br />
bends as the two surfaces move in the same direction.<br />
The generation <strong>of</strong> waves using both piezoelectric transducers and<br />
electromagnetic acoustic transducers (EMATs) are discussed in later sections.<br />
Keywords:<br />
Symmetrical = extensional mode<br />
Asymmetrical = flexural mode
When guided in layers they are referred to as Lamb waves, Rayleigh–Lamb<br />
waves, or generalized Rayleigh waves.<br />
Lamb waves – 2 modes
Symmetrical = extensional mode<br />
Asymmetrical = flexural mode
Symmetrical = extensional mode<br />
Asymmetrical = flexural mode
Symmetrical = extensional mode
Other Reading: Lamb Wave<br />
Lamb waves, also known as plate waves, are another type <strong>of</strong> ultrasonic wave<br />
used in the nondestructive inspection <strong>of</strong> materials. Lamb waves are<br />
propagated in plates (made <strong>of</strong> composites or metals) only a few wavelengths<br />
thick. A Lamb wave consists <strong>of</strong> a complex vibration that occurs throughout the<br />
thickness <strong>of</strong> the material. The propagation characteristics <strong>of</strong> Lamb waves<br />
depend on the density, elastic properties, and structure <strong>of</strong> the material as well<br />
as the thickness <strong>of</strong> the test piece and the frequency. Their behavior in general<br />
resembles that observed in the transmission <strong>of</strong> electromagnetic waves<br />
through waveguides.<br />
There are two basic forms <strong>of</strong> Lamb waves:<br />
• Symmetrical, or dilatational<br />
• Asymmetrical, or bending
The form is determined by whether the particle motion is symmetrical or<br />
asymmetrical with respect to the neutral axis <strong>of</strong> the test piece. Each form is<br />
further subdivided into several modes having different velocities, which can<br />
be controlled by the angle at which the waves enter the test piece.<br />
Theoretically, there are an infinite number <strong>of</strong> specific velocities at which Lamb<br />
waves can travel in a given material. Within a given plate, the specific<br />
velocities for Lamb waves are complex functions <strong>of</strong> plate thickness and<br />
frequency.<br />
In symmetrical (dilatational) Lamb waves, there is a compressional<br />
(longitudinal) particle displacement along the neutral axis <strong>of</strong> the plate and an<br />
elliptical particle displacement on each surface (Fig. 4a). In asymmetrical<br />
(bending) Lamb waves, there is a shear (transverse) particle displacement<br />
along the neutral axis <strong>of</strong> the plate and an elliptical particle displacement on<br />
each surface (Fig. 4b). The ratio <strong>of</strong> the major to minor axes <strong>of</strong> the ellipse is a<br />
function <strong>of</strong> the material in which the wave is being propagated.
Fig. 4 Diagram <strong>of</strong> the basic patterns <strong>of</strong> (a) symmetrical (dilatational) and (b)<br />
asymmetrical (bending) Lamb waves. The wavelength, , is the distance<br />
corresponding to one complete cycle.
Q1: The wave mode that has multiple or varying wave velocities is:<br />
A. Longitudinal waves<br />
B. Shear waves<br />
C. Transverse waves<br />
D. Lamb waves
2.2.7 Dispersive Wave:<br />
Wave modes such as those found in Lamb wave have a velocity <strong>of</strong><br />
propagation dependent upon the operating frequency, sample thickness and<br />
elastic moduli. They are dispersive (velocity change with frequency) in that<br />
pulses transmitted in these mode tend to become stretched or dispersed.
Dispersion refers to the fact that in a real medium such as water, air, or glass,<br />
a wave traveling through that medium will have a velocity that depends upon<br />
its frequency. Dispersion occurs for any form <strong>of</strong> wave, acoustic,<br />
electromagnetic, electronic, even quantum mechanical. Dispersion is<br />
responsible for a prism being able to resolve light into colors and defines the<br />
maximum frequency <strong>of</strong> broadband pulses one can send down an optical fiber<br />
or through a copper wire. Dispersion affects wave and swell forecasts at<br />
sea and influences the design <strong>of</strong> sound equipment. Dispersion is a physical<br />
property <strong>of</strong> the medium and can combine with other properties to yield very<br />
strange results. For example, in the propagation <strong>of</strong> light in an optical fiber, the<br />
glass introduces dispersion and separates the wavelengths <strong>of</strong> light according<br />
to frequency, however if the light is intense enough, it can interact with the<br />
electrons in the material changing its refractive index. The combination <strong>of</strong><br />
dispersion and index change can cancel each other leading to a wave that<br />
can propagate indefinitely maintaining a constant shape. Such a wave has<br />
been termed a soliton.<br />
http://www.rpi.edu/dept/chem-eng/WWW/faculty/plawsky/Comsol%20Modules/DispersiveWave/DispersiveWave.html
Plate or Lamb waves are generated at an incident angle in which the parallel<br />
component <strong>of</strong> the velocity <strong>of</strong> the wave in the source is equal to the velocity <strong>of</strong><br />
the wave in the test material.
Thickness Limitation:<br />
One can not generate shear / surface (or Lamb?) wave on a plate that is<br />
thinner than ½ the wavelength.
2.3: Sound Propagation in Elastic Materials<br />
In the previous pages, it was pointed out that sound waves propagate due to<br />
the vibrations or oscillatory motions <strong>of</strong> particles within a material. An<br />
ultrasonic wave may be visualized as an infinite number <strong>of</strong> oscillating masses<br />
or particles connected by means <strong>of</strong> elastic springs. Each individual particle is<br />
influenced by the motion <strong>of</strong> its nearest neighbor and both (1) inertial and (2)<br />
elastic restoring forces act upon each particle.<br />
A mass on a spring has a single resonant frequency determined by its spring<br />
constant k and its mass m. The spring constant is the restoring force <strong>of</strong> a<br />
spring per unit <strong>of</strong> length. Within the elastic limit <strong>of</strong> any material, there is a<br />
linear relationship between the displacement <strong>of</strong> a particle and the force<br />
attempting to restore the particle to its equilibrium position. This linear<br />
dependency is described by Hooke's Law.
Spring model- A mass on a spring has a single resonant frequency<br />
determined by its spring constant k and its mass m.
Spring model- A mass on a spring has a single resonant frequency<br />
determined by its spring constant k and its mass m.
In terms <strong>of</strong> the spring model, Hooke's Law says that the restoring force due to<br />
a spring is proportional to the length that the spring is stretched, and acts in<br />
the opposite direction. Mathematically, Hooke's Law is written as F =-kx,<br />
where F is the force, k is the spring constant, and x is the amount <strong>of</strong> particle<br />
displacement. Hooke's law is represented graphically it the bottom. Please<br />
note that the spring is applying a force to the particle that is equal and<br />
opposite to the force pulling down on the particle.
Elastic Model
Elastic Model / Longitudinal Wave
Elastic Model / Longitudinal Wave
Elastic Model / Shear Wave
Elastic Model / Shear Wave
The Speed <strong>of</strong> Sound<br />
Hooke's Law, when used along with Newton's Second Law, can explain a few<br />
things about the speed <strong>of</strong> sound. The speed <strong>of</strong> sound within a material is a<br />
function <strong>of</strong> the properties <strong>of</strong> the material and is independent <strong>of</strong> the amplitude<br />
<strong>of</strong> the sound wave. Newton's Second Law says that the force applied to a<br />
particle will be balanced by the particle's mass and the acceleration <strong>of</strong> the<br />
particle. Mathematically, Newton's Second Law is written as F = ma. Hooke's<br />
Law then says that this force will be balanced by a force in the opposite<br />
direction that is dependent on the amount <strong>of</strong> displacement and the spring<br />
constant (F = -kx). Therefore, since the applied force and the restoring force<br />
are equal, ma = -kx can be written. The negative sign indicates that the force<br />
is in the opposite direction.<br />
F= ma = -kx
Since the mass m and the spring constant k are constants for any given<br />
material, it can be seen that the acceleration a and the displacement x are the<br />
only variables. It can also be seen that they are directly proportional. For<br />
instance, if the displacement <strong>of</strong> the particle increases, so does its acceleration.<br />
It turns out that the time that it takes a particle to move and return to its<br />
equilibrium position is independent <strong>of</strong> the force applied. So, within a given<br />
material, sound always travels at the same speed no matter how much force<br />
is applied when other variables, such as temperature, are held constant.<br />
a ∝ x
What properties <strong>of</strong> material affect its speed <strong>of</strong> sound?<br />
Of course, sound does travel at different speeds in different materials. This is<br />
because the (1) mass <strong>of</strong> the atomic particles and the (2) spring constants are<br />
different for different materials. The mass <strong>of</strong> the particles is related to the<br />
density <strong>of</strong> the material, and the spring constant is related to the elastic<br />
constants <strong>of</strong> a material. The general relationship between the speed <strong>of</strong> sound<br />
in a solid and its density and elastic constants is given by the following<br />
equation:
Elastic constant<br />
→ spring constants<br />
Density<br />
→ mass <strong>of</strong> the atomic particles
Where V is the speed <strong>of</strong> sound, C is the elastic constant, and p is the material<br />
density. This equation may take a number <strong>of</strong> different forms depending on the<br />
type <strong>of</strong> wave (longitudinal or shear) and which <strong>of</strong> the elastic constants that are<br />
used. The typical elastic constants <strong>of</strong> a materials include:<br />
• Young's Modulus, E: a proportionality constant between uniaxial stress<br />
and strain.<br />
• Poisson's Ratio, n: the ratio <strong>of</strong> radial strain to axial strain<br />
• Bulk modulus, K: a measure <strong>of</strong> the incompressibility <strong>of</strong> a body subjected to<br />
hydrostatic pressure.<br />
• Shear Modulus, G: also called rigidity, a measure <strong>of</strong> a substance's<br />
resistance to shear.<br />
• Lame's Constants, l and m: material constants that are derived from<br />
Young's Modulus and Poisson's Ratio.
Q163 Acoustic velocity <strong>of</strong> materials are primary due to the material's:<br />
a) density<br />
b) elasticity<br />
c) both a and b<br />
d) acoustic impedance
Q50: The principle attributes that determine the differences in ultrasonic<br />
velocities among materials are:<br />
A. Frequency and wavelength<br />
B. Thickness and travel time<br />
C. Elasticity and density<br />
D. Chemistry and permeability
When calculating the velocity <strong>of</strong> a longitudinal wave, Young's Modulus and<br />
Poisson's Ratio are commonly used.<br />
When calculating the velocity <strong>of</strong> a shear wave, the shear modulus is used. It<br />
is <strong>of</strong>ten most convenient to make the calculations using<br />
Lame's Constants, which are derived from Young's Modulus and Poisson's<br />
Ratio.
E/N/G
It must also be mentioned that the subscript ij attached to C (C ij ) in the above<br />
equation is used to indicate the directionality <strong>of</strong> the elastic constants with<br />
respect to the wave type and direction <strong>of</strong> wave travel. In isotropic materials,<br />
the elastic constants are the same for all directions within the material.<br />
However, most materials are anisotropic and the elastic constants differ with<br />
each direction. For example, in a piece <strong>of</strong> rolled aluminum plate, the grains<br />
are elongated in one direction and compressed in the others and the elastic<br />
constants for the longitudinal direction are different than those for the<br />
transverse or short transverse directions.<br />
V longitudinal<br />
V transverse
Examples <strong>of</strong> approximate compressional sound velocities in materials are:<br />
Aluminum - 0.632 cm/microsecond<br />
1020 steel - 0.589 cm/microsecond<br />
Cast iron - 0.480 cm/microsecond.<br />
Examples <strong>of</strong> approximate shear sound velocities in materials are:<br />
Aluminum - 0.313 cm/microsecond<br />
1020 steel - 0.324 cm/microsecond<br />
Cast iron - 0.240 cm/microsecond.<br />
When comparing compressional and shear velocities, it can be noted that<br />
shear velocity is approximately one half that <strong>of</strong> compressional velocity. The<br />
sound velocities for a variety <strong>of</strong> materials can be found in the ultrasonic<br />
properties tables in the general resources section <strong>of</strong> this site.
Longitudinal Wave Velocity: V L<br />
The velocity <strong>of</strong> a longitudinal wave is described by the following equation:<br />
V L<br />
E<br />
μ<br />
P<br />
= Longitudinal bulk wave velocity<br />
= Young’s modulus <strong>of</strong> elasticity<br />
= Poisson ratio<br />
= Material density
Shear Wave Velocity: V S<br />
The velocity <strong>of</strong> a shear wave is described by the following equation:<br />
V s<br />
E<br />
μ<br />
P<br />
G<br />
= Shear wave velocity<br />
= Young’s modulus <strong>of</strong> elasticity<br />
= Poisson ratio<br />
= Material density<br />
= Shear modulus
2.4: Properties <strong>of</strong> Acoustic Plane Wave<br />
Wavelength, Frequency and Velocity<br />
Among the properties <strong>of</strong> waves propagating in isotropic solid materials are<br />
wavelength, frequency, and velocity. The wavelength is directly proportional<br />
to the velocity <strong>of</strong> the wave and inversely proportional to the frequency <strong>of</strong> the<br />
wave. This relationship is shown by the following equation.
The applet below shows a longitudinal and transverse wave. The direction <strong>of</strong><br />
wave propagation is from left to right and the movement <strong>of</strong> the lines indicate<br />
the direction <strong>of</strong> particle oscillation. The equation relating ultrasonic<br />
wavelength, frequency, and propagation velocity is included at the bottom <strong>of</strong><br />
the applet in a reorganized form. The values for the wavelength, frequency,<br />
and wave velocity can be adjusted in the dialog boxes to see their effects on<br />
the wave. Note that the frequency value must be kept between 0.1 to 1 MHz<br />
(one million cycles per second) and the wave velocity must be between 0.1<br />
and 0.7 cm/us.
http://www.ndt-ed.org/EducationResources/CommunityCollege/Ultrasonics/<strong>Physics</strong>/applet_2_4/applet_2_4.htm
http://www.ndt-ed.org/EducationResources/CommunityCollege/Ultrasonics/<strong>Physics</strong>/applet_2_4/applet_2_4.htm
Java don’t work? Uninstalled → Reinstalled → Then →<br />
http://jingyan.baidu.com/article/9f63fb91d0eab8c8400f0e08.html
Java don’t work?<br />
http://jingyan.baidu.com/article/9f63fb91d0eab8c8400f0e08.html
Java don’t work?<br />
http://jingyan.baidu.com/article/9f63fb91d0eab8c8400f0e08.html
Java don’t work?<br />
http://jingyan.baidu.com/article/9f63fb91d0eab8c8400f0e08.html
Java don’t work?<br />
http://jingyan.baidu.com/article/9f63fb91d0eab8c8400f0e08.html
As can be noted by the equation, a change in frequency will result in a<br />
change in wavelength. Change the frequency in the applet and view the<br />
resultant wavelength. At a frequency <strong>of</strong> .2 and a material velocity <strong>of</strong> 0.585<br />
(longitudinal wave in steel) note the resulting wavelength. Adjust the material<br />
velocity to 0.480 (longitudinal wave in cast iron) and note the resulting<br />
wavelength. Increase the frequency to 0.8 and note the shortened wavelength<br />
in each material.<br />
In ultrasonic testing, the shorter wavelength resulting from an increase in<br />
frequency will usually provide for the detection <strong>of</strong> smaller discontinuities. This<br />
will be discussed more in following sections.<br />
Keywords:<br />
the shorter wavelength resulting from an increase in frequency will usually<br />
provide for the detection <strong>of</strong> smaller discontinuities
The velocities sound waves<br />
The velocities <strong>of</strong> the various kinds <strong>of</strong> sound waves can be calculated from the<br />
elastic constants <strong>of</strong> the material concerned, that is the modulus <strong>of</strong> elasticity E<br />
(measured in N/m2), the density p in kg/m 3 , and Poisson's ratio μ (a<br />
dimensionless number).<br />
for longitudinal waves:<br />
for transverse waves:
The two velocities <strong>of</strong> sound are linked by the following relation:<br />
For all solid materials Poisson's ratio μ lies between 0 and 0.5, so that the<br />
numerical value <strong>of</strong> the expression<br />
always lies between 0 and 0.707. In steel and aluminum, μ= 0.28 and 0.34,<br />
respectively,<br />
--<br />
= 0.55 and 0.49 respectIvely.
2.5: Wavelength and Defect Detection<br />
2.5.1 Sensitivity & Resolution<br />
In ultrasonic testing, the inspector must make a decision about the frequency<br />
<strong>of</strong> the transducer that will be used. As we learned on the previous page,<br />
changing the frequency when the sound velocity is fixed will result in a<br />
change in the wavelength <strong>of</strong> the sound.<br />
The wavelength <strong>of</strong> the ultrasound used has a significant effect on the<br />
probability <strong>of</strong> detecting a discontinuity. A general rule <strong>of</strong> thumb is that a<br />
discontinuity must be larger than one-half the wavelength to stand a<br />
reasonable chance <strong>of</strong> being detected.
Sensitivity and resolution are two terms that are <strong>of</strong>ten used in ultrasonic<br />
inspection to describe a technique's ability to locate flaws. Sensitivity is the<br />
ability to locate small discontinuities. Sensitivity generally increases with<br />
higher frequency (shorter wavelengths). Resolution is the ability <strong>of</strong> the system<br />
to locate discontinuities that are close together within the material or located<br />
near the part surface. Resolution also generally increases as the frequency<br />
increases.
Keywords:<br />
• Discontinuity must be larger than one-half the wavelength to stand a<br />
reasonable chance <strong>of</strong> being detected.<br />
• Sensitivity is the ability to locate small discontinuities. Sensitivity generally<br />
increases with higher frequency (shorter wavelengths).<br />
• Resolution is the ability <strong>of</strong> the system to locate discontinuities that are<br />
close together within the material or located near the part surface.<br />
• Resolution also generally increases as the frequency increases, pulse<br />
length decrease, bandwidth increase (highly damp)
2.5.2 Grain Size & Frequency Selection<br />
The wave frequency can also affect the capability <strong>of</strong> an inspection in adverse<br />
ways. Therefore, selecting the optimal inspection frequency <strong>of</strong>ten involves<br />
maintaining a balance between the favorable and unfavorable results <strong>of</strong> the<br />
selection. Before selecting an inspection frequency, the material's grain<br />
structure and thickness, and the discontinuity's type, size, and probable<br />
location should be considered.<br />
As frequency increases, sound tends to scatter from large or course grain<br />
structure and from small imperfections within a material. Cast materials <strong>of</strong>ten<br />
have coarse grains and other sound scatters that require lower frequencies to<br />
be used for evaluations <strong>of</strong> these products.<br />
(1) Wrought and (2) forged products with directional and refined grain<br />
structure can usually be inspected with higher frequency transducers.
Keywords:<br />
• Coarse grains →Lower frequency to avoid scattering and noise,<br />
• Fine grains →Higher frequency to increase sensitivity & resolution.
Since more things in a material are likely to scatter a portion <strong>of</strong> the sound<br />
energy at higher frequencies, the penetrating power (or the maximum depth<br />
in a material that flaws can be located) is also reduced. Frequency also has<br />
an effect on the shape <strong>of</strong> the ultrasonic beam. Beam spread, or the<br />
divergence <strong>of</strong> the beam from the center axis <strong>of</strong> the transducer, and how it is<br />
affected by frequency will be discussed later.<br />
It should be mentioned, so as not to be misleading, that a number <strong>of</strong> other<br />
variables will also affect the ability <strong>of</strong> ultrasound to locate defects. These<br />
include the pulse length, type and voltage applied to the crystal, properties <strong>of</strong><br />
the crystal, backing material, transducer diameter, and the receiver circuitry <strong>of</strong><br />
the instrument. These are discussed in more detail in the material on signalto-noise<br />
ratio.
Coarse grains →Lower frequency to avoid scattering and noise,<br />
Fine grains →Higher frequency to increase sensitivity & resolution.<br />
http://www.cnde.iastate.edu/ultrasonics/grain-noise
Detectability variable:<br />
• pulse length,<br />
• type and voltage applied to the crystal,<br />
• properties <strong>of</strong> the crystal,<br />
• backing material,<br />
• transducer diameter, and<br />
• the receiver circuitry <strong>of</strong> the instrument.
Keywords:<br />
• Higher the frequency, greater the scattering, thus less penetrating.<br />
• Higher the frequency better sensitivity and better resolution<br />
• If the grain size is 1/10 the wavelength, the ultrasound will be significantly<br />
scattered.
Q7: When a material grain size is on the order <strong>of</strong> ______ wavelength or<br />
larger, excessive scattering <strong>of</strong> the ultrasonic beam affect test result.<br />
A. 1<br />
B. ½<br />
C. 1/10<br />
D. 1/100
2.5.3 Further Reading<br />
Detectability variable:<br />
• pulse length,<br />
• type and voltage applied to the crystal,<br />
• properties <strong>of</strong> the crystal,<br />
• backing material,<br />
• transducer diameter (focal length → Cross sectional area), and<br />
• the receiver circuitry <strong>of</strong> the instrument.<br />
Investigating on: Sonic pulse volume ∝ pulse length, transducer Φ
Pulse Length:<br />
A sound pulse traveling through a<br />
metal occupies a physical<br />
volume. This volume changes<br />
with depth, being smallest in the<br />
focal zone. The pulse volume, a<br />
product <strong>of</strong> a pulse length L and a<br />
cross-sectional area A, can be<br />
fairly easily measured by<br />
combining ultrasonic A-scans and<br />
C-scans, as will be seen shortly.<br />
For many cases <strong>of</strong> practical interest, the inspection simulation models predict<br />
that S/N (signal to noise ratio) is inversely proportional to the square root <strong>of</strong> the<br />
pulse volume at the depth <strong>of</strong> the defect. This is known as the “pulse volume<br />
rule-<strong>of</strong>-thumb” and has become a guiding principle for designing<br />
inspections. Generally speaking, it applies when both the grain size and the<br />
lateral size <strong>of</strong> the defect are smaller than the sound pulse diameter.<br />
http://www.cnde.iastate.edu/ultrasonics/grain-noise
Determining cross sectional area using reflector- A Scan (6db drop)
Determining cross sectional area using reflector- C Scan
“Sonic pulse volume” and S/N (defect resolution)
Pulse volume rule-<strong>of</strong>-thumb:<br />
Competing grain noise ∝√(pulse volume)
2.6: Attenuation <strong>of</strong> Sound Waves<br />
2.6.1 Material Attenuation:<br />
Attenuation by definition is the rate <strong>of</strong> decrease <strong>of</strong> sound energy when a<br />
ultrasound wave id propagating in a medium. The sound attenuation in<br />
material depends on heat treatment, grain size, viscous friction, crystal<br />
stricture (anisotropy or isotropy), porosity, elastic hysteresis, hardness,<br />
Young’s modulus, etc.<br />
Sound attenuations are affected by; (1) Geometric beam spread, (2)<br />
Absorption, (3) Scattering.<br />
Material attenuation affects item (2) & (3).
When sound travels through a medium, its intensity diminishes with distance.<br />
In idealized materials, sound pressure (signal amplitude) is only reduced by<br />
the (1) spreading <strong>of</strong> the wave. Natural materials, however, all produce an<br />
effect which further weakens the sound. This further weakening results from<br />
(2) scattering and (3) absorption. Scattering is the reflection <strong>of</strong> the sound in<br />
directions other than its original direction <strong>of</strong> propagation. Absorption is the<br />
conversion <strong>of</strong> the sound energy to other forms <strong>of</strong> energy. The combined<br />
effect <strong>of</strong> scattering and absorption (spreading?) is called attenuation.<br />
Ultrasonic attenuation is the decay rate <strong>of</strong> the wave as it propagates through<br />
material.<br />
Attenuation <strong>of</strong> sound within a material itself is <strong>of</strong>ten not <strong>of</strong> intrinsic interest.<br />
However, natural properties and loading conditions can be related to<br />
attenuation. Attenuation <strong>of</strong>ten serves as a measurement tool that leads to the<br />
formation <strong>of</strong> theories to explain physical or chemical phenomenon that<br />
decreases the ultrasonic intensity.
Absorption:<br />
Sound attenuations are affected by; (1) Geometric beam spread, (2) Absorption,<br />
(3) Scattering.<br />
Absorption processes<br />
1. Mechanical hysteresis<br />
2. Internal friction<br />
3. Others (?)<br />
For relatively non-elastic material, these s<strong>of</strong>t and pliable material include lead,<br />
plastid, rubbers and non-rigid coupling materials; much <strong>of</strong> the energy is loss as<br />
heat during sound propagation and absorption is the main reason that the<br />
testing <strong>of</strong> these material are limit to relatively thin section/
Scattering:<br />
Grain Size and Wave Frequency<br />
The relative impact <strong>of</strong> scattering source <strong>of</strong> a material depends upon their<br />
grain sizes in comparison with the Ultrasonic sound wave length. As the<br />
scattering size approaches that <strong>of</strong> a wavelength, scattering by the grain is a<br />
concern. The effects from such scattering could be compensated with the use<br />
<strong>of</strong> increasing wavelength ultrasound at the cost <strong>of</strong> decreasing sensitivity and<br />
resolution to detection <strong>of</strong> discontinuities.<br />
Other effect are anisotropic columnar grain with different elastic behavior at<br />
different grain direction. In this case the internal incident wave front becomes<br />
distorted and <strong>of</strong>ten appear to change direction (propagate better in certain<br />
preferred direction) in respond to material anisotropy.
Anisotropic Columnar Grains<br />
with different elastic behavior at different grain direction.
Spreading/ Scattering / adsorption (reflection is a form <strong>of</strong> scattering)<br />
Adsorption<br />
Scattering<br />
Spreading<br />
Scatterbrain
The amplitude change <strong>of</strong> a decaying plane wave can be expressed as:<br />
In this expression A o is the unattenuated amplitude <strong>of</strong> the propagating wave<br />
at some location. The amplitude A is the reduced amplitude after the wave<br />
has traveled a distance z from that initial location. The quantity α is the<br />
attenuation coefficient <strong>of</strong> the wave traveling in the z-direction. The α<br />
dimensions <strong>of</strong> are nepers/length, where a neper is a dimensionless<br />
quantity. The term e is the exponential (or Napier's constant) which is equal<br />
to approximately 2.71828.
The units <strong>of</strong> the attenuation value in Nepers per meter (Np/m) can be<br />
converted to decibels/length by dividing by 0.1151. Decibels is a more<br />
common unit when relating the amplitudes <strong>of</strong> two signals.
Attenuation is generally proportional to the square <strong>of</strong> sound frequency.<br />
Quoted values <strong>of</strong> attenuation are <strong>of</strong>ten given for a single frequency, or an<br />
attenuation value averaged over many frequencies may be given. Also, the<br />
actual value <strong>of</strong> the attenuation coefficient for a given material is highly<br />
dependent on the way in which the material was manufactured. Thus, quoted<br />
values <strong>of</strong> attenuation only give a rough indication <strong>of</strong> the attenuation and<br />
should not be automatically trusted. Generally, a reliable value <strong>of</strong> attenuation<br />
can only be obtained by determining the attenuation experimentally for the<br />
particular material being used.<br />
Attenuation ∝ Frequency (f ) 2
Attenuation can be determined by evaluating the multiple back wall reflections<br />
seen in a typical A-scan display like the one shown in the image at the bottom.<br />
The number <strong>of</strong> decibels between two adjacent signals is measured and this<br />
value is divided by the time interval between them. This calculation produces<br />
a attenuation coefficient in decibels per unit time Ut. This value can be<br />
converted to nepers/length by the following equation.<br />
Where v is the velocity <strong>of</strong> sound in meters per<br />
second and Ut is in decibels per second.
Amplitude at distance Z<br />
where:<br />
Where v is the velocity <strong>of</strong> sound in meters per<br />
second and Ut is in decibels per second.
A o<br />
Ut<br />
A
2.6.2 Factors Affecting Attenuation:<br />
1. Testing Factors<br />
• Testing frequency<br />
• Boundary conditions<br />
• Wave form geometry<br />
2. Base Material Factors<br />
• Material type<br />
• Chemistry<br />
• Integral constituents (fiber, voids, water content, inclusion, anisotropy)<br />
• Forms (casting, wrought)<br />
• Heat treatment history<br />
• Mechanical processes(Hot or cold working; forging, rolling, extruding,<br />
TMCP, directional working)
2.6.3 Frequency selection<br />
There is no ideal frequency; therefore, frequency selection must be made with<br />
consideration <strong>of</strong> several factors. Frequency determines the wavelength <strong>of</strong> the<br />
sound energy traveling through the material. Low frequency has longer<br />
wavelengths and will penetrate deeper than higher frequencies. To penetrate<br />
a thick piece, low frequencies should be used. Another factor is the size <strong>of</strong> the<br />
grain structure in the material. High frequencies with shorter wavelengths<br />
tend to reflect <strong>of</strong>f grain boundaries and become lost or result in ultrasonic<br />
noise that can mask flaw signals. Low frequencies must be used with coarse<br />
grain structures. However, test resolution decreases when frequency is<br />
decreased. Small defects detectable at high frequencies may be missed at<br />
lower frequencies. In addition, variations in instrument characteristics and<br />
settings as well as material properties and coupling conditions play a major<br />
role in system performance. It is critical that approved testing procedures be<br />
followed.
2.6.4 Further Reading on Attenuation
Q94: In general, which <strong>of</strong> the following mode <strong>of</strong> vibration would have the<br />
greatest penetrating power in a coarse grain material if the frequency <strong>of</strong><br />
the wave are the same?<br />
a) Longitudinal wave<br />
b) Shear wave<br />
c) Transverse wave<br />
d) All the above modes would have the same penetrating power<br />
Q: The random distribution <strong>of</strong> crystallographic direction in alloys with large<br />
crystalline structures is a factor in determining:<br />
A. Acoustic noise levels<br />
B. Selection <strong>of</strong> test frequency<br />
C. Scattering <strong>of</strong> sound<br />
D. All <strong>of</strong> the above
Q168: Heat conduction, viscous friction, elastic hysteresis, and scattering are<br />
four different mechanism which lead to:<br />
A. Attenuation<br />
B. Refraction<br />
C. Beam spread<br />
D. Saturation
Q7: When the material grain size is in the order <strong>of</strong> ____ wavelength or larger,<br />
excessive scattering <strong>of</strong> the ultrasound beam may affect test result:<br />
A. 1<br />
B. ½<br />
C. 1/10<br />
D. 1/100
2.7: Acoustic Impedance<br />
Acoustic impedance is a measured <strong>of</strong> resistance <strong>of</strong> sound propagation<br />
through a part.<br />
From the table air has lower acoustic impedance than steel and for a given<br />
energy Aluminum would travel a longer distance than steel before the same<br />
amount <strong>of</strong> energy is attenuated.
Transmission & Reflection Animation:<br />
http://upload.wikimedia.org/wikipedia/commons/3/30/Partial_transmittance.gif
Sound travels through materials under the influence <strong>of</strong> sound pressure.<br />
Because molecules or atoms <strong>of</strong> a solid are bound elastically to one another,<br />
the excess pressure results in a wave propagating through the solid.<br />
The acoustic impedance (Z) <strong>of</strong> a material is defined as the product <strong>of</strong> its<br />
density (p) and acoustic velocity (V).<br />
Z = pV<br />
Acoustic impedance is important in:<br />
1. the determination <strong>of</strong> acoustic transmission and reflection at the boundary<br />
<strong>of</strong> two materials having different acoustic impedances.<br />
2. the design <strong>of</strong> ultrasonic transducers.<br />
3. assessing absorption <strong>of</strong> sound in a medium.
The following applet can be used to calculate the acoustic impedance for any<br />
material, so long as its density (p) and acoustic velocity (V) are known. The<br />
applet also shows how a change in the impedance affects the amount <strong>of</strong><br />
acoustic energy that is reflected and transmitted. The values <strong>of</strong> the reflected<br />
and transmitted energy are the fractional amounts <strong>of</strong> the total energy incident<br />
on the interface. Note that the fractional amount <strong>of</strong> transmitted sound energy<br />
plus the fractional amount <strong>of</strong> reflected sound energy equals one. The<br />
calculation used to arrive at these values will be discussed on the next page.<br />
http://www.ndt-ed.org/EducationResources/CommunityCollege/Ultrasonics/<strong>Physics</strong>/applet_2_6/applet_2_6.htm
Reflection/Transmission Energy as a function <strong>of</strong> Z
Reflection/Transmission Energy as a function <strong>of</strong> Z
Q2.8: The acoustic impedance <strong>of</strong> material used to determined:<br />
A. Angle <strong>of</strong> refraction at the interface<br />
B. Attenuation <strong>of</strong> material<br />
C. Relative amount <strong>of</strong> sound energy coupled through and reflected at an<br />
interface<br />
D. Beam spread within the material
2.8: Reflection and Transmission Coefficients (Pressure)<br />
Ultrasonic waves are reflected at boundaries where there is a difference in<br />
acoustic impedances (Z) <strong>of</strong> the materials on each side <strong>of</strong> the boundary. (See<br />
preceding page for more information on acoustic impedance.) This difference<br />
in Z is commonly referred to as the impedance mismatch. The greater the<br />
impedance mismatch, the greater the percentage <strong>of</strong> energy that will be<br />
reflected at the interface or boundary between one medium and another.<br />
The fraction <strong>of</strong> the incident wave intensity that is reflected can be derived<br />
because particle velocity and local particle pressures must be continuous<br />
across the boundary.
When the acoustic impedances <strong>of</strong> the materials on both sides <strong>of</strong> the boundary<br />
are known, the fraction <strong>of</strong> the incident wave intensity that is reflected can be<br />
calculated with the equation below. The value produced is known as the<br />
reflection coefficient. Multiplying the reflection coefficient by 100 yields the<br />
amount <strong>of</strong> energy reflected as a percentage <strong>of</strong> the original energy.
Since the amount <strong>of</strong> reflected energy plus the transmitted energy must equal<br />
the total amount <strong>of</strong> incident energy, the transmission coefficient is calculated<br />
by simply subtracting the reflection coefficient from one.<br />
Formulations for acoustic reflection and transmission coefficients (pressure)<br />
are shown in the interactive applet below. Different materials may be<br />
selected or the material velocity and density may be altered to change the<br />
acoustic impedance <strong>of</strong> one or both materials. The red arrow represents<br />
reflected sound and the blue arrow represents transmitted sound.<br />
http://www.ndt-ed.org/EducationResources/CommunityCollege/Ultrasonics/<strong>Physics</strong>/applet_2_7/applet_2_7.htm
Reflection Coefficient:
Note that the reflection and transmission coefficients are <strong>of</strong>ten expressed in<br />
decibels (dB) to allow for large changes in signal strength to be more easily<br />
compared. To convert the intensity or power <strong>of</strong> the wave to dB units, take the<br />
log <strong>of</strong> the reflection or transmission coefficient and multiply this value times<br />
10. However, 20 is the multiplier used in the applet since the power <strong>of</strong> sound<br />
is not measured directly in ultrasonic testing. The transducers produce a<br />
voltage that is approximately proportionally to the sound pressure. The power<br />
carried by a traveling wave is proportional to the square <strong>of</strong> the pressure<br />
amplitude. Therefore, to estimate the signal amplitude change, the log <strong>of</strong> the<br />
reflection or transmission coefficient is multiplied by 20.
Using the above applet, note that the energy reflected at a water-stainless<br />
steel interface is 0.88 or 88%. The amount <strong>of</strong> energy transmitted into the<br />
second material is 0.12 or 12%. The amount <strong>of</strong> reflection and transmission<br />
energy in dB terms are -1.1 dB and -18.2 dB respectively. The negative sign<br />
indicates that individually, the amount <strong>of</strong> reflected and transmitted energy is<br />
smaller than the incident energy.
If reflection and transmission at interfaces is<br />
followed through the component, only a small<br />
percentage <strong>of</strong> the original energy makes it back<br />
to the transducer, even when loss by attenuation<br />
is ignored. For example, consider an immersion<br />
inspection <strong>of</strong> a steel block. The sound energy<br />
leaves the transducer, travels through the water,<br />
encounters the front surface <strong>of</strong> the steel,<br />
encounters the back surface <strong>of</strong> the steel and<br />
reflects back through the front surface on its way<br />
back to the transducer. At the water steel<br />
interface (front surface), 12% <strong>of</strong> the energy is<br />
transmitted. At the back surface, 88% <strong>of</strong> the<br />
12% that made it through the front surface is<br />
reflected. This is 10.6% <strong>of</strong> the intensity <strong>of</strong> the<br />
initial incident wave. As the wave exits the part<br />
back through the front surface, only 12% <strong>of</strong> 10.6<br />
or 1.3% <strong>of</strong> the original energy is transmitted back<br />
to the transducer.
Incident Wave other than Normal? – Oblique Incident<br />
http://www.slideshare.net/crisevelise/fundamentals-<strong>of</strong>ultrasound?related=1&utm_campaign=related&utm_medium=1&utm_sourc<br />
e=29
Incident Wave other than Normal? – Oblique Incident
Q: The figure above shown the partition <strong>of</strong> incident and reflected wave at<br />
water-Aluminum interface at an incident angle <strong>of</strong> 20, the reflected and<br />
transmitted wave are:<br />
A. 60% and 40%<br />
B. 40% and 60%<br />
C. 1/3 and 2/3<br />
D. 80% and 20%<br />
Note: if normal incident the reflected 70% Transmitted 30%
Further Reading (Olympus Technical Note)<br />
The boundary between two materials <strong>of</strong> different acoustic impedances is<br />
called an acoustic interface. When sound strikes an acoustic interface at<br />
normal incidence, some amount <strong>of</strong> sound energy is reflected and some<br />
amount is transmitted across the boundary. The dB loss <strong>of</strong> energy on<br />
transmitting a signal from medium 1 into medium 2 is given by:<br />
dB loss <strong>of</strong> transmission = 10 log 10 [ 4Z 1 Z 2 / (Z 1 +Z 2 ) 2 ]<br />
The dB loss <strong>of</strong> energy <strong>of</strong> the echo signal in medium 1 reflecting from an<br />
interface boundary with medium 2 is given by:<br />
dB loss <strong>of</strong> Reflection = 10 log 10 [ (Z 1 -Z 2 ) 2 / (Z 1 +Z 2 ) 2 ]
For example: The dB loss on transmitting from water (Z = 1.48) into 1020<br />
steel (Z = 45.41) is -9.13 dB; this also is the loss transmitting from 1020 steel<br />
into water. The dB loss <strong>of</strong> the backwall echo in 1020 steel in water is -0.57<br />
dB; this also is the dB loss <strong>of</strong> the echo <strong>of</strong>f 1020 steel in water. The waveform<br />
<strong>of</strong> the echo is inverted when Z2
Further Reading: Reflection & Transmission for Normal Incident<br />
http://www.slideshare.net/crisevelise/fundamentals-<strong>of</strong>ultrasound?related=1&utm_campaign=related&utm_me<br />
dium=1&utm_source=29
Q6: For an ultrasonic beam with normal incidence the transmission coefficient<br />
is given by:<br />
http://webpages.ursinus.edu/lriley/courses/p212/lectures/node19.html#eq:acousticR<br />
http://sepwww.stanford.edu/sep/pr<strong>of</strong>/waves/fgdp8/paper_html/node2.html
2.9: Refraction and Snell's Law
Refraction and Snell's Law<br />
When an ultrasonic wave passes through an<br />
interface between two materials at an oblique<br />
angle, and the materials have different indices<br />
<strong>of</strong> refraction, both reflected and refracted waves<br />
are produced. This also occurs with light, which<br />
is why objects seen across an interface appear<br />
to be shifted relative to where they really are.<br />
For example, if you look straight down at an<br />
object at the bottom <strong>of</strong> a glass <strong>of</strong> water, it looks<br />
closer than it really is. A good way to visualize<br />
how light and sound refract is to shine a<br />
flashlight into a bowl <strong>of</strong> slightly cloudy water<br />
noting the refraction angle with respect to the<br />
incident angle.
V s1<br />
Only If this medium support shear wave i.e. Solid<br />
V L1<br />
V L1<br />
V S2<br />
V L2
Refraction takes place at an interface due to the different velocities <strong>of</strong> the<br />
acoustic waves within the two materials. The velocity <strong>of</strong> sound in each<br />
material is determined by the material properties (elastic modulus and density)<br />
for that material. In the animation below, a series <strong>of</strong> plane waves are shown<br />
traveling in one material and entering a second material that has a higher<br />
acoustic velocity. Therefore, when the wave encounters the interface between<br />
these two materials, the portion <strong>of</strong> the wave in the second material is moving<br />
faster than the portion <strong>of</strong> the wave in the first material. It can be seen that this<br />
causes the wave to bend.<br />
http://www.ndt-ed.org/EducationResources/CommunityCollege/Ultrasonics/Graphics/Flash/waveRefraction.swf
http://www.ni.com/white-paper/3368/en/
Snell's Law describes the relationship between the angles and the velocities<br />
<strong>of</strong> the waves. Snell's law equates the ratio <strong>of</strong> material velocities V1 and V2 to<br />
the ratio <strong>of</strong> the sine's <strong>of</strong> incident (Ɵ 1 °) and refracted (Ɵ 2 °) angles, as shown in<br />
the following equation.<br />
Where:<br />
V L1 is the longitudinal wave velocity<br />
in material 1.<br />
V L2 is the longitudinal wave velocity<br />
in material 2.
Note that in the diagram, there is a reflected longitudinal wave (V L1' ) shown.<br />
This wave is reflected at the same angle as the incident wave because the<br />
two waves are traveling in the same material, and hence have the same<br />
velocities. This reflected wave is unimportant in our explanation <strong>of</strong> Snell's Law,<br />
but it should be remembered that some <strong>of</strong> the wave energy is reflected at the<br />
interface. In the applet below, only the incident and refracted longitudinal<br />
waves are shown. The angle <strong>of</strong> either wave can be adjusted by clicking and<br />
dragging the mouse in the region <strong>of</strong> the arrows. Values for the angles or<br />
acoustic velocities can also be entered in the dialog boxes so the that applet<br />
can be used as a Snell's Law calculator.
Snell Law<br />
http://www.ndt-ed.org/EducationResources/CommunityCollege/Ultrasonics/<strong>Physics</strong>/applet_2_8/applet_2_8.htm
Snell Law
When a longitudinal wave moves from a slower to a faster material, there is<br />
an incident angle that makes the angle <strong>of</strong> refraction for the wave 90 o . This is<br />
know as the first critical angle. The first critical angle can be found from<br />
Snell's law by putting in an angle <strong>of</strong> 90° for the angle <strong>of</strong> the refracted ray. At<br />
the critical angle <strong>of</strong> incidence, much <strong>of</strong> the acoustic energy is in the form <strong>of</strong> an<br />
inhomogeneous compression wave, which travels along the interface and<br />
decays exponentially with depth from the interface. This wave is sometimes<br />
referred to as a "creep wave." Because <strong>of</strong> their inhomogeneous nature and<br />
the fact that they decay rapidly, creep waves are not used as extensively as<br />
Rayleigh surface waves in NDT. However, creep waves are sometimes more<br />
useful than Rayleigh waves because they suffer less from surface<br />
irregularities and coarse material microstructure due to their longer<br />
wavelengths.
Snell Law
Refraction and mode conversion occur<br />
because <strong>of</strong> the change in L-wave<br />
velocity as it passes the boundary from<br />
one medium to another. The higher the<br />
difference in the velocity <strong>of</strong> sound<br />
between two materials, the larger the<br />
resulting angle <strong>of</strong> refraction. L-waves<br />
and S-waves have different angles <strong>of</strong><br />
refraction because they have dissimilar<br />
velocities within the same material.<br />
s the angle <strong>of</strong> the ultrasonic transducer<br />
continues to increase, L-waves move<br />
closer to the surface <strong>of</strong> the UUT.<br />
The angle at which the L-wave is parallel with the surface <strong>of</strong> the UUT is<br />
referred to as the first critical angle. This angle is useful for two reasons. Only<br />
one wave mode is echoed back to the transducer, making it easy to interpret<br />
the data. Also, this angle gives the test system the ability to look at surfaces<br />
that are not parallel to the front surface, such as welds.
Example: Snell’s Law<br />
L-wave and S-wave refraction angles are calculated using Snell’s law. You<br />
also can use this law to determine the first critical angle for any combination<br />
<strong>of</strong> materials.<br />
Where:<br />
Ɵ 2 ° = angle <strong>of</strong> the refracted beam in the UUT<br />
Ɵ 1 ° = incident angle from normal <strong>of</strong> beam in the wedge or liquid<br />
V 1 = velocity <strong>of</strong> incident beam in the liquid or wedge<br />
V 2 = velocity <strong>of</strong> refracted beam in the UUT
For example, calculate the first critical angle for a transducer on a plastic<br />
wedge that is examining aluminum.<br />
V 1 = 0.267 cm/µs (for L-waves in plastic)<br />
V 2 = 0.625 cm/µs (for L-waves in aluminum)<br />
Ɵ 2 ° = 90 degree (angle <strong>of</strong> L-wave for first critical angle)<br />
Ɵ 1 ° = unknown<br />
The plastic wedge must have a minimum angle <strong>of</strong> 25.29 ° to transmit only S-<br />
waves into the UUT. When the S-wave angle <strong>of</strong> refraction is greater than 90°,<br />
all ultrasonic energy is reflected by the UUT.
Snell Law: First critical angle
Snell Law: 1 st / 2 nd Critical Angles
Q155 Which <strong>of</strong> the following can occur when an ultrasound beam reaches the<br />
interface <strong>of</strong> 2 dissimilar materials?<br />
a) Reflection<br />
b) refraction<br />
c) mode conversion<br />
d) all <strong>of</strong> the above
Q. Both longitudinal and shear waves may be simultaneously generated in a<br />
second medium when the angle <strong>of</strong> incidence is:<br />
a) between the normal and the 1st critical angle<br />
b) between the 1st and 2nd critical angle<br />
c) past the second critical angle<br />
d) only at the second critical angle
Q: When angle beam contact testing a test piece, increasing the incident<br />
angle until the second critical angle is reached results in:<br />
A. Total reflection <strong>of</strong> a surface wave<br />
B. 45 degree refraction <strong>of</strong> the shear wave<br />
C. Production <strong>of</strong> a surface wave<br />
D. None <strong>of</strong> the above
Typical angle beam assemblies make use <strong>of</strong> mode conversion and Snell's<br />
Law to generate a shear wave at a selected angle (most commonly 30°, 45°,<br />
60°, or 70°) in the test piece. As the angle <strong>of</strong> an incident longitudinal wave<br />
with respect to a surface increases, an increasing portion <strong>of</strong> the sound energy<br />
is converted to a shear wave in the second material, and if the angle is high<br />
enough, all <strong>of</strong> the energy in the second material will be in the form <strong>of</strong> shear<br />
waves. There are two advantages to designing common angle beams to take<br />
advantage <strong>of</strong> this mode conversion phenomenon.<br />
• First, energy transfer is more efficient at the incident angles that generate<br />
shear waves in steel and similar materials.<br />
• Second, minimum flaw size resolution is improved through the use <strong>of</strong><br />
shear waves, since at a given frequency, the wavelength <strong>of</strong> a shear wave<br />
is approximately 60% the wavelength <strong>of</strong> a comparable longitudinal wave.
Snell Law:<br />
http://techcorr.com/services/Inspection-and-Testing/Ultrasonic-Shear-Wave.cfm
Depth & Skip
More on Snell Law<br />
Like light, when an incident ultrasonic wave encounters an interface to an<br />
adjacent material <strong>of</strong> a different velocity, at an angle other than normal to the<br />
surface, then both reflected and refracted waves are produced.<br />
Understanding refraction and how ultrasonic energy is refracted is especially<br />
important when using angle probes or the immersion technique. It is also the<br />
foundation formula behind the calculations used to determine a materials first<br />
and second critical angles.<br />
First Critical Angle<br />
Before the angle <strong>of</strong> incidence reaches the first critical angle, both longitudinal<br />
and shear waves exist in the part being inspected. The first critical angle is<br />
said to have been reached when the longitudinal wave no longer exists within<br />
the part, that is, when the longitudinal wave is refracted to greater or equal<br />
than 90°, leaving only a shear wave remaining in the part.
Second Critical Angle<br />
The second critical angle occurs when the angle <strong>of</strong> incidence is at such an<br />
angle that the remaining shear wave within the part is refracted out <strong>of</strong> the part.<br />
At this angle, when the refracted shear wave is at 90° a surface wave is<br />
created on the part surface<br />
Beam angles should always be plotted using the appropriate industry<br />
standard, however, knowing the effect <strong>of</strong> velocity and angle on refraction will<br />
always benefit an NDT technician when working with angle inspection or the<br />
immersion technique.<br />
The above calculator uses the following equation:<br />
ultrasonic snells law formula<br />
Where:<br />
A1 = The angle <strong>of</strong> incidence.<br />
V1 = The incident material velocity<br />
A2 = The angle <strong>of</strong> refraction<br />
V2 = The refracted material velocity
http://www.ndtcalc.com/calculators.html
2.10: Mode Conversion<br />
When sound travels in a solid material, one form <strong>of</strong> wave energy can be<br />
transformed into another form. For example, when a longitudinal waves hits<br />
an interface at an angle, some <strong>of</strong> the energy can cause particle movement in<br />
the transverse direction to start a shear (transverse) wave. Mode conversion<br />
occurs when a wave encounters an interface between materials <strong>of</strong> different<br />
acoustic impedances and the incident angle is not normal to the interface.<br />
From the ray tracing movie below, it can be seen that since mode conversion<br />
occurs every time a wave encounters an interface at an angle, ultrasonic<br />
signals can become confusing at times.
Mode Conversion<br />
http://www.ndt-ed.org/EducationResources/CommunityCollege/Ultrasonics/Graphics/Flash/ModeConversion/ModeConv.swf
In the previous section, it was pointed out<br />
that when sound waves pass through an<br />
interface between materials having different<br />
acoustic velocities, refraction takes place at<br />
the interface. The larger the difference in<br />
acoustic velocities between the two<br />
materials, the more the sound is refracted.<br />
Notice that the shear wave is not refracted<br />
as much as the longitudinal wave. This<br />
occurs because shear waves travel slower<br />
than longitudinal waves. Therefore, the<br />
velocity difference between the incident<br />
longitudinal wave and the shear wave is not<br />
as great as it is between the incident and<br />
refracted longitudinal waves.<br />
Also note that when a longitudinal wave is reflected inside the material, the<br />
reflected shear wave is reflected at a smaller angle than the reflected<br />
longitudinal wave. This is also due to the fact that the shear velocity is less<br />
than the longitudinal velocity within a given material.
Snell's Law holds true for shear waves as well as longitudinal waves and can<br />
be written as follows<br />
=<br />
Where:<br />
VL1 is the longitudinal wave velocity in material 1.<br />
VL2 is the longitudinal wave velocity in material 2.<br />
VS1 is the shear wave velocity in material 1.<br />
VS2 is the shear wave velocity in material 2.
Snell's Law
In the applet below, the shear (transverse) wave ray path has been added.<br />
The ray paths <strong>of</strong> the waves can be adjusted by clicking and dragging in the<br />
vicinity <strong>of</strong> the arrows. Values for the angles or the wave velocities can also be<br />
entered into the dialog boxes. It can be seen from the applet that when a<br />
wave moves from a slower to a faster material, there is an incident angle<br />
which makes the angle <strong>of</strong> refraction for the longitudinal wave 90 degrees. As<br />
mentioned on the previous page, this is known as the first critical angle and<br />
all <strong>of</strong> the energy from the refracted longitudinal wave is now converted to a<br />
surface following longitudinal wave. This surface following wave is sometime<br />
referred to as a creep wave and it is not very useful in NDT because it<br />
dampens out very rapidly.
Reflections
Creep wave
V S1<br />
V S2
Beyond the first critical angle, only the shear wave propagates into the<br />
material. For this reason, most angle beam transducers use a shear wave so<br />
that the signal is not complicated by having two waves present. In many<br />
cases there is also an incident angle that makes the angle <strong>of</strong> refraction for the<br />
shear wave 90 degrees. This is known as the second critical angle and at this<br />
point, all <strong>of</strong> the wave energy is reflected or refracted into a surface following<br />
shear wave or shear creep wave. Slightly beyond the second critical angle,<br />
surface waves will be generated.<br />
Keywords:<br />
■<br />
■<br />
Longitudinal creep wave<br />
Shear creep wave
Snell Law- 1 st & 2 nd Critical Angles
Note that the applet defaults to compressional velocity in the second material.<br />
The refracted compressional wave angle will be generated for given<br />
materials and angles. To find the angle <strong>of</strong> incidence required to generate a<br />
shear wave at a given angle complete the following:<br />
1. Set V1 to the longitudinal wave velocity <strong>of</strong> material 1. This material could<br />
be the transducer wedge or the immersion liquid.<br />
2. Set V2 to the shear wave velocity (approximately one-half its<br />
compressional velocity) <strong>of</strong> the material to be inspected.<br />
3. Set Q2 to the desired shear wave angle.<br />
4. Read Q1, the correct angle <strong>of</strong> incidence.
Transverse wave can be introduced into the test material by various methods:<br />
1. Inclining the incident L-wave at an angle beyond the first critical angle, yet<br />
short <strong>of</strong> second critical angle using a wedge.<br />
2. In immersion method, changing the angle <strong>of</strong> the normal search unit<br />
manipulator,<br />
3. Off-setting the normal transducer from the center-line for round bar or pipe.<br />
for 45° refracted transverse wave, the rule<br />
<strong>of</strong> thumb is the <strong>of</strong>fset d= 1/6 <strong>of</strong> rod diameter
Offset <strong>of</strong> Normal probe above circular object<br />
θ 1<br />
θ 1R<br />
θ 2
Calculate the <strong>of</strong>fset for following conditions:<br />
Aluminum rod being examined is 6" diameter, what is the <strong>of</strong>f set needed for (a)<br />
45 refracted shear wave (b) Logitudinal wave to be generated?<br />
(L-wave velocity for AL=6.3x10 5 cm/s, T-wave velocity for AL=3.1x10 5 cm/s,<br />
Wave velocity in water=1.5X10 5 cm/s)<br />
Question (a)
Refraction and mode conversion at non-perpendicular boundaries
Refraction and mode conversion at non-perpendicular boundaries<br />
http://static4.olympus-ims.com/data/Flash/HTML5/incident_angle/IncidentAngle.html?rev=5E62
Refraction and mode conversion at non-perpendicular boundaries
Refraction and mode conversion at non-perpendicular boundaries
Refraction and mode conversion at non-perpendicular boundaries
Q1. From the above figures, if the incident angle is 50 Degree, what are the<br />
sound wave in the steel?<br />
Answer: 65 Degree Shear wave in steel.<br />
Q2. If 50 Degree longitudinal wave in steel is used what is the possible<br />
problem?<br />
Answer: If 50 degree Longitudinal wave is generated in steel, shear wave at<br />
28 degree is also generated and this may cause fault indications.
Q118: At the water-steel interface, the angle <strong>of</strong> incidence in water is 7 degree.<br />
The principle mode <strong>of</strong> vibration that exist in steel is:<br />
A. Longitudinal<br />
B. Shear<br />
C. Both A & B (Possible incorrect answer)<br />
D. Surface<br />
Hint: The keyword is “the principle mode”
Q: On Calculation:<br />
Incident angle= 7°<br />
Refracted longitudinal wave = 29.11°<br />
Refracted shear wave = 15.49°
Q72. In a water immersion test, ultrasonic energy is transmitted into steel at<br />
an incident angle <strong>of</strong> 14. What is the angle <strong>of</strong> refracted shear wave within<br />
the material? V s = 3.2 x 10 5 cm/s, V w = 1.5 x 10 5 cm/s<br />
a) 45°<br />
b) 23°<br />
c) 31°<br />
d) 13°
Q1. If you were requested to design a plastid shoe to generate Rayleigh wave<br />
in aluminum, what would be the incident angle <strong>of</strong> the ultrasonic energy?<br />
VA = 3.1 x 105 cm/s, Vp = 2.6 x 105 cm/s<br />
a) 37°<br />
b) 57°<br />
c) 75°<br />
d) 48°
Q53. The term used to determined the relative transmittance and reflectance<br />
<strong>of</strong> an ultrasonic energy at an interface is called:<br />
a) Acoustic attenuation<br />
b) Interface reflection<br />
c) Acoustic impedance ratio<br />
d) Acoustic frequency
2.11: Signal-to-Noise Ratio<br />
In a previous page, the effect that frequency and wavelength have on flaw<br />
detectability was discussed. However, the detection <strong>of</strong> a defect involves many<br />
factors other than the relationship <strong>of</strong> wavelength and flaw size. For example,<br />
the amount <strong>of</strong> sound that reflects from a defect is also dependent on the<br />
acoustic impedance mismatch between the flaw and the surrounding material.<br />
A void is generally a better reflector than a metallic inclusion because the<br />
impedance mismatch is greater between air and metal than between two<br />
metals.<br />
Often, the surrounding material has competing reflections. Microstructure<br />
grains in metals and the aggregate <strong>of</strong> concrete are a couple <strong>of</strong> examples. A<br />
good measure <strong>of</strong> detectability <strong>of</strong> a flaw is its signal-to-noise ratio (S/N). The<br />
signal-to-noise ratio is a measure <strong>of</strong> how the signal from the defect compares<br />
to other background reflections (categorized as "noise"). A signal-to-noise<br />
ratio <strong>of</strong> 3 to 1 is <strong>of</strong>ten required as a minimum.
The absolute noise level and the absolute strength <strong>of</strong> an echo from a "small"<br />
defect depends on a number <strong>of</strong> factors, which include:<br />
1. The probe size and focal properties.<br />
2. The probe frequency, bandwidth and efficiency.<br />
3. The inspection path and distance (water and/or solid).<br />
4. The interface (surface curvature and roughness).<br />
5. The flaw location with respect to the incident beam.<br />
6. The inherent noisiness <strong>of</strong> the metal microstructure.<br />
7. The inherent reflectivity <strong>of</strong> the flaw, which is dependent on its acoustic<br />
impedance, size, shape, and orientation.<br />
8. Cracks and volumetric defects can reflect ultrasonic waves quite differently.<br />
Many cracks are "invisible" from one direction and strong reflectors from<br />
another.<br />
9. Multifaceted flaws will tend to scatter sound away from the transducer.
The following formula relates some <strong>of</strong> the variables affecting the signal-tonoise<br />
ratio (S/N) <strong>of</strong> a defect:
Sound Volume: Area x pulse length<br />
Material properties<br />
Flaw geometry: Figure <strong>of</strong> merit<br />
FOM and amplitudes responds
Rather than go into the details <strong>of</strong> this formulation, a few fundamental<br />
relationships can be pointed out. The signal-to-noise ratio (S/N), and<br />
therefore, the detectability <strong>of</strong> a defect:<br />
1. Increases with increasing flaw size (scattering amplitude). The detectability<br />
<strong>of</strong> a defect is directly proportional to its size.<br />
2. Increases with a more focused beam. In other words, flaw detectability is<br />
inversely proportional to the transducer beam width.<br />
3. Increases with decreasing pulse width (delta-t). In other words, flaw<br />
detectability is inversely proportional to the duration <strong>of</strong> the pulse (∆t)<br />
produced by an ultrasonic transducer. The shorter the pulse (<strong>of</strong>ten higher<br />
frequency), the better the detection <strong>of</strong> the defect. Shorter pulses<br />
correspond to broader bandwidth frequency response. See the figure<br />
below showing the waveform <strong>of</strong> a transducer and its corresponding<br />
frequency spectrum.
Acoustic Volume: w x w y ∆t
Determining cross sectional area using reflector- A Scan (6db drop)
Determining cross sectional area using reflector- C Scan
“Sonic pulse volume” and S/N (defect resolution)
4. Decreases in materials with high density and/or a high ultrasonic velocity.<br />
The signal-to-noise ratio (S/N) is inversely proportional to material density<br />
and acoustic velocity.<br />
5. Generally increases with frequency. However, in some materials, such as<br />
titanium alloys, both the "A flaw " and the "Figure <strong>of</strong> Merit (FOM)" terms in the<br />
equation change at about the same rate with changing frequency. So, in<br />
some cases, the signal-to-noise ratio (S/N) can be somewhat independent<br />
<strong>of</strong> frequency.
Pulse Length
Pulse Length Affect Resolution
2.12: The Sound Fields<br />
2.12.1 Wave Interaction or Interference<br />
Before we move into the next section, the subject <strong>of</strong> wave interaction must<br />
be covered since it is important when trying to understand the performance<br />
<strong>of</strong> an ultrasonic transducer. On the previous pages, wave propagation was<br />
discussed as if a single sinusoidal wave was propagating through the<br />
material. However, the sound that emanates from an ultrasonic transducer<br />
does not originate from a single point, but instead originates from many<br />
points along the surface <strong>of</strong> the piezoelectric element. This results in a<br />
sound field with many waves interacting or interfering with each other.
Transducer cut-out<br />
http://ichun-chen.com/ultrasonic-transducer
When waves interact, they superimpose on each other, and the amplitude <strong>of</strong><br />
the sound pressure or particle displacement at any point <strong>of</strong> interaction is the<br />
sum <strong>of</strong> the amplitudes <strong>of</strong> the two individual waves. First, let's consider two<br />
identical waves that originate from the same point. When they are in phase<br />
(so that the peaks and valleys <strong>of</strong> one are exactly aligned with those <strong>of</strong> the<br />
other), they combine to double the displacement <strong>of</strong> either wave acting alone.<br />
When they are completely out <strong>of</strong> phase (so that the peaks <strong>of</strong> one wave are<br />
exactly aligned with the valleys <strong>of</strong> the other wave), they combine to cancel<br />
each other out. When the two waves are not completely in phase or out <strong>of</strong><br />
phase, the resulting wave is the sum <strong>of</strong> the wave amplitudes for all points<br />
along the wave.
UT Transducer
UT Transducer<br />
http://www.fhwa.dot.gov/publications/research/infrastructure/structures/04042/index.cfm#toc
UT Transducer- Surface creep wave transducer
UT Transducer
UT Transducer
Wave Interaction<br />
Complete in-phase Complete out <strong>of</strong>-phase not in-phase
When the origins <strong>of</strong> the two interacting waves are not the same, it is a little<br />
harder to picture the wave interaction, but the principles are the same. Up<br />
until now, we have primarily looked at waves in the form <strong>of</strong> a 2D plot <strong>of</strong> wave<br />
amplitude versus wave position. However, anyone that has dropped<br />
something in a pool <strong>of</strong> water can picture the waves radiating out from the<br />
source with a circular wave front. If two objects are dropped a short distance<br />
apart into the pool <strong>of</strong> water, their waves will radiate out from their sources and<br />
interact with each other. At every point where the waves interact, the<br />
amplitude <strong>of</strong> the particle displacement is the combined sum <strong>of</strong> the amplitudes<br />
<strong>of</strong> the particle displacement <strong>of</strong> the individual waves.<br />
With an ultrasonic transducer, the waves propagate out from the transducer<br />
face with a circular wave front. If it were possible to get the waves to<br />
propagate out from a single point on the transducer face, the sound field<br />
would appear as shown in the upper image to the right. Consider the light<br />
areas to be areas <strong>of</strong> rarefaction and the dark areas to be areas <strong>of</strong><br />
compression.
With an ultrasonic transducer, the waves propagate out from the transducer<br />
face with a circular wave front. If it were possible to get the waves to<br />
propagate out from a single point on the transducer face, the sound field<br />
would appear as shown in the upper image to the right. Consider the light<br />
areas to be areas <strong>of</strong> rarefaction and the dark areas to be areas <strong>of</strong><br />
compression.
However, as stated previously, sound waves originate from multiple points<br />
along the face <strong>of</strong> the transducer. The lower image to the right shows what the<br />
sound field would look like if the waves originated from just two points. It can<br />
be seen that where the waves interact, there are areas <strong>of</strong> constructive and<br />
destructive interference. The points <strong>of</strong> constructive interference are <strong>of</strong>ten<br />
referred to as nodes.<br />
The points <strong>of</strong> constructive interference<br />
are <strong>of</strong>ten referred to as nodes
29. It is possible for a discontinuity smaller than the transducer to produce<br />
indications <strong>of</strong> fluctuating amplitude as the search unit is moved laterally if<br />
testing is being performed in the:<br />
(a) Fraunh<strong>of</strong>er zone<br />
(b) Near field<br />
(c) Snell field<br />
(d) Shadow zone
Q5: Acoustic pressure along the beam axis moving away from the probe has<br />
various maxima and minima due to interference. At the end <strong>of</strong> the near field<br />
pressure is:<br />
a) a maximum<br />
b) a minimum<br />
c) the average <strong>of</strong> all maxima and minima<br />
d) none <strong>of</strong> the above<br />
Q4: For a plane wave, sound pressure is reduced by attenuation in a<br />
_______ fashion.<br />
a) linear<br />
b) exponential<br />
c) random<br />
d) none <strong>of</strong> the above
2.12.2 Variations in sound intensity<br />
Intensity<br />
Distance
Of course, there are more than two points <strong>of</strong> origin along the face <strong>of</strong> a<br />
transducer. The image below shows five points <strong>of</strong> sound origination. It can be<br />
seen that near the face <strong>of</strong> the transducer, there are extensive fluctuations or<br />
nodes and the sound field is very uneven. In ultrasonic testing, this in known<br />
as the near field (near zone) or Fresnel zone. The sound field is more<br />
uniform away from the transducer in the far field, or Fraunh<strong>of</strong>er zone, where<br />
the beam spreads out in a pattern originating from the center <strong>of</strong> the<br />
transducer. It should be noted that even in the far field, it is not a uniform<br />
wave front. However, at some distance from the face <strong>of</strong> the transducer and<br />
central to the face <strong>of</strong> the transducer, a uniform and intense wave field<br />
develops.
The sound wave exit from a transducer can be separated into 2 zones or<br />
areas; The Near Field (Fresnel) and the Far Field (Fraunh<strong>of</strong>er).
2.12.3 Fresnel & Fraunh<strong>of</strong>er Zone<br />
Fresnel Field, the Near Field are region directly adjacent to the transducer<br />
and characterized as a collection <strong>of</strong> symmetrical high and low pressure<br />
regions cause by interference wave fronts emitting from the continuous or<br />
near continuous sound sources.<br />
http://blog.3bscientific.com/science_education_insight/2013/04/3b-scientific-makes-waves-with-new-physics-education-kit.html
The Near Field (Fresnel) and the Far Field (Fraunh<strong>of</strong>er).
The Near Field (Fresnel)– Wave Interference (Maxima & Minima)<br />
The sound field <strong>of</strong> a transducer is divided into two zones; the near field and<br />
the far field. The near field is the region directly in front <strong>of</strong> the transducer<br />
where the echo amplitude goes through a series <strong>of</strong> maxima and minima and<br />
ends at the last maximum, at distance N from the transducer.
Amplitude ←<br />
Near Field Effect: Because <strong>of</strong> the variations within the near field it can be<br />
difficult to accurately evaluate flaws using amplitude based techniques.<br />
Near Field Y o<br />
+<br />
Far Field<br />
Distance from Transducer face →
Fresnel / Fraunh<strong>of</strong>er Zone
Near field (near zone)<br />
or Fresnel zone<br />
far field (far zone)<br />
or Fraunh<strong>of</strong>er zone<br />
Z f
Near field (near zone)<br />
or Fresnel zone<br />
Crystal Focus<br />
Accoustical axis<br />
far field (far zone)<br />
or Fraunh<strong>of</strong>er zone<br />
Angle <strong>of</strong> divergence<br />
D 0<br />
6<br />
N<br />
Near field<br />
Far field<br />
Z f
Near/ Far Fields<br />
http://miac.unibas.ch/PMI/05-<strong>Ultrasound</strong>Imaging.html
Near/ Far Fields
where α is the radius <strong>of</strong> the<br />
transducer and λ the wavelength.
where D is the diameter <strong>of</strong> the transducer<br />
and λ the wavelength.<br />
K= is the spread factor<br />
K=1.22 for null edges<br />
K=1.08 for 20dB down point (10% <strong>of</strong> peak)<br />
K=0.88 for 10dB down point (32% <strong>of</strong> peak)<br />
K=0.7(0.56?) for 6dB down point (50% <strong>of</strong> peak)<br />
Source for K, ASNT Study Guide UT by Matthew J Golis
The curvature and the area over which the sound is being generated, the<br />
speed that the sound waves travel within a material and the frequency <strong>of</strong> the<br />
sound all affect the sound field. Use the Java applet below to experiment with<br />
these variables and see how the sound field is affected.<br />
http://www.ndt-ed.org/EducationResources/CommunityCollege/Ultrasonics/<strong>Physics</strong>/applet<strong>Ultrasound</strong>Propagation/Applet.html
Fresnel & Fraunh<strong>of</strong>er Zone<br />
10dB, K-0.88<br />
6dB, K=0.7? Or 0.56?
Fresnel & Fraunh<strong>of</strong>er Zone
Fresnel & Fraunh<strong>of</strong>er Zone
Fresnel & Fraunh<strong>of</strong>er Zone<br />
http://static1.olympus-ims.com/data/Flash/HTML5/beamSpread/BeamSpread.html?rev=6C43<br />
http://www.olympus-ims.com/en/ndt-tutorials/transducers/wave-front/
Q: Where does beam divergence occur?<br />
A. Near field<br />
B. Far field<br />
C. At the crystal<br />
D. None <strong>of</strong> the above
Q4: A transducer has a near field in water <strong>of</strong> 35 mm. When used in contact<br />
on steel the near zone will be about:<br />
a) 47 mm<br />
b) 35 mm<br />
c) 18 mm<br />
d) 9 mm<br />
Q8: A rectangular probe, 4 mm X 8 mm, will have its maximum half angle <strong>of</strong><br />
divergence:<br />
a) in the 4 mm direction<br />
b) in the 8 mm direction<br />
c) in no particular orientation<br />
d) constant in all directions
Q160 Beam divergence is a function <strong>of</strong> the dimensions <strong>of</strong> the crystal and the<br />
wavelength <strong>of</strong> the beam transmitted through a medium, and it:<br />
A. increase if the frequency or the crystal diameter is decrease<br />
B. Decrease if the frequency or the crystal diameter is decrease<br />
C. increase if the frequency is increase and the diameter is decrease<br />
D. decrease if the frequency is increase and the crustal diameter is decrease<br />
Q52: What is the transducer half-angle beam spread <strong>of</strong> a 1.25cm diameter<br />
2.25 MHz transducer in water (VL= 1.5 x 10 5 cm/s)?<br />
A. 2.5 degree<br />
B. 3.75 degree<br />
C. 37.5 degree<br />
D. 40.5 degree
2.12.4 Dead Zone<br />
In ultrasonic testing, the interval following the initial pulse where the<br />
transducer ring time <strong>of</strong> the crystal that prevents detection or interpretation <strong>of</strong><br />
reflected energy (echoes). In contact ultrasonic testing, the area just below<br />
the surface <strong>of</strong> a test object that can not be inspected because <strong>of</strong> the<br />
transducer is still ringing down and not yet ready to receive signals. The dead<br />
is minimized by the damping medium behind the crystal. The dead zone<br />
increase when the probe frequency decrease and it only found in single<br />
crystal contact techniques.
Dead Zone - The interval following the surface <strong>of</strong> a test object to the nearest<br />
inspectable depth. Any interval following a reflected signal where no direct<br />
echoes from discontinuities cannot be detected, due to characteristics <strong>of</strong> the<br />
equipment.<br />
dead zone after echo and dead zone after initial pulse, both are common<br />
phenomena. Actually the dead zone cannot be determined as a single figure<br />
without additional parameters, hence the echo can be recognized, however,<br />
signal quality is important. Useful parameters are linearity or signal in a nice<br />
ratio that can describe the echo amplitude quality within a dead zone. For this<br />
reason standards such as GE specifications are needed to check equipment<br />
capability. The appearance <strong>of</strong> inference effects, within the dead zone, has to<br />
be considered as well.<br />
Definition by: http://www.ndt.net/ndtaz/content.php?id=103
Dead Zone -The initial pulse is a technical necessity. It limits the detectability<br />
<strong>of</strong> near-surface discontinuities. Reflectors in the dead zone, the nonresolvable<br />
area immediately beneath the surface, cannot be detected (Figure<br />
8-10). The dead zone is a function <strong>of</strong> the width <strong>of</strong> the initial pulse which is<br />
influenced by the probe type, test instrument discontinuities and quality <strong>of</strong> the<br />
interface.<br />
The dead zone can be verified with an International Institute <strong>of</strong> Welding (IIW)<br />
calibration block. With the time base calibrated to 50 mm, and the transducer<br />
on position A (Figure 8-11), the extent <strong>of</strong> the dead zone can be inferred to be<br />
either less than or greater than 5 mm. With the probe at position B, the dead<br />
zone can be said to be either less than or greater than 10 mm.<br />
This is done by ensuring that the peak from the Perspex insert appears<br />
beyond the trailing edge <strong>of</strong> the initial pulse start. Excessive dead zones are<br />
generally attributable to a probe with excessive ringing in the crystal.
Dead Zone -The initial pulse is a technical necessity. It limits the detectability<br />
<strong>of</strong> near-surface discontinuities. Reflectors in the dead zone, the nonresolvable<br />
area immediately beneath the surface, cannot be detected. The<br />
dead zone is a function <strong>of</strong> the width <strong>of</strong> the initial pulse which is influenced by<br />
the probe type, test instrument discontinuities and quality <strong>of</strong> the interface.<br />
This is done by ensuring that the peak from the Perspex insert appears<br />
beyond the trailing edge <strong>of</strong> the initial pulse start. Excessive dead zones are<br />
generally attributable to a probe with excessive ringing in the crystal.
Dead Zone Illustration<br />
http://www.ndt.net/ndtaz/content.php?id=103
Dead Zone<br />
http://www.ni.com/white-paper/5369/en/
Q: On an A-scan display, the “dead zone” refers to:<br />
A. The distance contained within the near field<br />
B. The area outside the beam spread<br />
C. The distance covered by the front surface pulse with and recovery<br />
time<br />
D. The area between the near field and the far field
Q36: To eliminate the decrease in sensitivity close to a wall which is parallel<br />
to the beam direction, the transducer used should be:<br />
A. As small as possible<br />
B. As low frequency as possible<br />
C. Both A & B<br />
D. Large and with a frequency as high as possible<br />
Q45: The length <strong>of</strong> the near field for a 2.5cm diameter, 5MHz transducer<br />
placed in oil with V=1.4 x 10 5 cm/s is approximately:<br />
A. 0.028 cm<br />
B. 6.25 cm<br />
C. 22.3 cm<br />
D. 55.8 cm
2.13: Inverse Square Rule/ Inverse Rule<br />
Large Reflector, a reflector larger than the extreme edge <strong>of</strong> beam / 3D away<br />
from the Near Zone- Inverse Rule
Large Reflector Inverse Rule
Small Reflector, a reflector smaller than the extreme edge <strong>of</strong> beam / 3D away<br />
from the Near Zone – Inverse Square Rule
Small Reflector Inverse Square Rule
2.14: Resonance<br />
Another form wave interference occurred when the normal incidence and<br />
reflected plane wave interact within a narrow parallel interface. When the<br />
phase <strong>of</strong> the reflected wave match that <strong>of</strong> incoming incident wave, the<br />
amplitude <strong>of</strong> the superimposed wave doubling, creating a standing wave.<br />
http://hyperphysics.phy-astr.gsu.edu/hbase/waves/string.html#c3<br />
Resonance occurred when the thickness <strong>of</strong> the material is equal to half the<br />
wave length or multiple <strong>of</strong> it. It also occur when longitudinal wave travel thru<br />
a thin sheet <strong>of</strong> materials during immersion testing.
Fundamental Frequency<br />
The lowest resonant frequency <strong>of</strong> a vibrating object is called its fundamental<br />
frequency.<br />
Most vibrating objects have more than one resonant frequency and those<br />
used in musical instruments typically vibrate at harmonics <strong>of</strong> the fundamental.<br />
A harmonic is defined as an integer (whole number) multiple <strong>of</strong> the<br />
fundamental frequency.<br />
Vibrating strings, open cylindrical air columns, and conical air columns will<br />
vibrate at all harmonics <strong>of</strong> the fundamental. Cylinders with one end closed will<br />
vibrate with only odd harmonics <strong>of</strong> the fundamental. Vibrating membranes<br />
typically produce vibrations at harmonics, but also have some resonant<br />
frequencies which are not harmonics. It is for this class <strong>of</strong> vibrators that the<br />
term overtone becomes useful - they are said to have some non-harmonic<br />
overtones.<br />
http://hyperphysics.phy-astr.gsu.edu/hbase/waves/funhar.html
Thickness <strong>of</strong> Crystal at Fundamental Frequency<br />
Fundamental resonance frequency<br />
Harmonic resonance frequency<br />
= V/f<br />
= N. V/f (N = integer)<br />
Piezoelectric crystal will has the greatest sensitivity when it is driven at its<br />
fundamental frequency, this occurs when the thickness <strong>of</strong> the crystal is at ½<br />
λ.<br />
If the thickness is given, the fundamental frequency could be calculated:
Transducers Piezoelectric Thickness:<br />
The resonant phenomenon occurred when piezoelectric are electrically<br />
excited at their characteristic (fundamental resonance) frequency.<br />
http://bme240.eng.uci.edu/students/09s/patelnj/<strong>Ultrasound</strong>_for_Nerves/<strong>Ultrasound</strong>_Background.html
Resonance UT Testing- The diagram below shown how resonance is used<br />
to measured thickness and detect defect. However pulse-echo methods have<br />
been refined to perform most <strong>of</strong> function <strong>of</strong> flaw detections and resonant<br />
instruments are rarely used.
Application Case#1:<br />
The specimen's geometry determines the number <strong>of</strong> its natural frequencies: a<br />
rod has few whilst a complex work-piece has many such frequencies.<br />
Typically, the information that can be obtained by acoustic resonance<br />
analysis includes cracks, structural properties, cavities, layer separation,<br />
chipping, density fluctuations etc. Damping behaviour depends firstly on the<br />
material, and secondly, on how the specimen is positioned during its<br />
excitation. In order to achieve high frequency resolution, signal duration<br />
("ringing duration") should be as long as possible (> 50 ms).
From the natural frequencies it is possible to calculate specimen-specific<br />
characteristics and assign them to quality attributes, e. g. pass / OK, cracked,<br />
material structure, hardness deviation / partly hardened etc.<br />
Application<br />
Acoustic resonance testing can be applied to all work pieces that "sound".<br />
Summary<br />
Resonance analysis is a qualitative method, i.e. it can differentiate between<br />
defective and non-defective parts, so that it is especially suitable for quality<br />
assurance in the series production cycle. It compares the actual oscillatory<br />
situation with the target one derived from a learning base. This learning base<br />
is established by using defined standard parts. The number <strong>of</strong> self-resonant<br />
frequencies is determined by the geometry <strong>of</strong> the object under test. For<br />
instance a bar has few resonant frequencies, while a complex lattice-type<br />
object has many natural resonances. After a systematic engineering<br />
approach, it is possible to compensate the influence <strong>of</strong> the production scatter.<br />
http://ndttechnologies.com/products/AcousticResonance.html
Application Case#2:<br />
Electromagnetic Acoustic Resonance Nondestructive Testing (NDT)<br />
Equipment Datasheets<br />
Coating Thickness Gauge -- DTG-500<br />
from OMEGA Engineering, Inc.<br />
Digital coating thickness gauge with a range <strong>of</strong> 0 to 40.0 mils (0 to 1000<br />
micrometers). SPECIFICATIONS. Display: 3-digit LCD with max readout <strong>of</strong><br />
1999 counts. Range: 0 to 40 mils/0 to 1000 µm. Resolution: 0.<br />
Instrument Information<br />
Instrument Type: Coating Thickness<br />
Instrument Technology: Electromagnetic Acoustic Resonance<br />
Form Factor: Portable / Handheld / Mobile<br />
http://www.globalspec.com/specsearch/PartSpecs?partid={0DBF141D-6832-4F31-9AB8-<br />
B87F063BFDC4}&vid=99786&comp=2975
Q: The formula used to determine the fundamental resonance frequency is:<br />
A. F= V/T<br />
B. F= V/2T<br />
C. F= T/V<br />
D. F= VT<br />
Q: When maximum sensitivity is required from a transducer:<br />
A. A straight beam unit should be used<br />
B. A large diameter crystal should be used<br />
C. The piezoelectric element should be driven at its fundamental<br />
frequency<br />
D. The bandwidth <strong>of</strong> the transducer should be as large as possible
Q7: The resonance frequency <strong>of</strong> 2cm thick plate <strong>of</strong> Naval Brass (V=4.43 x 10 5<br />
cm/s) is:<br />
A. 0,903 MHz<br />
B. 0.443 MHz<br />
C. 0.222 MHz<br />
D. 0.111 MHz<br />
Q35: Resonance testing equipment generally utilized:<br />
A. Pulsed longitudinal; waves<br />
B. Continuous longitudinal waves<br />
C. Pulsed shear wave<br />
D. Continuous shear waves
2.15 Measurement <strong>of</strong> Sound
dB is a measures <strong>of</strong> ratio <strong>of</strong> 2 values in a logarithmic scale given by following<br />
equation:<br />
Unlike the SPL (standard pressure level) used in noise measurement, in UT testing,<br />
we do not know the exactly ultrasonic sound level energy generated by the probe<br />
(neither is it necessary). The used <strong>of</strong> the ratio <strong>of</strong> 2 values given by the above equation<br />
is used .
Ultrasonic Formula - Signal Amplitude Gain/Loss Expressed in dB<br />
The dB is a logarithmic unit that describes a ratio <strong>of</strong> two measurements. The<br />
equation used to describe the difference in intensity between two ultrasonic or<br />
other sound measurements is:<br />
where: ∆I is the difference in sound intensity expressed in decibels (dB), P1<br />
and P2 are two different sound pressure amplitude measurements, and the<br />
log is to base 10.
The Decibel<br />
The equation used to describe the difference in intensity between two<br />
ultrasonic or other sound measurements is:<br />
where: ∆I is the difference in sound intensity expressed in decibels (dB), P1<br />
and P2 are two different sound pressure measurements, and the log is to<br />
base 10.<br />
What exactly is a decibel?<br />
The decibel (dB) is one tenth <strong>of</strong> a Bel, which is a unit <strong>of</strong> measure that was<br />
developed by engineers at Bell Telephone Laboratories and named for<br />
Alexander Graham Bell. The dB is a logarithmic unit that describes a ratio <strong>of</strong><br />
two measurements. The basic equation that describes the difference in<br />
decibels between two measurements is:
where: delta X is the difference in some quantity expressed in decibels, X1<br />
and X2 are two different measured values <strong>of</strong> X, and the log is to base 10.<br />
(Note the factor <strong>of</strong> two difference between this basic equation for the dB and<br />
the one used when making sound measurements. This difference will be<br />
explained in the next section.)
Why is the dB unit used?<br />
Use <strong>of</strong> dB units allows ratios <strong>of</strong> various sizes to be described using easy to<br />
work with numbers. For example, consider the information in the table.
From this table it can be seen that ratios from one up to ten billion can be<br />
represented with a single or double digit number. Ease to work with numbers<br />
was particularly important in the days before the advent <strong>of</strong> the calculator or<br />
computer. The focus <strong>of</strong> this discussion is on using the dB in measuring sound<br />
levels, but it is also widely used when measuring power, pressure, voltage<br />
and a number <strong>of</strong> other things.
Use <strong>of</strong> the dB in Sound Measurements<br />
Sound intensity is defined as the sound power per unit area perpendicular to<br />
the wave. Units are typically in watts/m2 or watts/cm2. For sound intensity,<br />
the dB equation becomes:<br />
However, the power or intensity <strong>of</strong> sound is generally not measured directly.<br />
Since sound consists <strong>of</strong> pressure waves, one <strong>of</strong> the easiest ways to quantify<br />
sound is to measure variations in pressure (i.e. the amplitude <strong>of</strong> the pressure<br />
wave). When making ultrasound measurements, a transducer is used, which<br />
is basically a small microphone. Transducers like most other microphones<br />
produced a voltage that is approximately proportionally to the sound pressure<br />
(P). The power carried by a traveling wave is proportional to the square <strong>of</strong> the<br />
amplitude. Therefore, the equation used to quantify a difference in sound<br />
intensity based on a measured difference in sound pressure becomes:
However, the power or intensity <strong>of</strong> sound is generally not measured directly.<br />
Since sound consists <strong>of</strong> pressure waves, one <strong>of</strong> the easiest ways to quantify<br />
sound is to measure variations in pressure (i.e. the amplitude <strong>of</strong> the pressure<br />
wave). When making ultrasound measurements, a transducer is used, which<br />
is basically a small microphone. Transducers like most other microphones<br />
produced a voltage that is approximately proportionally to the sound pressure<br />
(P). The power carried by a traveling wave is proportional to the square <strong>of</strong> the<br />
amplitude.<br />
I α P 2 , I α V 2 where I=intensity, P=amplitude, V=voltage<br />
Therefore, the equation used to quantify a difference in sound intensity based<br />
on a measured difference in sound pressure becomes:<br />
(The factor <strong>of</strong> 2 is added to the equation because the logarithm <strong>of</strong> the square <strong>of</strong> a<br />
quantity is equal to 2 times the logarithm <strong>of</strong> the quantity.)
Since transducers and microphones produce a voltage that is proportional to<br />
the sound pressure, the equation could also be written as:<br />
where: ∆I is the change in sound intensity incident on the transducer and<br />
V1 and V2 are two different transducer output voltages.
Revising the table to reflect the relationship between the ratio <strong>of</strong> the measured<br />
sound pressure and the change in intensity expressed in dB produces<br />
From the table it can be seen that 6 dB equates to<br />
a doubling <strong>of</strong> the sound pressure. Alternately,<br />
reducing the sound pressure by 2, results in a – 6<br />
dB change in intensity.
Sound Levels- Relative
Sound Levels- Relative dB
Practice:
“Absolute" Sound Levels<br />
Sound pressure level (SPL) or sound level is a logarithmic measure <strong>of</strong> the<br />
effective sound pressure <strong>of</strong> a sound relative to a reference value. It is<br />
measured in decibels (dB) above a standard reference level. The standard<br />
reference sound pressure in air or other gases is 20 µPa, which is usually<br />
considered the threshold <strong>of</strong> human hearing (at 1 kHz).<br />
http://en.wikipedia.org/wiki/DB_SPL#Sound_pressure_level
“Absolute" Sound Levels<br />
Whenever the decibel unit is used, it always represents the ratio <strong>of</strong> two values.<br />
Therefore, in order to relate different sound intensities it is necessary to<br />
choose a standard reference level. The reference sound pressure<br />
(corresponding to a sound pressure level <strong>of</strong> 0 dB) commonly used is that at<br />
the threshold <strong>of</strong> human hearing, which is conventionally taken to be 2×10 −5<br />
Newton per square meter, or 20 micropascals (20μPa). To avoid confusion<br />
with other decibel measures, the term dB(SPL) is used.
dB meter<br />
97.3dB against standards sound pressure level<br />
20log(P/20X10 -6 )=97.3<br />
Absolute level =10 97.3/20 x 20 X 10 -6<br />
=1.46564 N/M 2<br />
Actual Sound pressure →<br />
↖ Standard reference pressure 20 μMpa
Absolute:<br />
The standard reference sound pressure in air or other gases is 20 µPa, which<br />
is usually considered the threshold <strong>of</strong> human hearing (at 1 kHz).<br />
Actual Sound pressure →<br />
↖ Standard reference pressure 20 μMpa<br />
Absolute:<br />
Sound pressure level in dB as a ratio to<br />
standard reference in logarithmic scale.<br />
76db= 20log(P/20 μPa)<br />
Log(P/20 μPa)=3.8dB<br />
P= 10 3.8 x 20 μPa<br />
=126191 μPa<br />
http://www.ncvs.org/ncvs/tutorials/voiceprod/equation/chapter9/index.html
Exercise:<br />
Find the absolute sound level in μPa for the following measurement <strong>of</strong> air<br />
traffic noise.
Exercise: ANSWER<br />
Find the absolute sound level in μPa for the following measurement <strong>of</strong> air<br />
traffic noise.<br />
SPL= 95.8 dB= 20log(P/20x10 -6 )<br />
log(P/20x10-6)= 95.8/20<br />
P= 10 95.8/20 x 20x10 -6<br />
P= 1.233 N/M 2 #
Practice:<br />
dB
Relative dB: Example Calculation 1<br />
Two sound pressure measurements are made using an ultrasonic<br />
transducer. The output voltage from the transducer is 600 mv for the first<br />
measurement and 100 mv for the second measurement. Calculate the<br />
difference in the sound intensity, in dB, between the two measurements?<br />
The sound intensity changed by -15.56dB. In other words, the sound<br />
intensity decreased by 15.56 dB
Example Calculation 2<br />
If the intensity between two ultrasonic measurements increases by 6 dB, and<br />
the first measurement produces a transducer output voltage <strong>of</strong> 30 mv, what<br />
was the transducer output voltage for the second measurement?
Example Calculation 3<br />
Consider the sound pressure difference between the threshold <strong>of</strong> human<br />
hearing, 0 dB, and the level <strong>of</strong> sound <strong>of</strong>ten produce at a rock concert, 120 dB.<br />
How much is the rock concert sound greater than that <strong>of</strong> the threshold <strong>of</strong><br />
human hearing.
What is the absolute rock concert sound pressure?
2.16 Practice Makes Perfect
Practice Makes Perfect<br />
28. An advantage <strong>of</strong> using lower frequencies during ultrasonic testing is that:<br />
(a) Near surface resolution is improved<br />
(b) Sensitivity to small discontinuities is improved<br />
(c) Beam spread is reduced<br />
(d) Sensitivity to unfavorable oriented flaws is improved
Q104: If an ultrasonic wave is transmitted through an interface <strong>of</strong> two<br />
materials in which the first material has a higher acoustic impedance value<br />
but the same velocity value as the secong material, the angle <strong>of</strong> refraction<br />
will be:<br />
a) A greater than the incidence<br />
b) Less than the angle <strong>of</strong> incidence<br />
c) The same as the angle <strong>of</strong> incidence<br />
d) Beyond the critical angle.
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