Introduction to Acoustics

Energy ratio
1.0
0.8
0.6
0.4
Calculated
Experimental
0.2
Water – Aluminium
0
0 4 8 12 16 20 24 28 32 36 40
Incident angle (deg)
Fig. 6.26 A 2 MHz ultrasonic wave reflected at a liquid–
solid interface
which the critical angles are indicated. Usually, vL >
vS >v,sothecurveinFig.6.25a is observed. It will
be noticed immediately that there is a critical angle for
both the longitudinal and transverse waves in the solid.
In optics there is no longitudinal wave; therefore the
curve has only one critical angle.
If one uses a pulse-echo system to verify the behavior
of an ultrasonic pulse at an interface between a liquid and
a solid, one gets results that can be graphed as shown in
Fig. 6.26. At an angle somewhat greater than the critical
angle for a transverse wave in the solid, one finds a dip
in the data. This dip is associated with the generation
of a surface wave. The surface wave is excited when
the projection of the wavelength of the incident wave
onto the interface matches the wavelength of the surface
wave. The effect of the surface wave can be seen in the
Schlieren photographs in Fig. 6.27.
Figure 6.27 shows the reflection at a water–
aluminum interface at an angle less than that for
excitation of a surface wave (a Rayleigh surface wave),
at the angle at which a surface wave is excited, and
an angle greater. When a surface wave is excited the
reflected beam contains two (or more) components:
the specular beam (reflected in a normal manner) and
a beam displaced down the interface. Since most of
the energy is contained in the displaced beam, the
minimum in the data shown in Fig. 6.24 is caused by
the excitation of the displaced beam by the surface
wave. This has been shown to be the case by displacing
the receiver to follow the displaced beam with
a goniometer system, as shown in Fig. 6.21. This minimizes
the dip in data shown in Fig. 6.24. Neubauer has
shown that the ultrasonic beam excited by the surface
wave is 180 ◦ out of phase with the specularly reflected
a)
b)
c)
αi = 20°
αi = α R
αi = 35°
Physical Acoustics 6.4 Surface Acoustic Waves 233
Interface
Interface
Interface
Fig. 6.27 Schlieren photographs showing the behavior of
a 4 MHz ultrasonic beam reflected at a water–aluminium
interface
beam [6.31]. Destructive interference resulting from
phase cancelation causes these beams to be separated
by a null strip. Although a water–aluminum interface
has been used in these examples, the phenomenon occurs
at all liquid–solid interfaces. It is less noticeable
at higher ultrasonic frequencies since the wavelength is
smaller.
Part B 6.4