Introduction to Acoustics

measured. Some resonances are caused by the geometry
of the sample (just as a string of fixed length has certain
resonant frequencies determined by the length of
the string). In the RUS technique, some fairly sophisticated
software eliminates the geometrical resonances;
the remaining resonances are resonances of the internal
lattice structure of the material. These resonances are determined
by the elastic constants. The RUS technique,
then, is used to evaluate all elastic constants from a single
sample from the spectrum of resonant frequencies
produced by the various internal resonances.
Measurement of Attenuation
with the RUS Technique
The RUS technique is also useful for measuring the attenuation
coefficients of solid materials. The resonance
curves generated by the RUS experiment are plots of the
response amplitude of the solid as a function of input
frequency (for a constant input amplitude). Every resonance
curve has a parameter known as the Q of the
system. The Q value can be related to the maximum
amplitude 1/e value, which in turn can be related to the
attenuation coefficient. Thus, the resonance curves generated
by the RUS experiment can be used to determine
the attenuation in the material at various frequencies.
6.2.3 Measurement Of Attenuation
(Classical Approach)
Measurement of attenuation at audible frequencies and
below is very difficult. Attenuation is usually measured
at ultrasonic frequencies since the plane-wave
approximation can be satisfied. The traditional means
of measuring the acoustic attenuation requires the measurement
of the echo train of an acoustic tone burst as
it travels through the medium. Sound travels down the
length of the sample, reflects from the opposite boundary
and returns to its origin. During each round trip, it
travels a distance twice the length of the sample. The
transducer used to emit the sound now acts as a receiver
and measures the amplitude as it strikes the initial surface.
The sound then continues to reflect back and forth
through the sample. On each subsequent round trip, the
sound amplitude is diminished.
Measured amplitude values are then fit to an exponential
curve, and the value of the absorption coefficient
is determined from this fit. Actually, this experimental
arrangement measures the insertion loss of the system,
the losses associated with the transducer and the adhesive
used to bond the transducer to the sample as well as
the attenuation of sound in the sample. However, the val-
Physical Acoustics 6.2 Applications of Physical Acoustics 221
ues of the insertion loss of the system and the attenuation
inside the sample are usually very close to each other.
If one needs the true attenuation in the sample, one can
a)
b)
c)
Fig. 6.11 (a) Fine rice on a plate; (b) as the plate is excited
acoustically the rice begins to migrate to the nodes; (c) the
Chladni pattern has formed
Part B 6.2