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Propagation of a Sound Wave Through an Interface BarrierWhat happens to a sound wave when it interacts with some type of discontinuity? Each material has some particular acoustic impedance. This acoustic impedance is given by the following equation:
Where
A sound wave that reaches an interface between two materials will generate a
reflected wave and a transmitted wave. The
Transmission coefficient
Physically we might expect that the difference between the acoustic impedance
values of the two materials might have something to do with how much sound is
transmitted and how much is reflected. Suppose
that we could adjust
It's also reasonable to expect that the total amplitude of in the Incident, Reflected and Transmitted waves must remain constant. Since all the waves meet at a thin layer, regardless of what happens on either side, the sound waves must smoothly join together. In other words, we expect the following to hold
It turns out that the reflection coefficient and the transmission coefficient can be written down as follows
Notice that if we set
If we have a wave that reaches a boundary and the wave has an amplitude
Note that the amplitude of the reflected wave can be positive or negative. A negative value corresponds to a 180 degree phase change. In other words, the wave will appear upside down with respect to the incident wave. The "coupling efficiency" between a transducer and a material is actually the transmission coefficient. In order to calculate this coupling efficiency it's necessary to know the acoustic impedance of the transducer and the material. If the acoustic impedance of the material is not known, then we can't calculate the transmission coefficient. |
Copyright © 2007 VN Instruments Ltd
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