Longitudinal wave transmission coefficients

The material for an acoustic lens should have a low attenuation, and a high velocity to minimize aberrations. Sapphire is an excellent material in both these respects. But the high velocity has a less desirable consequence. An acoustic impedance can be defined, which is equal to the product of the velocity and the density. The impedance of sapphire for longitudinal waves travelling parallel to the c-axis is thus 44.3 Mrayl, compared with the impedance of water which at room temperature is about 1.5 Mrayl, rising to 1.525 Mrayl at 60°C. When sound is transmitted across an interface between two materials of different impedance, the stress amplitude transmission coefficient is ( 6.4.1 Auld 1973 Brekhovskikh and Godin 1990)... 

These reflection and transmission coefficients relate the pressure amplitude in the reflected wave, and the amplitude of the appropriate stress component in each transmitted wave, to the pressure amplitude in the incident wave. The pressure amplitude in the incident wave is a natural parameter to work with, because it is a scalar quantity, whereas the displacement amplitude is a vector. The displacement amplitude reflection coefficient has the opposite sign to (6.90) or (6.94) the displacement amplitude transmission coefficients can be obtained from (6.91) and (6.92) by dividing by the appropriate longitudinal or shear impedance in the solid and multiplying by the impedance in the fluid. The impedances actually relate force per unit area to displacement velocity, but displacement velocity is related to displacement by a factor to which is the same for each of the incident, reflected, and transmitted waves, and so it all comes to the same thing in the end. In some mathematical texts the reflection... 

When the sound is incident obliquely on a plane interface (as shown in Fig.2a), and if both media support only one type of wave (a longitudinal wave if the medium is air or water), then Eg.15 can still be used to calculate the reflection and transmission coefficient. However, the expressions for Z and Z are modified as follows [2,7],... 

If the coating material is solid, such as a viscoelastic polymer, then an incident longitudinal wave may generate both longitudinal and shear waves in the coating. The expressions for the reflection and transmission coefficients are then more complicated than Eqs.l6 and 17 [8]. 

As the design matures, the direct measurement of the acoustic properties becomes necessary. These properties include the longitudinal wave speed, the coefficient of attenuation and the acoustic impedance, which can be obtained from measurements of the reflection and transmission of sound by the material. Two acoustic techniques are available for these measurements, the impedance tube and the panel test. 

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