Longitudinal wave attenuation coefficient

Note the presence of both viscosity coefficients in the expressions of the longitudinal amplitude attenuation and wave celerity. In case of low viscosity ... 

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)... 

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. 

The attenuation coefficient of the sample for longitudinal waves ar(l) is then calculated in Nepers/m by ... 

FIGURE 60.4. Ultrasound pulse-echo pattern obtained at 10 MHz in a polystyrene disk 3 mm thick. The interval between successive reflections indicates the velocity of the longitudinal wave, and the ratio of intensity of any two successive reflections the attenuation. The horizontal scale is 2.00 xs/division. in this material the (longitudinal) speed of sound is 2.14 km/s, the acoustic impedance is 2.25 MRayls (units of 10 kg/(cm -s) and the attenuation coefficient is ca. 12 db/cm. See text below for the calculation [57]. 

Fig. 13. Constant field attenuation coefficient CI33 (longitudinal sound wave propagating along the c-axis) for terbium (1) 77 = OkOe (2) 1.25 kOe (3) 2.5 kOe (4) 4kOe (5) 6kOe (6) llkOe. The sound fi equency is...

Applications of ultrasonic techniques to solid-gas systems rely on the fact that velocity and attenuation of US-waves in porous materials is closely related to pore size, porosity, tortuosity, permeability and flux resistivity. Thus, the flux resistivity of acoustic absorbents oan be related to US attenuation [118,119], while the velocity of slow longitudinal US is related to pore tortuosity and diffusion, and transport properties, of other porous materials [120]. Ultrasound attenuation is very sensitive to the presence of an external agent suoh as moisture in the pore space [121] and has been used to monitor wetting and drying prooesses [122] on the other hand, US velocity has been used to measure the elastic coefficients of different types of paper and correlate them with properties such as tensile breaking strength, compressive strength, etc. [123]. 

The loss component M" is frequently expressed in terms of the absorption coefficient for wave propagation, a cf Chapter 5, equation 35 and associated discussion). Often the acoustic attenuation is given in decibels/cm (= 8.686a). When aXflTT 1, the analog of equation 40 of Chapter 5 for bulk longitudinal... 

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