Attenuation longitudinal wave

Keywords— Bone marrow. Wave velocity. Wave attenuation, Longitudinal wave. 

Attenuation occurs because the tensile release, which is traveling at an elastic longitudinal wave speed, Q, overtakes the tensile front traveling at a plastic wave speed Cp < Q. Assuming a pulse as shown in Fig. 8.10 with a stress rate in the tensile front and tensile release of a and b, respectively, an approximate analysis shows that the peak will decay by an amount... 

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)... 

A second mechnism for sound attenuation is mode conversion. The sound waves in air or water are longitudinal waves, where the particle motion is parallel to the direction of sound propagation. With appropriate boundary conditions the longitudinal deformation can be converted to shear deformation or to viscous flow. Conversion to viscous flow is most readily achieved at... 

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. 

Fig. 2 Temperature dependences of ultrasonic attenuation for longitudinal waves propagating in ZnSe V along the [110] axis, measured at 270 MHz open circles), 156 MHz (filledcircles), and 52 MHz triangles). A a = a (T) - a (To), To = 16 K. The plot for 52 MHz is shifted downward by 0.7 dB for clarity. Concentration of the dopand = 5.6 X lO cm After Fig. 3 in [3]...

Fig. 5 Temperature dependences of velocity [vi (T) - vi(4.2)/vt (4.2)] open circles) and attenuation of ultrasound (filled circles) with respect to the level at T = 4.2 K obtained in ZnSe Ct + at 54.4 MHz. Concentration of the impurity cr = 10 cm l Longitudinal wave, ultrasound passage I = 0.717 cm, propagation direction [110]. After Fig. 1 in [17]...

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

Figure 14.1 Schematic diagram of the experimental setup for ultrasonic measurements by the immersion method. P, pulser Tl, transmitting transducer T2, receiving transducer S, sample a, incident ultrasonic beam b, refracted beam of longitudinal wave c, refracted beam of transverse wave d, transmitted beams. Sample and transducers immersed in silicone oil within the tank (LT). AT, attenuator AM, wide band amplifier CRO, oscilloscope CTR, time interval counter Si, triggering signal for CRO and start signal for the counter S2, signal viewed on CRO and stop signal for the counter. (Adapted from [4] by permission of Elsevier Science Ltd.)...

Acoustic attenuation for longitudinal waves in H0VO4 (above) and the corresponding direct spin-lattice rates for longitudinal phonons (below). The frequency / is in GHz and (f> = angle of magnetic field with [100] axis in the (001) plane. 

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]. 

Ultrasonic Attonuation. The frequency range of this technique is of the order of 1 MHz. The attenuation a of the longitudinal waves is related to the longitudinal loss modulus M" by M" = 2apu lco, and the longitudinal storage modulus M by M = pu, where p is the density and u is the ultrasonic velocity. For an example of the use of this techniques, see References 151 and 152. 

In a polymeric liquid with low enough viscosity to permit a receiving element to be moved through it, the liquid itself can be the sole transmitting medium for a bulk longitudinal wave and the attenuation and phase shift can be measured as... 

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