Characteristics of Sound Waves

Some of the problems often encountered during ultrasonic inspection of plane specimens are also found on cylindrical specimens. For example, problems associated with the directional characteristic of the ultrasonic transducer. Furthermore, the discontinuity influences the shape and propagation direction of a reflected pulse, causing wave mode transformation. In addition, the specimen influences the shape and amplitude of the reflected pulse by sound absorption. 

Ultrasonic absorption is a so-called stationary method in which a periodic forcing function is used. The forcing function in this case is a sound wave of known frequency. Such a wave propagating through a medium creates a periodically varying pressure difference. (It may also produce a periodic temperature difference.) Now suppose that the system contains a chemical equilibrium that can respond to pressure differences [as a consequence of Eq. (4-28)]. If the sound wave frequency is much lower than I/t, the characteristic frequency of the chemical relaxation (t is the... 

A self sustaining decomposition reaction propagating faster than the speed of sound by means of a shock wave (the characteristic property of high as opposed to low explosives). 

The sound absorption coefficient, a, is increased when the dynamics of the chemical system are of the same order of magnitude as the frequency of the sound wave,41 and experimentally this quantity is measured as a function of frequency of the ultrasonic sound wave (Fig. 4). When the frequency of the sound wave is of the same order as the frequency for the relaxation process, effects due to relaxation of the equilibrium give rise to characteristic changes in the quantity a//2, where a is the sound absorption coefficient measured at frequency /40 The variation of a with frequency, /, has an inflection point at the relaxation frequency of the system, fr, which is related to 1/t, where r is the relaxation time (1/t = 27i/r).40,41 The expression relating the quantity... 

One of the most important characteristics necessary to completely identify a wave is its intensity, where the intensity is a measure of the sound energy the wave produces. For a sound wave in air, the mass (m) of air moving with an average velocity (v) will have associated with it a kinetic energy of (mv )/2 (joules). In the strictest sense the intensity is the amount of energy carried per second per unit area by the wave. Since the units of energy are joules (J) and a joule per second is a watt (W), then the usual unit of sound intensity (especially in sonochemistry) will be W cm. As we will see later (Eq. 2.13), the maximum intensity (I) of the sound wave is proportional to the square of the amplitude of vibration of the wave (P ). This will have important repercussions in our study of chemical systems. 

Finally the velocity of the blast wave falls from supersonic to sonic (ca. 330 ms ) and its characteristics begin to resemble those of an ordinary sound wave. 

Another possible flow for weak detona tion is that of Fig 2b, where a different detonation front curve W gives values u and c2 along the characteristics in the sector between W and Q.0. For this flow the value of Cp along P will be Cp =Up—u2 +c2 and the value of p along P will also be different from that of the first solution. One of the possible flows is that for which both the front and the first sound wave move with sonic velocity relative to the gas behind the front. Such values are designated by a subscript, so that for this flow u2 = (u2) and c2 (c2),. ie hypothesis that the flow which, occurs is the C-J detonation is the Chapman-Jouguet hypothesis. For such.a detonation, equation 3.2,12 (p 140 of Ref 2) applies and W C coincide, as is shown in Fig 3. 

A measure of success has been achieved in the suppression of noise but usually as a by-product of the development of another type of muzzle device, such as a flash suppressor General Requirements. Noise is an inherent characteristic of a gun and is usually associated with three main producers the projectile, the muzzle, and the gun components other than the muzzle. The noises produced by the gun components are mostly mechanical such as the sounds of moving parts, impact, and vibration. The projectile noises are mainly those caused by air turbulence following the projectile and the supersonic shock wave or ballistic crack generated by the projectile nose. Muzzle noises are produced by the air pressure build-up in the tube ahead of the projectile and by the proplnt gases issuing from the muzzle after the projectile passage... 

FIGURE 3.5 Sound waves in air are waves of gas pressure. The positions of the maxima and minima change with time. The waves travel at a characteristic speed s = kv determined by properties of the air molecules and independent of wavelength or frequency. 

---