The sound wave

In this section, we shall examine first the relaxation behaviour of a polymer material when irradiated with a sound wave, acoustic relaxation. Then we consider how the interactions may be influenced by increasing the intensity of the sound wave. Since most of the work in this area has been carried out in the ultrasonic frequency region, the phenomena are sometimes designated as ultrasonic relaxation. The irradiation of materials with high intensity ultrasonic waves is usually referred to as sonochemistry. 

For an accurate analysis of the propagation, one must include the shear component. However, for many simple situations the relaxation processes associated with shear occur outside the frequency range of interest, and so for the rest of this section we shall ignore the shear component, and consider only the response of a system to a three-dimensional pressure wave. 

For most systems the change from high to low pressure in a sound wave occurs in such short times that the system cannot exchange heat with its surroundings, and so the pressure change is adiabatic. However, adiabatic compression causes the molecules to undergo more collisions and so raises the temperature. Adiabatic rarefaction lowers the temperature. So, the sound wave is effectively 

One-dimenslonal compression Three-dimensional compression Shear 

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Ultrasonic absorption is used in the investigation of fast reactions in solution. If a system is at equilibrium and the equilibrium is disturbed in a very short time (of the order of 10"seconds) then it takes a finite time for the system to recover its equilibrium condition. This is called a relaxation process. When a system in solution is caused to relax using ultrasonics, the relaxation lime of the equilibrium can be related to the attenuation of the sound wave. Relaxation times of 10" to 10 seconds have been measured using this method and the rates of formation of many mono-, di-and tripositive metal complexes with a range of anions have been determined. 

The sonic tool measures the time taken for a sound wave to pass through the formation. Sound waves travel in high density (i.e. low porosity) formation faster than in low density (high porosity) formation. The porosity can be determined by measuring the transit time for the sound wave to travel between a transmitter and receiver, provided the rock matrix and fluid are known. 

The previous subsection described single-experiment perturbations by J-jumps or P-jumps. By contrast, sound and ultrasound may be used to induce small periodic perturbations of an equilibrium system that are equivalent to periodic pressure and temperature changes. A temperature amplitude 0.002 K and a pressure amplitude 5 P ss 30 mbar are typical in experiments with high-frequency ultrasound. Fignre B2.5.4 illustrates the situation for different rates of chemical relaxation with the angular frequency of the sound wave... 

Xj 1. The sample relaxes fast with the displacement from equilibrium synclnonous with the sound wave. 

Figure B2.5.4. Periodic displacement from equilibrium through a sound wave. The frill curve represents the temporal behaviour of pressure, temperature, and concentrations in die case of a very fast relaxation. The other lines illustrate various situations, with 03Xj according to table B2.5.1. 03 is the angular frequency of the sound wave and x is the chemical relaxation time. Adapted from [110].

For sufficiently long times (index n ), the exponential can be neglected, leaving an oscillation of the turnover variable phase shifted with respect to the sound wave and with its amplitude reduced by the finite relaxation... 

Erequendy, a single ultrasonic transducer serves both as the sender of the ultrasonic pulse and as a receiver for the sound waves reflected from surfaces and interior discontinuities. The receiver transforms the stress pulse back into electrical oscillations. AH of the signals are displayed on an oscilloscope screen for interpretation. Eor a material of length E having a wave speed C, the anomaly shown in Eigure 4 would reflect a signal back to the... 

In the second technique, the flowing liquid must contain scatters in the form of particles or bubbles that will reflect the sound waves. These scatters should be travehng at the velocity of the hquid. A Doppler method is applied by transmitting sound waves along the flow path and measuring the frequency shift in the returned signal from the scatters in the process fluid. This frequency shift is proportional to liquid velocity. 

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... 

Figure 4-2. The phase lag between concentration and pressure in ultrasonic absorption. The cyclic pressure changes are produced by the sound wave. The cyclic concentration changes are a response to the pressure changes.

In Eq. (4-29) jc is the distance traveled by the wave, and a is the absorption coefficient. Sound absorption can occur as a result of viscous losses and heat losses (these together constitute classical modes of absorption) and by coupling to a chemical reaction, as described in the preceding paragraph. The theory of classical sound absorption shows that a is directly proportional to where / is the sound wave frequency (in Hz), so results are usually reported as a//, for this is, classically, frequency independent. 

With nondestructive ultrasonic test back and forth scanning of a specimen is accomplished with ultrasonics. This NDT can be used to find voids, delaminations, defects in fiber distribution, etc. In ultrasonic testing the sound waves from a high frequency ultrasonic transducer are beamed into a material. Discontinuities in the material interrupt the sound beam and reflect the energy back to the transducer, providing data that can be used to detect and characterize flaws. It can locate internal flaws or structural discontinuities by the use of high frequency reflection or attenuation (ultrasonic beam). 

This equation gives for the velocity of sound in air at 0° 280 metres per second instead of 331, as obtained by experiment. The discrepancy was explained by Laplace (1822), who pointed out that in the sound wave the changes of volume are so rapid that the conditions are adiabatic, and not isothermal. Hence e = Q,... 

Acoustic cavitation In this case, the pressure variations in the liquid are effected using the sound waves usually ultrasound (16 kHz to 100 MHz). The chemical changes taking place due to the cavitation induced by the passage of sound waves are commonly known as sonochemistry. 

In the preceding chapters many aspects of sonochemistry and its application have already been discussed in details and now to conclude, few experiments are being discussed here to make the beginners in the field of sonochemistry, especially the undergraduate students, to ride on the sound wave and begin their journey of sonochemistry with some of these experiments, which can be conveniently carried out with an ultrasonic cleaning bath (Fig. 15.1) or an ultrasonic probe (Fig. 15.2) of 20 kHz, available commercially abundantly. 

In ultrasonic relaxation measurements perturbation of an equilibrium is achieved by passing a sound wave through a solution, resulting in periodic variations in pressure and temperature.40,41 If a system in chemical equilibrium has a non-zero value of AH° or AV° then it can be cyclically perturbed by the sound wave. The system cannot react to a sound wave with a frequency that is faster than the rates of equilibration of the system, and in this case only classical sound absorption due to frictional effects occurs. When the rate for the host-guest equilibration is faster than the frequency of the sound wave the system re-equilibrates during the cyclic variation of the sound wave with the net result of an absorption of energy from the sound wave to supply heat to the reaction (Fig. 4). 

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... 

Many cells, especially bacteria, yeast, etc., require very drastic measures to disrupt them and various cell disintegrators are available for this purpose. Ultrasonic vibrations cause the formation of minute bubbles, a phenomenon known as cavitation, which is caused by the extreme variations in pressure generated by the sound waves, although the generation of heat may cause problems unless the samples are cooled frequently during the treatment. An additional... 

We have all felt resonance when we hear the sound of a lorry s engine begin to make the window pane vibrate. The natural frequency of the window is having energy supplied to it by the sound waves emanating from the lorry. The principle is best represented diagrammatically. 

Essentially all imaging from medical ultrasound to non-destructive testing relies upon the same pulse-echo type of approach but with considerably refined electronic hardware. The refinements enable the equipment not only to detect reflections of the sound wave from the hard, metallic surface of a submarine in water but also much more subtle changes in the media through which sound passes (e. g. those between different tissue structures in the body). It is high frequency ultrasound (in the range 2 to 10 MHz) which is used primarily in this type of application because by using these... 

Besides the variation in the molecules position when the sound wave travels through the air, there is a variation in pressure (Fig. 2.5). At the point where the layers are crowded together (i. e. where the molecules are compressed) the pressure is higher... 

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. 

Let us now turn our attention to the application of the sound wave to a liquid since this is the medium of importance to the practising chemist. The sound wave is usually introduced to the medium by either an ultrasonic bath or an ultrasonic horn (see Chapter 7). In either case, an alternating electrical field (generally in the range 20-50 kHz) produces a mechanical vibration in a transducer, which in turn causes vibration of the probe (or bottom of the bath) at the applied electric field frequency. The horn (or bath bottom) then acts in a similar manner to one prong of a tuning fork. As in the case of air, the molecules of the liquid, under the action of the applied acoustic field, will vibrate about their mean position and an acoustic pressure (P = P sin 2k ft) will be superimposed upon the already ambient pressure (usually hydrostatic, Pjj) present in the liquid. The total pressure, P, in the liquid at any time, t, is given by Eq. 2.4. 

Increasing the external pressure (Pjj) leads to an increase in both the cavitation threshold and the intensity of bubble collapse. Qualitatively it can be assumed that there will no longer be a resultant negative pressure phase of the sound wave (since Pj, — > 0) and so cavitation bubbles cannot be created. Clearly, a sufficiently large... 

An alternative approach to dust and mist suppression is the use of acoustic standing waves. When a sonic standing wave is set up in air the particles suspended in the air will migrate to the nodes of the sound wave and this phenomenon has been used in a variety of applications. Smoke particles normally remain suspended in air for a considerable period because of they are extremely light. In an acoustic field they will become concen-... 

Sound waves provide a periodic oscillation of pressure and temperature. In water, the pressure perturbation is most important in non-aqueous solution, the temperature effect is paramount. If cu (= 2 nf, where/is the sound frequency in cps) is very much larger than t (t, relaxation time of the chemical system), then the chemical system will have no opportunity to respond to the very high frequency of the sound waves, and will remain sensibly unaffected. 

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