Waves sound

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... 

Miscellaneous Properties. The acoustical properties of polymers are altered considerably by their fabrication into a ceUular stmcture. Sound transmission is altered only slightly because it depends predominandy on the density of the barrier (in this case, the polymer phase). CeUular polymers by themselves are, therefore, very poor materials for reducing sound transmission. They are, however, quite effective in absorbing sound waves of certain frequencies (150) materials with open ceUs on the surface are particulady effective. The combination of other advantageous physical properties with fair acoustical properties has led to the use of several different types of plastic foams in sound-absorbing constmctions (215,216). The sound absorption of a number of ceUular polymers has been reported (21,150,215,217). 

CeUular urea—formaldehyde and phenoHc resin foams have been used to some extent in interior sound-absorbing panels and, in Europe, expanded polystyrene has been used in the design of sound-absorbing doors (233). In general, cost, dammabUity, and cleaning difficulties have prevented significant penetration of the acoustical tile market. The low percent of redection of sound waves from plastic foam surfaces has led to their use in anechoic chambers (216). 

Fibrous ndFoa.medMa.teria.ls, Most sound-absorbiag materials are fibrous or porous and are easily penetrated by sound waves. Air particles excited by sound energy move rapidly to and fro within the material and mb against the fibers or porous material. The frictional forces developed dissipate some of the sound energy by converting it iato heat. 

When a sound wave comes in contact with a soHd stmcture, such as a wall between two spaces, some of the sound energy is transmitted from the vibrating air particles into the stmcture causing it to vibrate. The vibrating stmcture, in turn, transmits some of its vibrational energy into the air particles immediately adjacent on the opposite side, thereby radiating sound to the adjacent space. For an incomplete barrier, such as a fence or open-plan office screen, sound also diffracts over the top and around the ends of the barrier. The subject of this section is confined to complete barriers that provide complete physical separation of two adjacent spaces. Procedures for estimating the acoustical performance of partial barriers can be found in References 5 and 7. 

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... 

This frequency is a measure of the vibration rate of the electrons relative to the ions which are considered stationary. Eor tme plasma behavior, plasma frequency, COp, must exceed the particle-coUision rate, This plays a central role in the interactions of electromagnetic waves with plasmas. The frequencies of electron plasma waves depend on the plasma frequency and the thermal electron velocity. They propagate in plasmas because the presence of the plasma oscillation at any one point is communicated to nearby regions by the thermal motion. The frequencies of ion plasma waves, also called ion acoustic or plasma sound waves, depend on the electron and ion temperatures as well as on the ion mass. Both electron and ion waves, ie, electrostatic waves, are longitudinal in nature that is, they consist of compressions and rarefactions (areas of lower density, eg, the area between two compression waves) along the direction of motion. 

Ultrasonic Spectroscopy. Information on size distribution maybe obtained from the attenuation of sound waves traveling through a particle dispersion. Two distinct approaches are being used to extract particle size data from the attenuation spectmm an empirical approach based on the Bouguer-Lambert-Beerlaw (63) and a more fundamental or first-principle approach (64—66). The first-principle approach implies that no caHbration is required, but certain physical constants of both phases, ie, speed of sound, density, thermal coefficient of expansion, heat capacity, thermal conductivity. 

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. 

FIGURE 9.60 Sound-waves generation by a tuning fork. 

On the basis of a sound wave eejuation, it is shown that the povs er ol a noise Source is equal to... 

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. 

Schsilwelle, /. sound wave, schsilzuleitend, a. sound-conducting. 

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