Sound waves, absorption

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. 

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). 

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. 

The PAS phenomenon involves the selective absorption of modulated IR radiation by the sample. The selectively absorbed frequencies of IR radiation correspond to the fundamental vibrational frequencies of the sample of interest. Once absorbed, the IR radiation is converted to heat and subsequently escapes from the solid sample and heats a boundary layer of gas. Typically, this conversion from modulated IR radiation to heat involves a small temperature increase at the sample surface ( 10 6oC). Since the sample is placed into a closed cavity cell that is filled with a coupling gas (usually helium), the increase in temperature produces pressure changes in the surrounding gas (sound waves). Since the IR radiation is modulated, the pressure changes in the coupling gas occur at the frequency of the modulated light, and so does the acoustic wave. This acoustical wave is detected by a very sensitive microphone, and the subsequent electrical signal is Fourier processed and a spectrum produced. 

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... 

In situations where absorption of the incident radiation by the transducing gas is troublesome a piezoelectric transducer (made from barium titanate, for example) can be attached to the sample (or sample cuvette in the case of liquids) to detect the thermal wave generated in the sample by the modulated light (8,9). The low frequency, critically damped thermal wave bends the sample and transducer thus producing the piezoelectric response. The piezoelectric transducer will also respond to a sound wave in the solid or liquid but only efficiently at a resonant frequency of the transducer typically of the order of 10 to 100 KHz (see Figure 4). Thus neither in the case of microphonic nor piezoelectric detection is the PA effect strictly an acoustic phenomenon but rather a thermal diffusion phenomenon, and the term "photoacoustic" is a now well established misnomer. 

However when values of the calculated absorption coefficient are compared with those obtained experimentally, the agreement is often poor. For example if we take water at 20 °C for which = ICp, p = 1 g cm and c = 1500 m s and we pass a sound wave of 20 kHz, then a can be calculated to be approx. 3.5 x 10 cm". Experimentally a is found to be 8.6 x 10 cm i. e. approx, two and a half times larger. In fact only in the case of monatomic gases is the observed absorption, equal to the classical absorption. In all other cases the observed absorption is greater than the classical absorption by an amount called the excess absorption, (given by the expression 2n i1b/p complete accuracy, Eq. 2.16 should be further modified to take... 

Time-resolved Photoacoustic Spectroscopy. In photoacoustic spectroscopy (PAS) the heat evolved by the absorption of light in the sample is transformed into sound waves which are detected by a microphone. In steady-state spectroscopy the light is continuous, but it is also possible to use a pulsed laser and to observe the change in the intensity of the sound signal with time. In this respect time-resolved PAS is somewhat similar to thermal lensing, but both techniques have different limitations and advantages. 

When a sound wave strikes a material a fraction of its energy is reflected and a fraction is dissipated, or absorbed, by the material. The fraction of sound energy absorbed by a material is designated by its sound-absorption coefficient (oc). The sound-absorption coefficient of a given material is between zero and one if it is zero all the impinging energy is reflected and none absorbed if it is one all the eneigy is absorbed and none reflected. 

In nearly all natural wave phenomena, losses increase with frequency. Distributed losses due to air drag and internal bulk losses in the string tend to increase with frequency. Similarly, air absorption increases with frequency, adding loss for sound waves in acoustic tubes or open air [Morse and Ingard, 1968],... 

These are two extremes. An intermediate situation, where the period of the sound wave is comparable to the relaxation time, occurs when reaction is fast enough to allow the concentrations to alter with time, but the change in concentration is out of phase with the sound wave. This shows up as an increase in the velocity of sound, or as a maximum in the absorption of sound by the reaction mixture as the frequency of the sound wave alters. This is the region where all the useful information is obtained. 

The Photoacoustic Effect ( 7). The modulated absorption of light by material in a cell leads to the production of a sound wave at the modulation frequency. The sound wave is due to modulated pressure pulses in the cell arising from the liberation, as heat, of a portion of the absorbed light. The sound wave thus produced can be detected with a sensitive microphone and associated electronics, i.e., a spectrophone. 

Figure 40. Dependence of ota/v2 (where aa is the amplitude absorption coefficient and v the frequency of the sound wave) on mole fraction of t-butyl alcohol in aqueous mixtures at 70 MHz and 298 K.

Absorption is a material property, usually symbolised by a, which is a measure of the energy removed from the sound wave by conversion to heat as the wave propagates through a given thickness l of material. It is expressed in units of decibel/cm (dB/cm). 

The method consists of detecting flaws by measuring the energy of the reflected beam from the sample surface, or the time taken by the beam to traverse the sample, or attenuation of the sound waves by absorption and scattering within the sample, or the pattern in the response of either a transmitted or reflected signal. 

Fig. 7. Electromagnetic waves and sound waves. When the frequency of the waves (light or sound) equals the natural frequency of the chemical group or polymer, an absorption peak is found. The energy is converted into molecular motion, i.e., heat. Illustrated for the damping curve are the / -transition, the glass transition, and the liquid-liquid transition.

Scharnhorst, K. P. Madigosky, W. M. and Balizer, E., "Scattering Coefficients and the Absorption Edge of Longitudinal Coherent Sound Waves in Selected Inhomogeneous Materials," NSWC Technical Report 85-196. Silver Spring, MD, Jun 1985. 

Some detectors employ the optothermal effect the absorbed modulated infrared radiation heats the sample and its environment, thus producing sound waves which are recorded with a microphone. They can be combined with scanning spectrometers and interferometers. A Golay cell (Golay, 1949) measures the optothermal pressure change by a light beam which is deflected by a reflecting membrane. The first infrared process spectrometer, the URAS, alieady employed the absorption bands of a detector gas to specifically analyze the concentration of this particular gas in a sample. This is a non-dispersive spectrometer already mentioned in Sec. 1. 

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