5/3/2023 0 Comments Speed of sound in waterThroughout this work it will be assumed that, in the absence of scattering, this is the case, and frequency will not generally be quoted for sound velocity measurements. Pierce also shows (1981c) that sound velocity in the adiabatic approximation is virtually independent of frequency. This case is dealt with in detail in Chapter 4. Under these conditions isothermal propagation may occur over small regions at the boundary between two materials, resulting in so-called thermal scattering of the sound wave. The adiabatic approximation also breaks down when applied to inhomogeneous materials. Pierce shows that the adiabatic approximation begins to break down at frequencies above 10 12 Hz in water and 10 9 Hz in air. Hence, the lower the frequency, the more accurate the adiabatic approximation. Overall, the rate of dissipation of heat falls as wavelength increases. Although this result may appear counterintuitive, it is correct, and anyone unconvinced after reading Pierce can find a separate proof in Zemansky (1957b). This gives the important result that the limit of frequency tending to zero (f → 0, the adiabatic limit) is not the same as frequency equals zero (f = 0). Pierce (1981c) shows that the adiabatic approximation holds at the very lowest frequencies of sound propagation. In the static case, it is the isothermal constants which are measured. Care must therefore be taken when comparing ultrasound-determined elastic constants with those determined using static methods. This means that, despite the temperature fluctuations which inevitably accompany the pressure fluctuations of sound, thermal dissipation is small and it is the adiabatic compressibility which matters. POVEY, in Ultrasonic Techniques for Fluids Characterization, 1997 1.6 THE ADIABATIC IDEALIZATIONĪt all frequencies considered in this work, propagation is adiabatic in homogeneous media. Changes in osmotic potential of the continuous phase could be used to alter cell turgor and the effects of changing turgor studied through its impact on compressibility. For example, the effects of cell bonding could be studied by the addition of calcium ions to a pectin-containing suspension. The cell suspension method can be used to investigate the effects on cells of changes in their condition. These data can then be used in more complex models of acoustic propagation in whole plant tissue so that, for example, changes in cell turgor may be measured. From these data for the single cell and the density of the cell of 1130 kg m − 3, Equation 2.8 gives 2061 m s − 1for the velocity of sound in a single cell. The velocity showed little frequency dependence between one and six megahertz. The adiabatic compressibility of these cells was determined to be 2.08 × 10 10 Pa − 1 ± 0.03 × 10 10 Pa − 1. Measurements of velocity and attenuation have been made ( Self et al., 1992) in suspensions of carrot cells from the taproot cortex. The adiabatic compressibility has been determined for suspensions of animal cells, such as red blood cells ( Shung et al., 1982) and velocity and attenuation has been determined in suspensions of unicellular plant cells, such as algae and diatoms ( Meister and St. (1992) have reviewed ultrasound measurements in fruit and vegetables. In Chapter 2 it was shown that ultrasound is an effective method for determining the adiabatic compressibility of a dispersed phase in a liquid medium. POVEY, in Ultrasonic Techniques for Fluids Characterization, 1997 3.2.5 CELL SUSPENSIONS
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