(24) Sound Waves in an Ideal Gas

(24) Sound Waves in an Ideal Gas - Sound Waves in an Ideal...

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Sound Waves in an Ideal Gas Consider a uniform ideal gas of equilibrium mass density and equilibrium pressure . Let us investigate the longitudinal oscillations of such a gas. Such oscillations are known as sound waves. Generally speaking, a sound wave in an ideal gas oscillates sufficiently rapidly that heat is unable to flow fast enough to smooth out any temperature perturbations generated by the wave. Under these circumstances, the gas obeys the adiabatic gas law (Reif 2008), (323) where is the pressure, the volume, and the ratio of specific heats (i.e., the ratio of the gas's specific heat at constant pressure to its specific heat at constant volume) (ibid.). This ratio is for ordinary air (Haynes and Lide 2011b). Consider a sound wave in a column of gas of cross-sectional area . Let measure distance along the column. Suppose that the wave generates an -directed displacement of the column, . Consider a small section of the column lying between and . The change in volume of the section is . Hence, the relative change in volume, which is assumed to
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(24) Sound Waves in an Ideal Gas - Sound Waves in an Ideal...

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