On a freezing morning the air is at C

PHYSICS · Multi-part · Fermi University Physics · Oscillations, Waves & Acoustics · Acoustics of fluids: generation, propagation and attenuation · Acoustics of fluids: generation, propagation and attenuation

Fluids and Continuum Physics, Ch Acoustics: sound propagation, radiation and attenuation

Problem

On a freezing morning the air is at

0\ ^{\circ}

C, with

p_0 = 1.013\times10^{5}

Pa and

\rho_0 = 1.293

kg m

^{-3}

; the ratio of specific heats is

\kappa = 1.40

. A student argues: "Air obeys Boyle's law,

p \propto 1/V

at fixed temperature, so the stiffness of the air is the isothermal bulk modulus

K_T = p_0

, and the speed of sound must be

c = \sqrt{p_0/\rho_0}

." ((a)) Evaluate the speed the student's argument predicts. ((b)) Evaluate the speed that follows from the adiabatic modulus

K_s = \kappa p_0

, and give the ratio of the two speeds. ((c)) In two or three sentences, say which modulus governs sound in air and why, referring to the time available for heat to move within one cycle of the wave.

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