Review. As a sound wave passes through a gas, the compressions are either so rapid or so far apart that thermal conduction is prevented by a negligible time interval or by the effective thickness of insulation. The compressions are refractions are adiabatic. (a) Show that the speed of sound in an ideal gas is
where M is the molar mass. The speed of sound in a gas is given by Equation 16.35; use that equation and the definition of the bulk modulus. (b) Compute the theoretical speed of sound in air at 20.0°C and state how it compares with the value in Table 16.1. Take M=28.9 g/mol. (c) Show that the speed of sound in an ideal gas is
where mois the mass of one molecule. (d) Show how the result in part (c) compares with the most probable, average, and rms molecular speeds.
