Physics

Problem

Consider dry air that may be treated as an ideal gas of molar mass

M

and ratio of specific heats

\gamma

. Let the absolute temperature be

T

. (a) Derive an expression for the speed of sound

v

in terms of

\gamma,\,R,\,T

and

M

. (b) Hence obtain an expression for the minimum distance

d_{\min}

from a sound source to a reflecting surface such that an echo is heard distinctly. (c) Using your result, calculate

d_{\min}

0^{\circ}\text{C}

and at

40^{\circ}\text{C}

, taking

\gamma =1.4

and

M=29\,\text{g\,mol}^{-1}