Question

The temperature at which the speed of sound in air becomes double of its value at ${27}^{\circ }C$ is

• A. ${54}^{\circ }C$
• B. ${327}^{\circ }C$
• C. ${927}^{\circ }C$
• D. $-{123}^{\circ }C$

Answer 1

The correct option is C ${927}^{\circ }C$

The speed of the sound is given as:

$v=\sqrt{\frac{\gamma RT}{M}}$

$\Rightarrow v\propto \sqrt{T}$

ie. if $v$ is doubled then $T$ becomes four times,

hence $T_2=4T_1=4(273+27)=1200K={927}^{\circ }C$