Question

The speed of sound in air at temperature $T$ and pressure $p$ is $v .$ When the temperature is increased to $2\, T$ and the pressure is reduced to $\frac{p}{2}$, then the speed is changed to

• A. $2\, v$
• B. $v$
• C. $\sqrt{2} v$
• D. $\frac{V}{\sqrt{2}}$

Answer 1

Answer: (C)

Speed of sound in air does not depend on pressure, but directly proportional to the root of temperature, i.e.
$v \propto \sqrt{T} \Rightarrow \frac{v_{2}}{v_{1}}=\sqrt{\frac{T_{2}}{T_{1}}}$
Given, $T_{1}=T$ and $T_{2}=2 T$,
$v_{1}=v, v_{2}=?$
$\frac{v_{2}}{v}=\sqrt{\frac{2 T}{T}}$
$\Rightarrow v_{2}=\sqrt{2} v$