Question

The velocity of sound at $0^{\circ }C$ is $332m{s}^{-1}$. At what temperature will it be $664m{s}^{-1}$?

• A. ${273}^{\circ }C$
• B. ${546}^{\circ }C$
• C. ${819}^{\circ }C$
• D. ${1092}^{\circ }C$

Answer 1

The correct option is C ${819}^{\circ }C$

Velocity of sound in air is proportional to $\sqrt{T}$, where T is temperature in Kelvin unit. So,

$\frac{v^{\prime }}{v}=\sqrt{\frac{T^{\prime }}{T}}\Rightarrow \frac{664}{332}=\sqrt{\frac{T^{\prime }}{273}}\Rightarrow 4=\frac{T^{\prime }}{273}\Rightarrow T^{\prime }=4\times 273\text{K}=4\times 273-273={819}^0\text{C}$.