Question

On a winter day, sound travels $336\text{meters}$ in $\text{one second}$. Find the atmospheric temperature. Speed of sound at $0{}^{\circ }\text{C}$ is $332{\text{ms}}^{-1}$.

• A. $7{}^{\circ }\text{C}$
• B. $12{}^{\circ }\text{C}$
• C. $16{}^{\circ }\text{C}$
• D. $19{}^{\circ }\text{C}$

Answer 1

The correct option is A $7{}^{\circ }\text{C}$

The speed of sound in air is given by,

$V=\sqrt{\frac{\gamma RT}{M_0}}$

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

Given,

Speed of sound at $0^{\circ }\text{C}=273\text{K}$ is $332{\text{ms}}^{-1}$

Speed of sound at atmospheric temperature $\left(T\right)$ is $336{\text{ms}}^{-1}$.

$\Rightarrow \frac{336}{332}=\sqrt{\frac{T}{273}}$

$\Rightarrow T=273\times {\left(\frac{336}{332}\right)}^2=280\text{K}$

$\therefore T=7{}^{\circ }\text{C}$

Hence, option $\left(\text{A}\right)$ is correct.

Why this question ? Concept : If pressure of the gas is changed, but the temperature is kept constant, the density of gas varies proportionally. Hence, temperature is constant, then speed of sound also remains constant