Question

The velocity of sound in dry air at $0^0$C and at $74cm$ of Hg pressure is $332m{s}^{-1}$ . Then, the velocity of sound (in $m{s}^{-1}$) at ${50}^0$C and at $77.5cm$ of Hg pressure will be

• A. $322.7$
  
• B. $352.4$
  
• C. $347.1$
  
• D. $361.1$
  

Answer 1

Answer: (D)

$361.1$

Velocity of sound in air $v=\sqrt{\frac{\gamma P}{\rho }}$
Using $P=\rho RT$
We get $v=\sqrt{\gamma RT}$
$⟹v\propto \sqrt{T}$ $(\because \gamma$ and $R$ are constants $)$
Thus we get $\frac{v_2}{v_1}=\sqrt{\frac{T_2}{T_1}}$
Given : $v_1=332m/s$ $T_1=0^{o}C=273K$ and $T_2={50}^{o}C=273+50=323K$
$\therefore$ $\frac{v_2}{332}=\sqrt{\frac{323}{273}}$
$⟹v_2=361.1m/s$