Question

The velocity of sound in air at a certain temperature is $350m{s}^{-1}$. What will be the velocity of sound in helium at the same temperature? $({\gamma }_{air}=\frac{7}{5})$
[molecular mass of air = 29, molecular mass of helium = 4]

• A. 1032 m/s
• B. 1100 m/s
• C. 925 m/s
• D. 1513 m/s

Answer 1

The correct option is A 1032 m/s

$\gamma$ of helium =$\frac{5}{3}={\gamma }_{He}$
$\gamma$ of air =$\frac{7}{5}={\gamma }_a$
$V_a=\sqrt{\frac{{\gamma }_{a}RT}{M_a}}{\gamma }_{He}=\sqrt{\frac{{\gamma }_{He}RT}{M_{He}}}$
Dividing $\frac{V_a}{V_{He}}=\sqrt{\frac{{\gamma }_a}{{\gamma }_H}.\frac{M_{He}}{M_a}}=\sqrt{\frac{\left(\frac{7}{5}\right)}{\left(\frac{5}{3}\right)}.\frac{4}{29}}=\sqrt{\frac{21}{25}\times \frac{4}{29}}=\frac{4.58\times 2}{5\times 5.39}=0.339V_{He}=\frac{V_a}{0.339}=\frac{350}{0.339}=1032.45m{s}^{-1}$

Ans: $V_{He}=1032$ m/s