Question

The ratio of the speed of sound in helium gas to that in nitrogen gas at same temperature is (γHe = $\frac {5}{3}$, γN2 = 4 , M N2 =28)

• A. $\frac {5}{\sqrt {3}}$
• B. $\sqrt{\frac {7}{5}}$
• C. $\sqrt{\frac {2}{7}}$
• D. $\sqrt{\frac {5}{3}}$

Answer 1

Answer: (A)

$\frac {5}{\sqrt {3}}$

Answer 2

We know that
v = $\sqrt {\frac {rRT}{M}}$
$\frac {v_{He}}{v_{N_2}}$ = $\frac {\sqrt {\frac {5/3 RT}{4}}}{\sqrt {\frac {7/5 RT}{14}}}$
$\frac {v_{He}}{v_{N_2}}$ = $\sqrt {\frac {5\times 28}{7R}} \sqrt {\frac {5RT}{3\times 4}}$
$\frac {v_{He}}{v_{N_2}}$ = $\frac {5}{\sqrt {3}}$
Therefore the correct option is (A) $\frac {5}{\sqrt {3}}$