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14.Waves and Sound
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The velocities of sound at the same pressure in two monatomic gases of densities ${\rho _1}$ and ${\rho _2}$ are $v_1$ and $v_2$ respectively. ${\rho _1}/{\rho _2} = 2$, then the value of $\frac{{{v_1}}}{{{v_2}}}$ is
A
$\frac{1}{{\sqrt 2 }}$
B
$2$
C
$\frac{1}{2}$
D
None of these
Solution
$\mathrm{V}=\sqrt{\frac{\gamma \mathrm{P}}{\rho}} \mathrm{V} \propto \frac{1}{\sqrt{\rho}} \quad \frac{\mathrm{V}_{1}}{\mathrm{V}_{2}}=\sqrt{\frac{\rho_{2}}{\rho_{1}}}=\sqrt{\frac{1}{2}}=\frac{1}{\sqrt{2}}$
Standard 11
Physics
