First slide

Speed of wave

Question

Change in velocity of sound in a gas per degree rise in temperature at 27^oC is ‘x’. Then change in velocity of sound per degree rise in temperature in the same gas at 127^oC will be

Moderate

A

$x / \sqrt{3}$
B

$2 x / \sqrt{3}$
C

$\frac{\sqrt{3} x}{2}$
D

$\sqrt{3} x$

Solution

Velocity of sound $V = \sqrt{\frac{δRT}{M}}$
$\frac{dV}{dT} = \frac{1}{2} \sqrt{\frac{δR}{MT}} \Rightarrow \frac{dV}{dT} \propto \frac{1}{\sqrt{T}}$
$∴ \frac{x^{1}}{x} = \sqrt{\frac{T}{T^{1}}} = \sqrt{\frac{273 + 27}{273 + 127}} = \frac{\sqrt{3}}{2} \Rightarrow x^{1} = \frac{\sqrt{3} x}{2}$

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