First slide

Introduction to waves

Question

When the temperature of an ideal gas is increased by 600 K, the velocity of sound in the gas becomes $\sqrt{3}$ times the initial velocity in it. The initial temperature of the gas is

Moderate

A

$- 73^{o} C$
B

$27^{o} C$
C

$127^{o} C$
D

$327^{o} C$

Solution

By using $v = \sqrt{\frac{γRT}{M}} \Rightarrow v \propto \sqrt{T}$
$\frac{v_{2}}{v_{1}} = \sqrt{\frac{T_{2}}{T_{1}}} = \sqrt{\frac{T + 600}{T}} = \sqrt{3} \Rightarrow T = 300 K = 27^{o} C$

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