First slide

Introduction to waves

Question

At which temperature the speed of sound in Hydrogen will be same as that of speed of sound in Oxygen at 100^oC

Moderate

A

– 148^oC
B

– 212.5^oC
C

– 317.5^oC
D

– 249.7^oC

Solution

Speed of sound in gases is $v = \sqrt{\frac{γRT}{M}} \Rightarrow T \propto M$
(Because v, $γ$ -constant). Hence $\frac{T_{H_{2}}}{T_{O_{2}}} = \frac{M_{H_{2}}}{M_{O_{2}}}$
$\Rightarrow \frac{T_{H_{2}}}{(273 + 100)} = \frac{2}{32} \Rightarrow T_{H_{2}} = 23 .2 K = - 249 .7 ° C$

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