First slide

Introduction to waves

Question

The ratio of densities of nitrogen and oxygen is 14:16. The temperature at which the speed of sound in nitrogen will be same at that in oxygen at 55^oC is

Moderate

A

35°C
B

48°C
C

65°C
D

14°C

Solution

$v = \sqrt{\frac{γ RT}{M}} \Rightarrow \frac{T_{N}}{T_{0}} = \frac{M_{N}}{M_{0}} \Rightarrow \frac{T_{N}}{273 + 55} = \frac{14}{16} = \frac{7}{8}$
$\Rightarrow T_{N} = 287 K = 14 ° C$

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