Question

The speed of sound as measured by a student in the laboratory on a winter day is 340 m s⁻¹ when the room temperature is C17°. What speed will be measured by another student repeating the experiment on a day when the room temperature is 32°C?

Answer 1

Given:
Velocity of sound v₁ = 340 m/s
Temperature T₁ = 17°C = 17 + 273 = 290 K
Let the velocity of sound at a temperature T₂ be v₂.
T₂ = 32°C = 273 + 32 = 305 K
Relation between velocity and temperature:
$$\begin{gathered} v\propto \sqrt{T} \\ \mathrm{So}, \\ \frac{v_1}{v_2}=\frac{\sqrt{T_1}}{\sqrt{T_2}} \\ \Rightarrow v_2=\frac{\sqrt{v_1}\times \sqrt{T_2}}{\sqrt{T_1}} \\ \mathrm{On}\mathrm{substituting}\mathrm{the}\mathrm{respective}\mathrm{values},\mathrm{we}\mathrm{get}: \\ {v}_2=340\times \sqrt{\frac{305}{290}}=349\mathrm{m}/\mathrm{s} \end{gathered}$$
Hence, the final velocity of sound is 349 m/s.