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?

#### Solution

Given:

Velocity of sound *v*_{1} = 340 m/s

Temperature *T*_{1} = 17°C = 17 + 273 = 290 K

Let the velocity of sound at a temperature *T*_{2 }be *v*_{2}.*T*_{2} = 32°C = 273 + 32 = 305 K

Relation between velocity and temperature:

\[v \propto \sqrt{T}\]

\[So, \]

\[\frac{v_1}{v_2} = \frac{\sqrt{T_1}}{\sqrt{T_2}}\]

\[ \Rightarrow v_2 = \frac{\sqrt{v_1} \times \sqrt{T_2}}{\sqrt{T_1}}\]

\[\text { On substituting the respective values, we get: }\]

\[ v_2 = 340 \times \sqrt{\frac{305}{290}} = 349 \text { m/s }\]

Hence, the final velocity of sound is 349 m/s.