Question

A man stands before a large wall at a distance of$50m$ and claps his hands at regular intervals. Initially, the interval is large. He gradually reduces the interval and fixes it at a value when the echo of a clap merges with the next clap. If he has to clap $10times$ during every$3seconds$, find the velocity of sound in air.

Answer 1

Step 1. Given data:

Distance of man from wall, $S=50m$

Man has to clap $10$ times in $3sec$

Step 2. Calculate time interval and time taken by sound

So, the time interval between two claps $=\frac{3}{10}sec$

Time taken by the sound to reach the wall and come back to man $=\frac{3}{10}sec$

Time taken by the sound to reach wall only, $t=\frac{{\displaystyle \raisebox{1ex}{$3$}\!\left/ \!\raisebox{-1ex}{$10$}\right.}}{2}sec$

Step 3. Velocity of sound

Velocity, $v=\frac{S}{t}$

$\Rightarrow v=\frac{50}{{\displaystyle \raisebox{1ex}{$3$}\!\left/ \!\raisebox{-1ex}{$20$}\right.}}$

$\Rightarrow v=333m/sec$

Hence, the required velocity is $333m/sec$