Question

A man standing in front of a vertical wall at a certain distance beats a drum at regular intervals. The drumming rate is gradually increased and he finds that the echo is not heard dsitinctly when the drumming rate becomes $2$ beats in $3$ seconds. He then moves nearer to the wall by $90m$ and finds the echo is again not heard when the drumming rate becomes $1$ per second. From this data, the velocity of sound must be :

• A. $330m/s$
• B. $340m/s$
• C. $360m/s$
• D. $180m/s$

Answer 1

Answer: (C)

$360m/s$

Let the distance from the wall be initially $d$

In first case sounds takes $1.5sec$ to cover the distance between the man and the wall and return to man

$v_s=\frac{2d}{(\frac{3}{2})}$

In the second case it takes $1sec$ for the sound to go to wall and return to man

$v_s=\frac{2(d-90)}{1}$

By comparing both the equations $d=270$

Velocity of sound$\left(v_s\right)=360m{s}^{-1}$