Question

A man standing in front of a vertical cliff fires a gun. He hears the echo after $3$ seconds. On moving closer to the cliff by $82.5m$, he fires again. This time, he hears the echo after $2.5$ seconds. Calculate the velocity of sound.

• A. $330m/s$
• B. $340m/s$
• C. $320m/s$
• D. $300m/s$

Answer 1

Answer: (A)

$330m/s$

Let speed of sound be $v$.

Let distance of cliff from man be $d$.

time taken initially $t_1=3s$

time taken after man gets closer to cliff $t_2=2.5s$

$Speed=\frac{Distance}{Time}$

$time=\frac{Distance}{speed}$

So case 1

$3=\frac{2d}{v}$.............(1)

(Distance travelled by sound is 2d as it goes to cliff and comes back)

So case 2

$2.5=\frac{2(d-82.5)}{v}$...........(2)

Dividing 1 by 2

$\frac{3}{2.5}=\frac{d}{(d-82.5)}$

$3d-247.5=2.5d$

$0.5d=247.5$

$d=495m$

From 1

$v=\frac{2d}{3}=\frac{2\times 495}{3}=330m/s$