Question

A man fires a gun and hears its echo after 5 s. The man then moves 310 m towards the hill and fires his gun again. This time he hears the echo after 3 s. Calculate the speed of sound.

• A. $330m{s}^{-1}$
• B. $350m{s}^{-1}$
• C. $210m{s}^{-1}$
• D. $310m{s}^{-1}$

Answer 1

Answer: (D)

$310m{s}^{-1}$

The speed of the sound is calculated as follows.
Let d be the distance between the man and the hill in the beginning.
$v=\frac{2\times d}{t}$ = $\frac{2\times d}{5}\to eqn1$
He moves 310 m towards the hill. Therefore the distance will be (d - 310) m. Therefore,
$v=\frac{2(d-310)}{3}\to eqn2$
Since velocity of sound is same, equating (1) and (2), we get
$\frac{2d}{5}=\frac{2(d-310)}{3}$
3d = 5d - 1550
2d = 1550
d = 775 m
Hence, the velocity of sound v=$\frac{2\times 775}{5}$ (substituting in equation 1)
$v=310m/s$