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.

Answer 1

Here, t1 =5s. Let d be the distance of the hill from the man and v be the velocity of sound.
Then t= ${\displaystyle \frac{2\text{d}}{\text{v}}}$
5 = ${\displaystyle \frac{2\text{d}}{\text{v}}\text{or}\text{d}=\frac{5\text{v}}{2}}$ .................................. (1)
When the man moves, through a distance 310 m towards the wall, then d' = d  - 310  and  t' = 3s .
. ·. 3= ${\displaystyle \frac{2\text{d}-310}{\text{v}}}$
or, d - 310 = ${\displaystyle \frac{\text{v}}{2}}$; .................................... (ii)
Subtracting (ii) from (i)
d - d + 310 = ${\displaystyle \frac{5\text{v}}{2}-\frac{3\text{v}}{2}=\frac{2\text{v}}{2}}$= v
${\displaystyle \therefore }$ v = 310m/s