Question

A man fires a bullet standing between two cliffs. First echo is heard after $3\, s$ and second echo is heard after $5\, s$. If the velocity of sound is $330\, m/s$, then the distance between cliffs is :

• A. 660 m
• B. 990 m
• C. 1320 m
• D. 1950 m

Answer 1

Answer: (C)

Echo is defined as the reflection of a sound wave back to its source in sufficient strength and with a sufficient time lag to be separately distinguished.
Time $=\frac{\text { distance }}{\text { speed }}$
Given that first echo is heard after $3 s$, hence time taken for the echo to travel from first cliff to man is

$t_{1}=\frac{3}{2}=1.5 \,s$
Similarly, time taken for the echo to travel from second cliff to man is
$t_{2}=\frac{5}{2}=2.5 \,s$
Distance between man and first cliff is
$d_{1}=\text { time } \times \text { velocity }=1.5 \times 330=495\, m$
Distance between man and second cliff is
$d_{2}=\text { time } \times \text { velocity }=2.5 \times 330=825\, m$
Hence, distance between two cliff's is
$=d_{1}+d_{2}=495+825=1320\, m$