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A boy standing in a quarry claps his hands sharply once every second and heard an echo from the face of the opposite cutting. He moves until the echo is heard midway between the claps. How far is he then from the reflecting surface ( velocity of sound = 360 m/s ) .
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Given :
The boy claps every second.
So in 1 s he claps 1 time .
So in every n seconds n times he will clap.
Let's focus on the question more :
Time
He moves until the echo is heard midway between the claps.
Hence the echo is heard in 0.5 s
This is because he claps in 1 s and the midway will be 1/2 s = 0.5 s.
Formula
Speed = distance / time
Time he heard the echo = 0.5 s
Distance travelled by the echo
Let Distance from the surface be d.
The distance traveled by echo is 2 d since it has to move twice from the source to reflecting surface and from the reflecting surface to the source.
Speed
Speed given is = 360 m/s
Distance
Speed = distance / time
⇒ 360 m/s = 2 d / 0.5 s
⇒ 2 d = 360 m/s × 0.5 s
⇒ 2 d = 180 m
⇒ d = 180 m / 2
⇒ d =90 m
ANSWER:
Distance is 90 m
Speed = distance/time
t = 0.5s
let distance be 2d
360 = 2d/0.5
= 2d=180
= d=180/2
= d=90
The distance is 90m. Hope it helps