Question

: If a man standing unsymmetrically between parallel cliffs claps his hands and starts hearing a series of echoes at intervals of 1s. If the speed of sound in air is 340 m/s, the distance between two cliffs will be:
(a) 340 m
(b) 510 m
(c) 170 m
(d) 680 m

Answer 1

Echo is caused by reflection of sound waves back to the source. The sound wave travels towards the obstacle, reflects back upon hitting it and then travels towards the source. Here there are 2 different obstacles so sound reaches the man from the opposite direction with the delay of 1s.

Formula Used:
Velocity is given by:
$v = \dfrac{x}{t}$ …… (1)
where,
x is the distance covered by a particle.
v is velocity.
t is time taken to cover y distance.

Complete step-by-step answer:

Given:
1. Speed of sound (v) = 340m/s
2. Time after which echo is heard (t) =1s

To find: The distance between the two cliffs.

Step 1 of 2:
Let the distance from the man to 1st cliff be $x$. Distance travelled by sound wave to reflect from 1st cliff and reach the man is $2x$.1st echo is heard after 1s so t=1s.
Use eq (1) to obtain $x$ :
$\begin{gathered} 340 = \dfrac{{2x}}{1} \\\ x = 170m \\\ \end{gathered}$

Step 2 of 2:
Let distance between the 2 cliffs be $l$. The distance travelled by sound wave to reflect from 2nd cliff and reach the man is $(l - x)$. 2nd echo is heard after 2s so t=2s.
Use eq (1) to obtain l:
$\begin{gathered} 340 = \dfrac{{2(l - x)}}{2} \\\ 340 = l - 170 \\\ l = 510m \\\ \end{gathered}$
Correct Answer:
The distance between the two cliffs is: (b) 510m

Additional Information: Reflection of sound waves are many more applications. for example- several highly accurate SONAR navigation systems are based on reflection on sound. There is imaging method used to visualize internal tissue is also based on reflection of sound wave.

Note: In questions where we have to find the distance between 2 obstacles given a series of echoes, try finding the distance between the source and obstacles using the formula for speed.