Question

A man is standing between two cliffs. If he claps his hands once, a series of echoes at the interval of one second are heard. If the speed of sound is \[340\text{ m}{{\text{s}}^{-1}}\], the distance between the cliffs is
A. \[170\text{ m}\]
B. \[680\text{ m}\]
C. \[340\text{ m}\]
D. \[510\text{ m}\]

Answer 1

Hint: As the man is standing between two cliffs the sound is reflected from both the cliffs. The sound travels twice the distance between the man and first cliff before coming back to the man. Similarly, the sound travels twice the distance between the man and second cliff before coming back to the man. The interval between the echoes produced by the two cliffs is same.

Formula used:
If d is the distance between the source and the obstacle, and the v is the speed of the sound, then total distance travelled by the sound to reach the obstacle and return back to the source is \[2d\].If the time taken by the sound to travel \[2d\] distance is t, then the distance-speed-time relation is given by:
\[2d=vt\]

Complete step by step answer:
Speed of sound, \[v=340\text{ m}{{\text{s}}^{-1}}\]
The time interval in which the series of echoes are heard is the time taken by the sound to travel between the each cliff and the man, so, \[t=1\text{ s}\]
Let the distance between the two cliffs be d, and the distance between the first cliff and the man be \[{{d}_{1}}\]
To find the distance \[{{d}_{1}}\], substitute the values of v and t in the distance formula:
$ 2{{d}_{1}}=(340\text{ m}{{\text{s}}^{-1}})(1\text{ s)} $
$ \text{2}{{d}_{1}}=340\text{ m} $
$ {{d}_{1}}=170\text{ m} $

Therefore, the distance between the first cliff and the man is \[170\text{ m}\].
Now, the distance between the second cliff and the man will be \[(d-{{d}_{1}})\]
To find the distance \[(d-{{d}_{1}})\], substitute the values of v and t in the distance formula:

$ 2(d-{{d}_{1}})=(340\text{ m}{{\text{s}}^{-1}})(1\text{ s)} $
 $ \text{2(}d-{{d}_{1}})=340\text{ m} $
$ \text{ }d-{{d}_{1}}=170\text{ m} $
Substituting the value \[{{d}_{1}}=170\text{ m}\] in the above equation:
$ d-170\text{ m}=170\text{ m} $
 $ d=340\text{ m} $
So, the distance between the two cliffs is \[340\text{ m}\].
Hence, option C is the correct answer.

Note:
The question can also be solved assuming that the man is equidistant from each cliff, as the echoes from each cliff is heard after the same interval of time.