Question

A man standing in front of a large wall claps at a regular frequency of $10Hz$. He finds echoes coincide with his clapping. (The speed of sound in air is $330m{s^{ - 1}}$).

1. Time taken between successive clapping is $0.1s$
2. The distance between the man and the wall, after the clapping, if he hears one more echo is $33m$
3. The distance between the man and the wall, after he stops clapping, if he hears four more claps is $66m$.

A) Only (i) and (ii) are correct
B) Only (ii) and (iii) are correct
C) Only (i) and (iii) are correct
D) All (i), (ii) and (iii) are correct.

Answer 1

An echo is defined as the sound caused by the reflection of the sound waves. These sound waves are listened to by the listener. Also frequency is defined as the calculation of the number of times an event or activity that repeats itself in a unit time.

Complete step by step answer:
Step I:
Hard objects such as wall caves reflect the sound waves back in the same direction. That is why an echo is heard when the man claps in front of a large wall.
-Given that the frequency of the sound waves is $10Hz$
The time period is the reciprocal of frequency. So time period between two successive claps is given by
$t = \dfrac{1}{f}$
$t = \dfrac{1}{{10}}$
$t = 0.1\sec$
Step II:
-Also it is given that he hears one more echo after he stops clapping. The time period can be written as
$t = \dfrac{1}{{10}}\sec$
Given the speed of sound in air is $330m{s^{ - 1}}$
Distance between the man and the wall is given by
$Dis\tan ce = Speed \times Time$
Substitute the given values in the formula and find the value of distance,
$Dis\tan ce = 330 \times \dfrac{1}{{10}}$
$Dis\tan ce = 33m$
The distance between the man and the wall, after he stops clapping is $= 33m$
Therefore, the given statement is true.
Step III:
-Now if he hears four echoes after he stops clapping, then time period is given by
$t = 4 \times \dfrac{1}{{10}}$
$t = 0.4\sec$
Again the distance will be
$Dis\tan ce = 330 \times 0.4$
$Dis\tan ce = 132m$
The given statement is not true. The distance between the man and the wall if he hears four echoes is $132m$ and not $66m$
Step IV:
Therefore only statements (i) and (ii) are correct.

Hence option A is the right answer.

Note: It is to be noted that the terms echo and reverberation are different. Echo is the reflection of sound waves, but reverberation is the reflection of sound waves created by superimposing the echoes. The echoes can be distinguished and are clear, but the reverberations are not distinguished easily.