Question

Two persons A and B are standing in front of a cliff in the same line 170 m apart as shown in the diagram. Person B fires the gun and hears the echo in 3 s. Then the person A standing in front of the person B fires the gun.

(The speed of sound in air is 340 m/s.)

1. Calculate:
   1. the distance of the person B from the cliff.
   2. the minimum time in which B hears the gunshot fired by A.
2. Fill in the blank.
   The echo is softer (less loud) than the original sound due to the decease in ______ of the wave.
   1. amplitude
   2. frequency

Answer 1

a. Given: Distance between A and B = 170 m

Time taken by person B to hear the echo = 3 s

Speed of sound in air = 340 ms⁻¹

1. Let the distance of person B from the cliff be d.

d = `("Speed of sound in air" xx "Time taken")/2`

= `(340 xx 3)/2`

= 170 × 3

= 510 m

Hence, the distance of person B from the cliff is 510 m.

2. Person B first hears the direct sound of the gunshot and only afterwards hears its echo from the cliff. Therefore, the minimum time in which B hears the gunshot is the time taken by the sound to travel directly from person A to person B, who is 170 m away.

Then, the minimum time (t) is given by,

t = `"Distance between A and B"/"Speed of sound in air"`

= `170/340`

= 1/2`

= 0.5 s

Hence, the minimum time in which B hears the gunshot fired by A is 0.5 seconds.

b. The echo is softer (less loud) than the original sound due to the decease in amplitude of the wave.

Explanation:

The loudness of a sound wave is determined by its amplitude. An echo is the reflection of sound. During reflection, some of the sound energy is absorbed by the reflecting surface, and the energy also spreads out over a larger area. This results in the reflected wave having a smaller amplitude than the original wave. Therefore, the echo is softer due to the decrease in amplitude.