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

Hint:

For echo problems, remember the distance traveled by the sound is twice the distance to the reflector (2d).

Answer 1

Step 1: Understanding the Concept:
An echo is heard when sound travels to a reflecting surface and back to the listener.
Step 2: Key Formula or Approach:
\(v = \frac{2d}{t} \implies d = \frac{v \times t}{2}\)
Step 3: Detailed Explanation:
Speed of sound, \(v = 340 \text{ m/s}\)
Time for echo, \(t = 3 \text{ s}\)
Let \(d\) be the distance of B from the cliff.
\[d = \frac{340 \times 3}{2}\]
\[d = 170 \times 3 = 510 \text{ m}\]
Step 4: Final Answer:
The distance of person B from the cliff is 510 m.
(b)
Step 1: Understanding the Concept:
The time taken for sound to travel directly from source to listener is simply Distance / Speed.
Step 2: Detailed Explanation: Distance between A and B = 170 m.
Speed of sound = 340 m/s.
Time = \(\frac{\text{Distance}}{\text{Speed}}\)
Time = \(\frac{170}{340} = 0.5 \text{ s}\).
Step 3: Final Answer:
Person B hears the gunshot from A after 0.5 s.
(c)
Step 1: Understanding the Concept:
Loudness is a characteristic of sound that depends on the amplitude of the vibration.
Step 2: Detailed Explanation:
When a sound wave travels through air and reflects off a cliff, some of its energy is absorbed by the air and the surface of the cliff.
A decrease in energy results in a decrease in the amplitude of the wave.
Since loudness \(\propto \text{Amplitude}^{2}\), the sound becomes softer. The frequency (pitch) remains the same as it depends on the source.
Step 3: Final Answer:
The echo is softer due to the decrease in the amplitude of the wave.