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)
Show Hint
For echo problems, remember the distance traveled by the sound is twice the distance to the reflector (2d).
(a) 1. Distance of person B from the cliff:
Let the distance of person B from the cliff be \(d\). When B fires a gun, the sound travels to the cliff and reflects back to B. The total distance traveled by the sound is \(d + d = 2d\).
- Time taken for the echo, \(t = 3\) s.
- Speed of sound, \(v = 340\) m/s.
Using the formula, Distance = Speed \(\times\) Time:
\[ 2d = v \times t \]
\[ 2d = 340 \text{ m/s} \times 3 \text{ s} = 1020 \text{ m} \]
\[ d = \frac{1020}{2} = 510 \text{ m} \]
So, person B is 510 m from the cliff. (a) 2. Minimum time for B to hear gunshot from A:
The minimum time is the time taken for the sound to travel directly from person A to person B.
- Distance between A and B = 170 m.
- Speed of sound = 340 m/s.
\[ \text{Time} = \frac{\text{Distance}}{\text{Speed}} = \frac{170 \text{ m}}{340 \text{ m/s}} = 0.5 \text{ s} \]
(b) Fill in the blank:
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.
