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. (Speed of sound in air is 340 m s-1)
Calculate the minimum time in which B hears the gunshot fired by A.
Topic: Speed of sound and travel time
Answer
Given: A and B are 170 m apart, speed of sound v = 340 m s⁻¹.
When A fires, the sound reaches B by two routes: straight across to B, or on to the cliff and back. The MINIMUM time is for the shorter, direct path.
t = distance ÷ speed = 170 ÷ 340 = 0.5 s
Minimum time in which B hears the gunshot = 0.5 s
The word MINIMUM is the instruction: of the possible paths the sound can take, pick the shortest. That is the direct one from A to B, 170 m.
There is no factor of 2 here. The sound goes one way only — A to B — so this is not an echo. Applying the 2d = vt habit automatically gives 1 s, and that is the trap the question is built around. Ask yourself each time whether the sound comes BACK to where it started; only then does the 2 belong.
B would also hear a second, later sound — the reflection off the cliff — but that is not the minimum.