In the above diagram Lata stands between two cliffs and claps her hands. Determine the time taken by her to hear the first echo. Speed of sound in air = 320 m s⁻¹.
Topic: Echo time
Answer
From the diagram, the nearer cliff is 160 m away.
Given: speed of sound v = 320 m s⁻¹
The first echo to reach Lata is the one reflected from the NEARER cliff, because that sound has the shortest path.
For an echo, 2d = v t: t = 2d ÷ v = (2 × 160) ÷ 320 = 320 ÷ 320 = 1 s
Time taken to hear the first echo = 1 s
With two cliffs, two echoes come back — and the FIRST one is from the nearer cliff, since sound travels at the same speed both ways and the shorter path takes less time. Using the far cliff's distance answers a question that was not asked.
Keep the factor of 2: the sound travels to the cliff and back, so 320 m in all, not 160 m.
For an echo to be heard as a separate sound at all, it must arrive at least 0.1 s after the original — which needs a reflector at least about 17 m away. At 160 m there is no difficulty.