A man stands in front f a high wall and produces a sound. If he receives the echo of the sound four seconds…

Analyze the question A sound travels from the man to the wall and back again as an echo. The total time for this round trip is 4 s. We need the distance from the man to the wall.

Concept For an echo, the sound covers the distance twice (to the wall and back):

2d = v × t

so d = (v × t) / 2

Solution

• Speed of sound, v = 330 m/s
• Total time, t = 4 s

Total distance travelled by the sound = 330 × 4 = 1320 m

This is the round trip, so the distance to the wall is:

d = 1320 / 2 = 660 m

Answer The man is 660 m from the wall.

Tip Whenever you see "echo," always divide by 2. Option A (1320 m) is the trap answer, because it forgets that the sound travels to the wall and back. Also remember that if the question had said the echo came after 4 s from the wall, the one-way time would be 2 s. In echo problems, the time given is usually the full round trip.