A boy standing some distance from the foot of a tall cliff claps his hands and hears an echo 0.5s later. If…

Analyze the question The boy claps, the sound travels to the cliff, reflects, and returns to him. The echo is heard 0.5 s after the clap. We need the distance from the boy to the cliff.

Concept An echo involves the sound travelling to the cliff and back, so the total distance covered is twice the distance to the cliff:

2d = v × t

Solution

• Speed of sound, v = 340 m/s
• Time for the round trip, t = 0.5 s

Total distance travelled = 340 × 0.5 = 170 m

Since this is the there-and-back distance:

d = 170 ÷ 2 = 85 m

Answer The boy is 85 m from the cliff, which is option D.

Common mistake Option B (170 m) is the trap. It is what you get if you forget that the sound travels to the cliff and back. Always divide by 2 for echo problems.

Tip For echo questions, use d = vt / 2. Whenever you see "echo", think "round trip", so halve the distance.