Sound: Edge Cases and Subtle Traps (1)

Question

A man stands $170$ m from a tall cliff and claps his hands. He hears the echo $1.0$ s later. Then he walks $34$ m closer and claps again — when does he hear this echo? Take the speed of sound in air as $340$ m/s. The trap is that students confuse “distance to cliff” with “distance travelled by sound.”

Solution — Step by Step

Why This Works

Echo time depends on the round-trip path of sound — to the obstacle and back. The man’s distance halves only the one-way trip. We always multiply by 2.

A second concept hidden in this problem: for an echo to be heard distinctly, the round-trip time must be at least $\sim 0.1$ s (the persistence of hearing). Both clap echoes here are well above that threshold, so both are audible.

Alternative Method

Direct ratio: if distance to cliff scales by $136/170 = 0.8$, the echo time scales by the same factor. So new $t = 0.8 \times 1.0 = 0.8$ s. This shortcut works when speed of sound is unchanged.

Common Mistake