A hiker determines the length of a lake by listening for the echo of her shout reflected by a cliff at the far end of the lake. She hears the echo 2.9 s after shouting. The speed of sound in air is 343 m/s. Determine the length of the lake.

497.35 m.

Explanation:

Echo: This is the sound heard after the reflection of sound wave on a plane surface.

v = 2x/t ... Equation 1

Where v = speed of sound in air, x = length of the lake, t = time taken to hear the echo.

Making x the subject of the equation,

x = vt/2 ... Equation 2

Given: v = 343 m/s, t = 2.9 s.

Substitute into equation 2

x = 343*2.9/2

x = 497.35 m

Thus the length of the lake = 497.35 m.