A helicopter is hovering at an altitude of 200m above the surface of the lake. A speaker on the helicopter is sending out sound waves which are reflected from both the surface of the water and bottom of the lake. If the differences in arrival times of the two echoes is measured to be 0.24s, what is the depth of the lake? (The atmospheric temperature is 20°C)

Question

Bailey Terry

Physics

7 November, 00:06

A helicopter is hovering at an altitude of 200m above the surface of the lake. A speaker on the helicopter is sending out sound waves which are reflected from both the surface of the water and bottom of the lake. If the differences in arrival times of the two echoes is measured to be 0.24s, what is the depth of the lake? (The atmospheric temperature is 20°C)

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Nicholson · Answer 1

The first echo travels from the helicopter to the surface and back. The second echo travels from the helicopter to the surface to the bottom of the lake and then back.

We know the difference in time is 0.24 s, so the time it takes the sound wave to travel through only the water is 0.24 s. Since the sound wave covers the distance twice (first from the surface to the bottom, then the bottom to the surface), we only want half the time, 0.12 s.

The speed of sound in water at 20°C is 1481 m/s. Therefore:

d = 1481 m/s * 0.12 s

d = 178 m

The depth of the lake is 178 meters (round as needed).