Question

If a sound signal is emitted from the oscillator of a fathometer, and two seconds elapse before the returning signal is picked up, what depth of water is indicated?

Answer 1

The depth of the ocean as indicated by a fathometer that receives the signal two seconds after it was emitted is 1450 meters, calculated using the known speed of sound in seawater (1450 m/s) and the time lapse for the signal's round trip (2 seconds).

Step-by-step explanation:

When a sound signal from a fathometer is emitted and takes two seconds to return, the depth of the water indicated can be calculated with the knowledge of the speed of sound in sea water. Given the speed of sound in sea water as 1450 m/s, to determine the depth of the ocean, we use the time it takes for the sound to travel to the ocean floor and back to the ship. Since the time includes the journey to the bottom and back to the surface, we need to halve the time to calculate the one-way distance.

Using the formula distance = speed × time, we calculate the depth as follows:

Depth = speed of sound in sea water × (time/2)

Depth = 1450 m/s × (2 s / 2) = 1450 m/s × 1 s = 1450 meters

Therefore, the indicated ocean depth is 1450 meters.