How to calculate depth of sea whan a ship receives sound produced by its fathometer after 3.5 second

Answer: the depth is around d = 1.75s*1450m/s = 2537.5 m

Explanation: A fathometer creates a sound pulse and receives the echo of that sound, and in this way, the instrument can obtain a difference of time (the time between the wave is released and received)

Now, knowing that the velocity of the sound in water is around 1450 m/s

now, the lecture is 3.5 seconds, but in this time the wave goes to the bottom and bounces, so the time needed to reach the bottom is half that:

3.5s/2 = 1.75s

then the distance traveled by the wave in that lapse of time is:

d = 1.75s*1450m/s = 2537.5 m

this is a simplification of the math that the device does.