Question

An oceanic depth-sounding vessel surveys the ocean bottom with ultrasonic waves that travel 1530 m/s in seawater. How deep is the water directly below the vessel if the time delay of the echo to the ocean floor and back is 6 s?

Answer 1

Answer:

The water below the vessel is 4590 m deep.

Explanation:

Calling d the distance between the vessel and the ocean floor, v the ultrasonic wave velocity, and t the time it takes for the ultrasonic wave to reach the bottom from the vessel, we get:

[1] $d=t*v$

v is already provided (1530 m/s), so we need to find t.

We know that the delay of the echo is 6 seconds. That is the time it takes the wave to travel to the ocean floor and come back to the vessel, which is twice the time it takes to go from vessel to the floor, so:

$2*t=6s\\t=\frac{6}{2}s$

$t=3s$

Replacing and solving on [1], we get

$d=3s*1530\frac{m}{s}\\d=4590m$

Which is the distance from the vessel to the ocean floor.