Question

1. A sonar pulse is sent to the ocean bottom which is 25◦ Celsius. It takes 4.2 seconds for the wave echo to return to the ship. How deep is the ocean bottom?
Medium m/s
Air 0○C 331
Air 20○C 343
Helium 0○C 972
Water 25○C 1,493
Seawater 25○C 1,533
Copper 25○C 3,560
Iron 25○C 5,130

Answer 1

The sonar pulse takes t=4.2 s to reach the ocean bottom and then to travel back tothe ship. If we call d the depth of the ocean bottom, this means that the sonar pulse covered a distance equal to 2d in a time of 4.2 s.

The speed of the sonar pulse is the speed of sound in water at 25C, so looking at the table is v=1493 m/s. Using the relationship $v= \frac{S}{t}$ between space and time for a uniform motion, and keeping in mind that the total distance covered by the pulse is 2d, we can write:
$v= \frac{2d}{t}$
which becomes
$d= \frac{vt}{2}= \frac{(1493 m/s)(4.2 s)}{2}=3135 m$
so, the ocean bottom is 3135 m deep.