Question

a sailor strikes the side of his ship just below the surface of the sea. he hears the echo of the wave reflected from the ocean floor directly below 2.8 s later. how deep is the ocean at this point?

Answer 1

Approximately
`2.1 * 10^(3)\; {\rm m}` (
`2.1\; {\rm km}`) assuming that the speed of sound in the water is
`1482\; {\rm m\cdot s^(-1)}` (
`20\; ^(\circ){\rm C}`.)

Step-by-step explanation:

Multiply speed
`v` by time
`t` to find the distance
`s` travelled.

The sound wave in this question has travelled a distance of at least:

`\begin{aligned}s &= v\, t\\ &= (1482\; {\rm m\cdot s^(-1)})\, (2.8\; {\rm s}})\\ &\approx 4.15* 10^(3)\; {\rm m}\end{aligned}`.

Note that this distance is for a round trip- from the ship to the ocean floor and back. The depth of the ocean at this location will be one-half the distance of a round trip:

`\begin{aligned} \frac{4.15* 10^(3)\; {\rm m}}{2} \approx 2.1* 10^(3)\; {\rm m} = 2.1\; {\rm km}\end{aligned}`.