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

Answer:

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

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:

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

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:

$\begin{aligned} \frac{4.15\times 10^{3}\; {\rm m}}{2} \approx 2.1\times 10^{3}\; {\rm m} = 2.1\; {\rm km}\end{aligned}$.