Question

A submerged scuba driver hear the sound of a boat on directly above her on the surface of the lake. at the same time, a friend on dry land 22.0m from the board also hears the horn. The horn is 1.2 m above the surface of the water. what is the distance ( labeled by "?") from the horn to the driver? both air and water are at 20 degree C.

Answer 1

The following fact will help us to solve the problem: the time that the dry friend measured is equal to the time the diver measured. Say that the diver is h meters below the surface of the water. So, first, express the time for the dry friend:

$$t=\frac{D}{v_a},$$

where $v_a$ is the speed of sound in air.

For the submerged friend, this time will be expressed another way:

$$t=\frac{H}{v_a}+\frac{h}{v_w},$$

where $v_w$ is the speed of sound in water.

Express the depth:

$$h=v_w\bigg(t-\frac{H}{v_a}\bigg).$$

Substitute the time expressed in the first equation:

$$h=\frac{v_w}{v_a}(D-H)=\frac{1482}{343}(22-1.2)=89.9\text{ m}.$$