Problem 35.

A rock is dropped from rest into a well.

(a) The sound of the splash is heard 4 s after the rock is released from rest.

How far below to top of the well is the surface of the water? (the speed of sound in air at ambient temperature is 336m/s).

(b) If the travel time for the sound is neglected, what % error is introduced when the depth of the well is calculated?

Solution:

(a) If h is the depth of the well then to find the time of the rock's fall we need to use the following equation:

From this equation we can find time:

After the rock hits the water the sound of splash will propagate the distance h with speed 336 m/s. After time the sound reaches the ground. Then total time is

This time is equal to 4 s. Then

From this equation we can find h:

(b) If we neglect the sound velocity then t=4 s and we can find the height from the equation:

If we compare this result with the result from part (a) then we can find an error: