Calculating the Depth of a Well Using the Speed of Sound

[mrross]

A stone is dropped into a well. The sound of the splash is heard 3.96 s later. What is the depth of the well?

 

[Danger]

Welcome to PF, Mrross.
This would appear to be a homework question, in which case it's in the wrong sub-forum. What have you done to try solving the problem? What is the speed of sound at STP? What is the atmospheric pressure and temperature in the well, if other than STP? Both make a difference to the speed of sound, and thus to the calculation.

 

[nlightner]

To calculate the depth of the well, we can use the formula d = (1/2)gt^2, where d is the depth, g is the acceleration due to gravity (9.8 m/s^2), and t is the time it takes for the sound to reach the surface. In this case, t = 3.96 s.

Substituting the values into the formula, we get d = (1/2)(9.8 m/s^2)(3.96 s)^2 = 77.35 m. Therefore, the depth of the well is 77.35 meters.

It is important to note that this calculation assumes that the speed of sound is constant and unaffected by any environmental factors. In reality, the speed of sound can be affected by temperature, humidity, and other factors, which may result in a slight variation in the calculated depth. However, for most practical purposes, this calculation should provide a fairly accurate estimate of the depth of the well.