How to find distance using sound waves

AI Thread Summary
To find the distance using sound waves, it's essential to consider both the time it takes for the stone to fall and the time for the sound to travel back. The displacement of the stone during free fall can be calculated using the equation x = -(1/2)gt^2, yielding -44.1 m for a 3-second fall. However, this calculation does not account for the time taken by sound to travel back after the splash. To accurately determine the total distance, one must add the time for the sound to reach the observer to the fall time. Understanding the finite speed of sound is crucial for solving this problem correctly.
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Homework Statement


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Homework Equations


x = (v_0)^2 - (1/2)gt^2


The Attempt at a Solution


Well, since the stone is dropped from rest, and the down direction is negative, the displacement is:

x = -(1/2)gt^2
x = -(1/2)(9.8 m/s^2)(3.00 s)^2
x = -44.1 m.

But this is incorrect and I don't recall any equation to express distance using sound waves given only the time since there isn't any other information we can assume from the free-fall I think.
 
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Sound has a finite speed; you can look up its value. The time between dropping the stone and hearing the splash is the time the stone takes to fall plus the time the sound takes to reach your ears.
 
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