# Drop a stone in a well - Waves problem

• ghostanime2001

## Homework Statement

You drop a stone from rest into a well that is 7.35 m deep. How long does it take before you
hear the splash?

d=7.35 m
v=343 m/s (because the disturbance is air molecules and the medium is air not water)

## Homework Equations

$d=\dfrac{1}{2}gt_{1}^{2}$

$\lambda=4d$ and $v=\lambda f$ and we know that f is $f=\dfrac{1}{T}$

## The Attempt at a Solution

The time taken for the stone to drop in water:
$t_{1}=\sqrt{\dfrac{2d}{g}}=1.22 s$

The time taken for the reflected wave to make it outside the well
$v=\dfrac{4d}{T}$
So, $T=\dfrac{4d}{v}=\dfrac{4(7.35)}{343}=0.0857 s$

Finally,
$t_{total}=t_{1}+t_{2} = 1.22 s + 0.0857 s = 1.3 s$

However this is wrong! the answer is 1.24 seconds. What am i doing wrong?

My first initial thought is to think of the well as an open-closed tube. When those relevant equations are applied to a open-closed tube I get the wrong answer. Why is thinking of the well as a open-closed tube wrong ?

1. Is it because a little portion of the well at the bottom is filled with water so that the ENTIRE well is not actually 7.35 m ? OR

2. Is it because we have no information about its wavelength regardless if it's a open-closed tube? OR

3. Does the wavelength calculated above does not make sense ? (e.g. How can the wavelength be 29.4 m when the well itself is 7.35 m ? (Assuming the well as a long cylinder)