# Drop a stone in a well - Waves problem

• ghostanime2001
In summary, the time taken for the stone to drop in water is 1.3 seconds and the time taken for the reflected wave to make it outside the well is 0.0857 seconds.
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)

You have the time for the stone to fall and hit the water correct = 1.22s
This makes a noise and the sound has to travel to the top of the well, 7.35m and the speed of sound = 343m/s. Calculate the time taken for sound to travel this distance.
How much time has passed since you dropped the stone??

But what about the wavelength of the sound wave? I can't change the wavelenght.

## What is the "Drop a stone in a well - Waves problem"?

The "Drop a stone in a well - Waves problem" is a physics problem that involves calculating the time it takes for waves to travel through a well after a stone is dropped into it.

## Why is this problem important?

This problem helps us understand the behavior of waves and how they travel through different mediums. It also has real-world applications in fields like seismology and acoustics.

## What are the key concepts involved in solving this problem?

To solve this problem, one must understand the concept of wave speed, which is affected by factors such as the density and elasticity of the medium. Additionally, knowledge of basic kinematics, such as distance, time, and acceleration, is necessary.

## What formula can be used to solve this problem?

The formula used to solve this problem is t = √(2d/g), where t is the time for the wave to travel through the well, d is the depth of the well, and g is the acceleration due to gravity.

## Are there any assumptions made when solving this problem?

Yes, this problem assumes that the well is straight and uniform in depth, and that the stone is dropped from the top of the well. It also assumes that the waves travel at a constant speed and that there are no external forces acting on the stone or the waves.

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