Sound waves of stone in a well

In summary, the problem involves calculating the depth of a well based on the time it takes for a stone to fall and the sound of the splash to reach the observer. Using the formula d = (0.5)gt^2, the value of t can be determined by solving the equations T = t1 + t2 and d = (0.5)gt1^2 = vt2. Substituting the value of t1 into the formula for d, the depth of the well can be calculated to be 10.2 meters.
  • #1
anil
30
0
Hello I am trying to solve a problem:

You drop a stone into a well and hear the splash 1.47 s later. How deep is the well?

Answer is 10.2 but how do I solve it?

D = (0.5) gt squared

D = VT
 
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  • #2
Let d be the distance the particle falls. Let T be the time take for the ball to drop and the sound to reach the observer. Let t1 be the time taken for the particle to fall, and let t2 be the time taken for the sound to reach the top of the well. Also let v be the speed of sound.

[tex]\[
T = t_1 + t_2
\]
[/tex]

[tex]\[
d = \frac{1}{2}gt_1^2 = vt_2
\]
[/tex]

[tex]\[
\frac{1}{2}gt_1^2 = v(T - t_1 )
\]
[/tex]

[tex]\[
\frac{1}{2}gt_1^2 + vt_1 - vT = 0
\]
[/tex]

[tex]\[
t_1 = \frac{{ - v \pm \sqrt {v^2 + 2gvT} }}{g}
\]
[/tex]

Now take the positive root and use that value of t1 in the formula for d and you get,

[tex]\[
d = \frac{1}{2}g(\frac{{ - v + \sqrt {v^2 + 2gvT} }}{g})^2 = 10.2
\]
[/tex]
 

1. What are "sound waves of stone in a well"?

"Sound waves of stone in a well" refers to the phenomenon of sound waves being produced when an object, typically a stone, is dropped into a deep well or hole. This is due to the echoes created by the sound bouncing off the walls of the well.

2. How do sound waves travel through stone in a well?

Sound waves travel through stone in a well through a process called conduction. This is when vibrations from the sound source are transferred to the particles of the stone, causing them to vibrate and create a sound wave.

3. Why do sound waves travel faster through stone in a well compared to air?

Sound waves travel faster through stone in a well compared to air because the particles in the stone are closer together, allowing for faster conduction of the vibrations. In air, the particles are more spread out, causing the sound waves to travel at a slower pace.

4. Can sound waves of stone in a well be used for communication?

Yes, sound waves of stone in a well can be used for communication. In the past, people used to communicate by dropping stones into wells and listening for the echoes to determine if someone was signaling from a distance. This method is still used in some places today.

5. How do sound waves of stone in a well affect the environment?

The impact of sound waves of stone in a well on the environment is minimal. However, if the intensity of the sound is too high, it can cause disturbance to animals living near the well or damage the surrounding structures. It is important to be mindful of the volume when recreationally dropping stones into a well.

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