Sound Waves - Dropping a coin down a well

In summary, the question is asking about the distance of the water surface in a well after dropping a coin and hearing the sound of it splashing after 3.2 seconds. The answer is 46.0 m, but there is also a second solution of 25,120 m which is not applicable in this scenario. This second solution would result in a negative distance and would mean that the coin arrived at the water surface before the sound.
  • #1
Physicsman69
5
0
The question is:

You drop a coin down a well. After 3.2 seconds you hear the sound of the coin splashing into the water surface below. How far below lies the water surface in the well?

After doing all the work the answer comes out to d = 46.0 m. However, when solving for "d" I had to solve a quadratic so I got two answers (two roots). The first was 46.0, but the other was 25,120 m. Obviously using common sense you can pick out that the correct answer was 46, but just out of curiosity what is the significance of the second answer?
 
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  • #2
The other solution should be negative.

If you let a coin drop from above (using the second, negative solution), the coin arrives 3.2 seconds before a sound emitted at the same time and place (neglecting air resistance). Not what you want here, but still 3.2 seconds difference.
 

1. How far can a sound wave travel down a well?

The distance a sound wave can travel down a well depends on various factors such as the depth and width of the well, the material of the well walls, and the quality of the sound source. Generally, sound waves can travel up to a few hundred meters down a well before dissipating.

2. Why does a coin sound different when dropped down a well?

When a coin is dropped down a well, the sound waves produced travel down the well and bounce off the walls multiple times before reaching the listener's ear. This creates a reverberation effect, making the sound seem louder and more echoey compared to dropping the coin in an open space.

3. Can sound waves travel through water in a well?

Yes, sound waves can travel through water in a well. Water is a denser medium compared to air, which means sound waves travel faster and more efficiently through it. This is why sounds can be heard more clearly when dropped down a well filled with water.

4. How does the depth of a well affect the sound of a dropped coin?

The depth of a well can affect the sound of a dropped coin in two ways. Firstly, the deeper the well, the longer it takes for the sound waves to travel back up to the listener's ear, resulting in a longer echo. Secondly, the deeper the well, the more sound waves will be absorbed by the well walls, leading to a softer and less distinct sound.

5. Can sound waves travel upwards in a well?

Yes, sound waves can travel upwards in a well. However, as the sound waves travel upwards, they lose energy and become weaker. This is because the sound waves are constantly being absorbed by the well walls and the surrounding air. Therefore, the further the sound waves travel upwards, the softer and less distinct the sound will be.

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