Why is velocity of sound inversely proportional to square r

In summary, the velocity of sound is inversely proportional to the square of the distance it travels. This means that as the distance increases, the velocity of sound decreases due to sound energy dissipating through the medium. The medium can also affect the velocity of sound, with denser mediums allowing for faster sound propagation. However, regardless of the medium, the inverse square relationship between velocity of sound and distance always holds true. It cannot be directly proportional to distance, as the relationship must be linear for that to occur.
  • #1
Ajit Kumar
14
0
A. Sound is nothing more than a local disturbance whose propagation is facilitated by the collisions between particles

B. The distances between molecules in solids are very small, i.e., solids are more dense - as compared to liquids and gases. Because they are so close, than can collide very quickly.

So why is velocity of sound inversely proportional to square root of density?
 
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  • #2
You want a reason for a mathematical relationship so the derivation must be mathematical. A search on Google for Speed of sound derivation gives many hits. This link seems to look OK.
 

Related to Why is velocity of sound inversely proportional to square r

1. What is the relationship between velocity of sound and square of the distance?

The velocity of sound is inversely proportional to the square of the distance. This means that as the distance increases, the velocity of sound decreases and vice versa.

2. Why does the velocity of sound decrease as the distance increases?

This is because sound energy dissipates as it travels through a medium. As the distance increases, the sound waves spread out and the energy from the sound is spread over a larger area, resulting in a decrease in velocity.

3. How does the medium affect the relationship between velocity of sound and distance?

The medium through which sound travels can affect the velocity of sound. In general, sound travels faster in denser mediums, such as solids, and slower in less dense mediums, such as gases. However, regardless of the medium, the velocity of sound will always be inversely proportional to the square of the distance.

4. Is the relationship between velocity of sound and distance always true?

Yes, the inverse square relationship between velocity of sound and distance is a fundamental principle of sound propagation. It is applicable in all situations where sound is traveling through a medium.

5. Can the velocity of sound be directly proportional to distance?

No, the velocity of sound cannot be directly proportional to distance. This is because as the distance increases, the velocity of sound decreases at a faster rate due to the inverse square relationship. In order for the velocity of sound to be directly proportional to distance, the relationship would have to be linear, which is not the case for sound propagation.

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