Why does sound pressure vary with 1/r?

In summary, the conversation discusses the relationship between sound intensity and distance, as well as how pressure can be calculated using intensity formulas. The speaker also poses a question about the intuitive explanation for why pressure decreases with distance and not distance squared. The analogy of a compressed spring is mentioned as a possible way to understand how a gas behaves.
  • #1
Bitruder
1
0
I didn't follow the template because this is more of a conceptual question that I can't get a clear answer for.

I understand that sound intensity varies with 1/r^2 because the total intensity at a point in the wave is constant and if you have spherical propagation then the area of the surface of that sphere increases with r^2.

I can also calculate pressure from the formulas of intensity that include pressure.

But can anybody give an intuitive explanation for why pressure drops off with distance and not distance squared? Since sound is a traveling pressure wave, I suppose we can pretend that we are riding a pressure peak out in space along a ray.

Thanks
 
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  • #2
The force of a compressed spring is F = kx and the energy in a compressed spring is kx^2/2

Can you convince yourself that a gas acts like a compressible spring?
 

Related to Why does sound pressure vary with 1/r?

1. Why does sound pressure decrease as distance from the source increases?

The decrease in sound pressure with distance is due to the spreading of sound waves in all directions as they travel away from the source. This causes the same amount of energy to be spread over a larger area, resulting in a decrease in sound pressure.

2. How does the inverse square law explain the variation of sound pressure with 1/r?

The inverse square law states that the intensity of a sound wave is inversely proportional to the square of the distance from the source. This means that as distance increases, the sound wave must spread out over a larger area, resulting in a decrease in sound pressure.

3. Can sound pressure vary differently depending on the medium it travels through?

Yes, sound pressure can vary depending on the medium it travels through. For example, sound waves travel more easily through air than through water, resulting in a faster decrease in sound pressure as distance from the source increases in water compared to air.

4. How does the size and shape of the sound source affect the variation of sound pressure with 1/r?

The size and shape of the sound source can affect the variation of sound pressure with 1/r. A larger or more concentrated source will produce a stronger sound wave, causing a slower decrease in sound pressure with distance compared to a smaller or less concentrated source.

5. Is the variation of sound pressure with 1/r a universal phenomenon?

Yes, the variation of sound pressure with 1/r is a universal phenomenon. This is due to the fundamental principles of sound propagation and the inverse square law, which apply to all sound waves regardless of the source or medium they travel through.

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