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Old Oct 30th 2012, 06:46 AM   #1
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Why does power of a sound wave remain constant with distance, but not its amplitude?

Suppose a sound wave is emitted uniformly in all directions by a speaker.

We know that Intensity of sound = Power/Area.

1) As distance increases, the power of the sound wave has to remain constant. Intensity thus decreases right?

2) if power of the sound wave remains constant, this also means that the amplitude of sound wave remains constant since power is proportional to amplitude squared.

However i came across this question:
At a distance of 1.1m from the speaker, the amplitude of sound is 1.2x10^ -8m. What is the amplitude of sound at a distance of 1.7m from the speaker?

Why does the amplitude of sound change based on my explanation above? which part of my explanation is flawed? I have thought about this for many hours its really troubling me! please help!
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Old Oct 30th 2012, 07:36 AM   #2
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Originally Posted by aznking1 View Post
We know that Intensity of sound = Power/Area.

1) As distance increases, the power of the sound wave has to remain constant. Intensity thus decreases right?
Right.

Originally Posted by aznking1 View Post
2) if power of the sound wave remains constant, this also means that the amplitude of sound wave remains constant since power is proportional to amplitude squared.
Actually power is proportional to particle displacement squared times the area. So as A increases (as you get further from the source) the magnitude of particle displacement decreases. I think perhaps the confusion here is that sound waves are not sinusoidal waves, like ripples on a pond, but are pressure waves. Air particles are displaced forward and back in line with the source, and the magnitiude of that displacement varies with distance from the source.

Originally Posted by aznking1 View Post
However i came across this question:
At a distance of 1.1m from the speaker, the amplitude of sound is 1.2x10^ -8m. What is the amplitude of sound at a distance of 1.7m from the speaker?
As noted the displacement of air particles at 1.7m from the source will be less than the displacement of air particles at 1.1m, by a factor of (1.1/1.7)^2

Last edited by ChipB; Oct 30th 2012 at 08:53 AM.
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Old Oct 31st 2012, 08:57 PM   #3
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Thanks Chip.The fall in intensity is mainly due to the increase in the surface area and this generally follows the inverse square law when we consider a spherical surface and a point source. However if we consider a parallel beam, the intensity does not fall at all ideally. Lasers are a good example . Hence at large distances where we can consider rays to be parallel, the intensity does not vary much with a change in distance. I know this is not directly related to the question, but just thought i would put in a word.
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