Sound Waves

[MedPR]

This is from TBR Physics chapter 6 passage 1 question 4.

"As we move away from the source of a sound from a distance r to a distance 3r, the intensity of that wave:"

A. decreases by a factor of 3
B. decreases by a factor of 9
C. increases by a factor of 3
D. increases by a factor of 9

Answer is B. Makes sense, since I=P/A where A is 4pir^2

However, in the passage, they cite the equation I=0.5*sqrt(pB)w^2A^2 as an equation that "accurately describes the intensity of sound waves in a liquid." It doesn't tell you what the variables stand for, but A is presumably area, right?

So, according to that equation the answer would be D.

How do you know which equation to use?

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[milski]

I'm not sure what they mean with pB in the first formula but it's very similar to the general formula for intensity of a wave. Note that A here is the area of the source, not the area over which the wave has spread. That should make sense, since increasing the area of the source and keeping everything the same should give you higher intensity - you're moving more air/liquid in that case.

 

[SaintJude]

I=0.5*sqrt(pB)w^2A^2

The equation stated above, I would think is a derived from the intensity equation stated in EK, where A is actually the amplitude of the wave.

 

[milski]

I=0.5*sqrt(pB)w^2A^2

The equation stated above, I would think is a derived from the intensity equation stated in EK, where A is actually the amplitude of the wave.

You're actually right, A^2 is much more likely to be amplitude. Either way, it is not the area over which the wave has spread.

 

[MedPR]

Ah crap that makes sense. Thank you both.