Reducing Decibel Levels: How Far Should You Move from a Loudspeaker?

[duhduhduh]

Homework Statement

You are at a rock concert, standing 12.1 m from one of the loudspeakers. Based on the pain in your ears, you estimate the decibel level to be about 112 dB at this location. You are worried that this intensity level may be harmful to your ears and result in a degradation of your hearing in years to come, so you want to move farther away from the loudspeaker to reduce the sound to a "dull roar" at a decibel level of 89 dB. From your present location, how much farther away from the loudspeaker would you have to move to reach this reduced decibel level?

Homework Equations

B = 10log(I/I(0))

P = I(4pi*r^2)

The Attempt at a Solution

I have a solution, but want to make sure I'm not going down the wrong path.

First, I calculated the Intensity for 112dB and 89 dB and got 0.158 and 7.94e-4, respectively. Then, I calculated the Power using the given distance and first intensity and got 290.7W. Then, I used that Power and the 2nd intensity to solve for r.

Does this look like the right method? Thank you.

 

[cepheid]

I tried to work backwards to figure out what you're using for your value of I(0) by using the value of I that you got for each of your B's, and the first equation you posted. However, I got a different answer for I(0) in each case. This tells me that your I values can't be right. You should show your work.

Also, although your method sounds like it should work, it isn't necessary to compute the total power to solve the problem. The difference in decibel levels tells you the ratio of the corresponding intensities. To see this, just write down an expresession for B1 - B2, and simplify it. Once you have I1/I2, you can just use the inverse-square law to figure out how much farther away you need to be for the intensity level to drop off by that factor.