May 30, 2015

Homework Help: Physics

Posted by Reed on Wednesday, February 10, 2010 at 1:20am.

Point A is 5 m from a loudspeaker. At point B, the loudspeaker sounds half as loud as at point A. How far is point B from the loudspeaker?

I get 50 m, but the answer is supposed to be 15.8 m. I need to know what I'm doing wrong.

By my (apparently flawed) reasoning:
Point A is 10 dB louder than Point B because +10 db = ~2x louder
+10 dB = *10 Intensity (I), because the dB scale is log 10
Therefore, I(A) = 10*I(B) and I(A)/I(B) = 10
Using the formula I(A)/I(B) = r(B)/r(A), I find that
10 = r(B)/r(A)
Plug in 5 m for the value of r(A), and solve for r(B), which comes out to be 50 m.

So what am I screwing up?

Thanks for your help.

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