At a recent rock concert, a dB meter registered 128 dB when placed 2.30 m in fro

Question

At a recent rock concert, a dB meter registered 128 dB when placed 2.30 m in front of a loudspeaker on the stage.
(a) What was the power output of the speaker, assuming a hemispherical radiation of the sound and neglecting absorption in the air?
W
(b) How far away would the intensity level be a somewhat reasonable 85 dB?
m


I was able to find the Intensity given B=10log(I/Io)
I=6.31W/m^2
I stupidly assumed that I just needed to use the equation P=IA, but it doesn't seem to be working. I seem to have my area wrong, I am using 4(pi)r^2. This is the one that the book is using.

For b) 324.9m is correct, which is how I found that my intensity must be correct.

Any help past this point would be greatly appreciated.

Explanation / Answer

Part A)

You seem to be doing everyhting correctly.

First find the intensity at the location of 2.3 m using B = 10 log (I/Io)

You will get, as you have found, an intensity of 6.31 W/m2

Then, yes, since I = P/A, P = IA

P = (6.31)(4)(2.3)2

P = 419 Watts

Part B)

B = 10 log (I/Io)

85 = 10log(I/1 X 10-12)

I = 3.16 X 10-4 W/m2

A = P/I

4r2 = (419)/(3.16 X 10-4)

r = 183.2 m

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