Find the distance from the source of power

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A point source power of 100 W produces a decibel reading of 118 dB, leading to a calculated intensity of 0.6309 W/m². The initial attempt to find the distance resulted in a value of 4.471 meters, which did not match the expected intensity. After reviewing the calculations, it was determined that the error occurred in rearranging the formula for distance. The correct distance, using the formula r = sqrt((P/I)/(4π)), is approximately 3.55 meters. Properly applying the logarithmic conversion and rearranging the equation is crucial for accurate results.
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Homework Statement


A point source power outputs a power of 100 W. If a decibel reading of 118 dB is heard, what is the distance to the observer.


Homework Equations


I = P/(4*pi*r^2)



The Attempt at a Solution


This should be simple, but for some reason my numbers aren't matching up.

First I converted 118 dB to an intensity of .6309 w/m^2 Then I plug it back into the equation and solve for r which comes out to be 4.471 meters.

So then to check it I put the 4.471 m back into the equation to see if it equals my intensity which it doesn't. I'm not sure where I went wrong on this one. Any help would be greatly appreciated.
 
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What are you using to convert dB to intensity? Are you using the log function correctly?
 
Yes, I think so. 118 = 10 log (I/Io) Io = 10^(-12) so,
118 = 10 log (I/10^(-12))
11.8 = log (I/10^(-12))
10^(11.8) = (I/10^(-12)
I = 0.6309 w/m^2
Is that correct?
 
demonslayer42 said:
Yes, I think so. 118 = 10 log (I/Io) Io = 10^(-12) so,
118 = 10 log (I/10^(-12))
11.8 = log (I/10^(-12))
10^(11.8) = (I/10^(-12)
I = 0.6309 w/m^2
Is that correct?

Sorry, that seems fine. Read it wrong the first time.
 
Right, gone through it properly I get r = 3.55m.

Your values are correct, check how you re-arrange your equation.

I = P / (4*pi*r2)

(4*pi*r2) = P / I

r2 = ((P / I) / 4*pi)

r = sqrt( (P/I) / 4*pi )
 
omg, I feel so dumb lol yeah that's where I messed up. Instead of (P/I)/(4*pi) I did (P/I*4*pi). Thank you for your help :)
 
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