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Physics Help - Question pertaining to decibels, intensity and average power in watts per meter squared?
I am stuck on a physics homework problem and I have tried so many ways and cannot get it, please tell me where I am going wrong. The question is:
A sound source of (1000Hz) emits uniformly in all directions. An observer 2.34m from the source measures a sound level of 34.5dB. Calculate the average power output of the source? Answer in units of μW.
Sound level is 34.5 dB so my first step was to use the 10log(I/Io) formula to convert it into an intensity (I)value. My result for "I" came out to 1*10^-8.55 W/m2.
I then used the formula of Intensity=Avg Power/Avg Area or
I=P/A
Area is 4*pi*(r)^2.
We know that r=2.34m and we know that I equals 10^-8.55 so when I plug it all in I get Power equal to 1.93928 * 10^-7.
But it's wrong. Can anyone tell me where I went wrong? Thank you.
The reference power level I0 is 10^-12 W/m²
10*log(I/I0) = 34.5
log(I/I0) = 3.45
I/I0 = 10^3.45 = 2818
I = 2818*10^-12 W//m²
This is over an area of 4*π*r² so the power output is 4*π*2.34²*2818*10^-12 = 1.94*10^-7 W = 19.4 µW
That is assuming that 34.5 is sound intensity db, db SIL
However, if it is sound pressure level db, db SPL then the formula is 20*log(SP/SP0) and SP0 = 20 µPa. The SPL at 2.34 m is then p = 1061 µPa. The sound intensity is I = p²/Z, where Z is the characteristic impedance. For air at 25ºC Z = 410 N-s/m³;
I = (1.061*10^-3)²/410 = 2.75*10^-9 W/m²
I*A = 0.19 µW
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