I am stuck on a physics homework problem and Ihave tried so many ways and cannot

Question

I am stuck on a physics homework problem and Ihave tried so many ways and cannot get it, please tell me where Iam going wrong. The question is:
A sound source of (1000Hz) emitsuniformly in all directions. An observer 2.34m from the sourcemeasures a sound level of 34.5dB. Calculate the average poweroutput of the source? Answer in unitsof W.
Sound level is 34.5 dB so my first stepwas 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 Iplug it all in I get Power equal to 1.93928 * 10^-7.

But it's wrong. Can anyone tell me where I went wrong? Thankyou.
A sound source of (1000Hz) emitsuniformly in all directions. An observer 2.34m from the sourcemeasures a sound level of 34.5dB. Calculate the average poweroutput of the source? Answer in unitsof W.
Sound level is 34.5 dB so my first stepwas 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 Iplug it all in I get Power equal to 1.93928 * 10^-7.

But it's wrong. Can anyone tell me where I went wrong? Thankyou.

Explanation / Answer

I think you may be mixing up dimensions. The 4r^2 is thesurface area of a sphere, you converted the 34.5 dB into W/m^2, and the sound propagates along a straightline. Start thinking from here and see whether you need somemodification. Also, did you consider to apply the inverse square lawI_1/I_2=r_2^2/r_1^2 ?

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