How Far is a Loudspeaker from Two Observers Based on Sound Levels?

[Lipd]

I've been stuck on this one problem for a bit, any help is really appreciated.

"A loudspeaker is placed between two observers who are 110m apart, along the line connecting them. If one observer records a sound level of 60.0 dB and the other records a sound level of 80.0dB, how far is the speaker from each observer?"

I've been having a tough time grasping sound waves in general actually. These problems usually take me a lot longer than the previous chapter on wave motion. So I was also wondering if anyone knew some good help sites with sound waves, I seem to only find ones with formula's on them.

 

[Loren Booda]

My guess is that the decibel scale was created for just such a problem. That is,

80~P/x^3.2 and 60~P/(110-x)^3.2

where P is the power at the speaker, x is the distance for the 80dB observer, (110-x) for the 60dB observer, and the approximation that the sound intensity drops off as the 3.2 power of distance is assumed. (Remember, 2^3.2=10) Solve the two equations by eliminating P.

 

[Lipd]

thanks a lot!

 

[Loren Booda]

I hope I'm right, Lipd.