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[Phys-l] decibel dilemma



While searching for some good review problems regarding sound, I came
across this in Tipler's physics text:

It says the "background" sound level in a room is 40 dB. With 100 people
talking, it rises to 60 dB. What's the sound level when 55 people leave?

deltaB = 10log(100/45) = 3.46 ---> sound level is 60 - 3.46 = 56.54 dB

This problem seemed trivial to me, so I took it farther.

So what if 90 people leave? deltaB = 10 log(100/10) = 10 ---> now 50 dB

And if only 1 person remains (99 leave): deltaB = 10log(100/1) = 20 --->
back to 40 dB (background)

But 40 dB was the background for an EMPTY room! If ALL people leave, the
sound level should be 40 dB.

Something doesn't seem right.

After struggling with this for some time, I found the solution manual and
it read:

"The room background noise is 20 dB less than or 1/100 of the noise of 100
people, so it can be neglected. Total intensity after 55 people leave
is... 3.46 dB less..."

Does this make sense? Can't we just make the 40 dB background our
"threshold," so it would, in effect, cancel out? The 40 dB is always there
no matter how many people are present. How does one take this into
account? What background noise level would be "significant"?