Re: [Phys-l] decibel dilemma

[Leigh Palmer <palmer@sfu.ca>]

> > 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?

Ignoring absurdity in the precision, this problem is easy, but it  
requires clear reasoning. Since the SPL with 100 people in the room  
is 20 dB greater than it is with the room empty, we know that the  
sound intensity is 100 times as great with the room full as it was  
with the room vacant. Thus 100 people contribute 99 times the  
intensity of the room's background, I0. With 45 people present one  
would expect those people to contribute 45/100 of 99 times the  
background intensity. Adding the background intensity to this gives a  
total intensity

I = (45x99/100 + 1) x I0 = (4555/100) x I0

SPL(I) = SPL(I0) + 10 log 45.55 dB = 40 dB + 16.585 dB = 56.6 dB

The precision required is just +/- 0.1 dB, as that is the approximate  
contribution of one person more or less of 45 in a negligible  
background. Theoretically!

This is not a practical problem, of course. I am presently involved  
in a practical problem. I have rock concerts being staged for 8,000  
people with the outdoor stage and speakers less than 100 meters from  
my back porch! See http://www.sfu.ca/~palmer/NewsLeaderstory1.pdf and  
http://www.sfu.ca/~palmer/NewsLeaderstory2.pdf to get some idea of my  
problem.

Leigh