Decibel Drop of 1 Singer in Choir

[vande060]

Homework Statement

Imagine a choir of 10 singers, all of different frequencies, but each singing at the same decibel level β if heard
separately. Suddenly one gets bashful and stops singing. By how many decibels does the sound of the full choir drop?

Homework Equations

I = I1 +I2 + I3 ...β = 10log10(I/Io)

Io = 1.0 * 10^-2

The Attempt at a Solution

can i just call the combined decibel level of 10 singers x

x = 10log10(10I/(10^-2)

then call the combined decibel level of 9 singers y

y = 10log10(9I/10^-2)

then subtract them, i have a feeling there is not enough information to solve this :(

 

[Mindscrape]

You don't actually need the intensities. Do you know how to add decibel levels?

 

[vande060]

You don't actually need the intensities. Do you know how to add decibel levels?

no, do i divide them based on a logarithmic rule ??

logx-logy = log(x/y)

or am i way off here

beta change = 10log10(10/9) = .457 according to my calculator

 

[Mindscrape]

Well, let's forget about the general case of adding decibels, and just focus on how the sound intensities will contribute to the total decibel level

dBtot=10log(I1/I0 + I2/I0 + ... + I10/I0)

In this case, all the sound sources are the same. Simplify what I started, use a log rule, and I think you'll be able figure out the rest.

 

[rl.bhat]

no, do i divide them based on a logarithmic rule ??

logx-logy = log(x/y)

or am i way off here

beta change = 10log10(10/9) = .457 according to my calculator

Let 10ⁿ be the intensity of each singer.Then

β= 10*log[10ⁿ/10^-12] = 10(12 + n)

Similarly write down the equation for 10 β and 9 β and find the difference.