# Decibel question

## 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 :(

Last edited:

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

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

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
Homework Helper
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.