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Decibel question

  • Thread starter vande060
  • Start date
  • #1
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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:

Answers and Replies

  • #2
1,860
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You don't actually need the intensities. Do you know how to add decibel levels?
 
  • #3
186
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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
 
  • #4
1,860
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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.
 
  • #5
rl.bhat
Homework Helper
4,433
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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.
 

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