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Combining two different sound intensities

by ebmather
Tags: sound intensity
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ebmather
#1
Feb19-13, 11:34 PM
P: 3
Consider a fixed sound of intensity level SIL1 = 70 dB and another (of different frequency) whose intensity level takes on the series of values SIL2 = 50, 60, 70, 80 and 90 dB.
(a) To the nearest dB, what is the level of the combined sound in each case?
(b) Make a general statement about the combined level for any two sounds when one is much stronger than the other.

Relevant equations
SIL=10log(I/Io)

I tried to do SIL=10log(70+50) for the first one, but I dont think thats right. Do you divide them instead?
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Simon Bridge
#2
Feb20-13, 12:23 AM
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##70\text{dB} = 10\log(I_1/I_0)##
##50\text{dB} = 10\log(I_2/I_0)##
... and so on. Do you see where you are going wrong?
ebmather
#3
Feb20-13, 12:28 AM
P: 3
No, your equations don't seem to make sense to me....?

Simon Bridge
#4
Feb20-13, 12:47 AM
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Combining two different sound intensities

Definition of "decibels":

SIL=10log(I/Io) is what you wrote down. Make sure you understand this relation.

SIL is the decibel intensity level.
I is the actual sound intensity.
I0 is some reference intensity.
When you wrote SIL=10log(70+50) you put the decibel levels inside the log where actual intensities go.

Thus, SIL1=70dB implies a sound intensity of I so that 70dB=10log(I/I0).
ebmather
#5
Feb20-13, 07:16 AM
P: 3
okay yes that makes much more sense, but how do I solve it? Do i replace Io with the W/m^2 number? Ex for 70dB=10log(I1/Io) : Io-10^-12 and I=10^-5?
and then just add the two answers together to create the combined sound in each case?
Simon Bridge
#6
Feb20-13, 11:39 PM
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From the definition of SLI:##SLI_{tot}=10\log(I_{tot}/I_0)##
You need to know how to get the total intensity from the individual intensities.

What you have to do then, is derive the relation that gives you ##SLI_{tot}## in terms of ##SLI_1## and ##SLI_2##. I mean - in general. Just do the algebra first, then put the numbers in.

Does it matter if you don't know what ##I_0## is?


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