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Combining two different sound intensitiesby ebmather
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#1
Feb1913, 11:34 PM

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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? 


#2
Feb2013, 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? 


#3
Feb2013, 12:28 AM

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No, your equations don't seem to make sense to me....?



#4
Feb2013, 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. I_{0} 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/I_{0}). 


#5
Feb2013, 07:16 AM

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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) : Io10^12 and I=10^5?
and then just add the two answers together to create the combined sound in each case? 


#6
Feb2013, 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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