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Combining two different sound intensities

  1. Feb 19, 2013 #1
    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. jcsd
  3. Feb 20, 2013 #2

    Simon Bridge

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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?
     
  4. Feb 20, 2013 #3
    No, your equations don't seem to make sense to me....?
     
  5. Feb 20, 2013 #4

    Simon Bridge

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    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).
     
  6. Feb 20, 2013 #5
    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?
     
    Last edited: Feb 20, 2013
  7. Feb 20, 2013 #6

    Simon Bridge

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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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