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Intensity Level of 76 trombones

  1. Feb 14, 2012 #1
    1. The problem statement, all variables and given/known data

    If the intensity level at distance d of one trombone is 70 dB, what is the intensity level of 76 identical trombones, all at distance d?

    2. Relevant equations

    β = (10 dB) log10(I/I0)

    I0= 1.0 x 10-12 W/m2

    I = power/area

    3. The attempt at a solution

    70db = 10db log10(I/I0)

    7db = log10(I/I0)

    107 = 10log10(I/I0)

    107 = (I/I0)

    I = 0.00001 W/m2

    Then I multiplied that by 76 and put it back in the general equation to generate β = 98db, which is wrong. β = 89db.
     
  2. jcsd
  3. Feb 14, 2012 #2

    PeterO

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    Homework Helper

    Your argument seems sound, but you arithmetic must have gone astray.

    For each doubling of intensity, we increase 3 dB [10*log102 = 3]

    1 trombone = 70dB
    2 -> 73 dB
    4 -> 76 dB
    8 -> 79 dB
    16 -> 82 dB
    32 -> 85 dB
    64 -> 88 dB
    128 -> 91 dB

    so 89 dB seems quite possible

    indeed 10*log1076 = 18.8,
    so final intensity is 70 + 18.8 = 88.8, or perhaps 89 dB

    [must be annoying to see it is that simple to calculate]
     
  4. Feb 14, 2012 #3
    You're right, it was an arithmetic error.

    Working it through again gave me 88.57dB this time (did it twice to make sure).
     
  5. Feb 14, 2012 #4

    PeterO

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    Homework Helper

    You actually should be getting 88.808 dB. Not sure why the discrepecy? your figure is the sound of 72 trombones!
     
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