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Uniform Sound and Its Power

  1. Jul 6, 2010 #1
    1. The problem statement, all variables and given/known data

    A spherical source radiates sound uniformly in all directions. At a distance of 9 m, the sound intensity level is 100 dB. What power is radiated by this source?

    Just a simple answer check to see if my answer is reasonable.

    2. Relevant equations

    [tex]\beta[/tex] = 10 db log (I/I0)
    Intensity = power/area

    3. The attempt at a solution
    First convert the given decibels to Intensity then convert the found intensity to power via the second equation.
    100 dB = 10 dB log (I/(1*10^-12)
    Divide by 10 on both sides.
    10 = log ((I/(1*10^-12)
    Raise both sides to the tenth power to get rid of log
    1010 = (I/(1*10^-12))
    Multiple both sides by 1*10-12 I get. . .
    I = 0.01 (Can someone confirm that I doesn't have units?)
    Plugging in I to the second equation I get. . .
    0.01 = [tex]\frac{Power}{4*\pi*9^2}[/tex]
    Divide both sides by area I get Power. . .
    Power = 10.178 (I know the units should be watt but if Intensity has no units and area only gives m2 then how do I get the units for watt? Does this mean this is wrong?)

    Thanks in advance for your help.
  2. jcsd
  3. Jul 6, 2010 #2


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    Homework Helper
    Gold Member

    Hello shards5,
    It does have units! :tongue: Here, your 1010 figure does not have units because it is a ratio of intensities in terms of power fluxes (a ratio of things with the same units has no units because the units cancel). But I0 Has units! That means your I = 0.01 has units too (which you should be able to figure out going forward from here).

    The standard reference sound intensity is

    I0 = 1 x 10-12 W/m2

    (i.e. units of Watts per square meter).
    Last edited: Jul 6, 2010
  4. Jul 6, 2010 #3
    Ah, then the whole problem makes sense since m2 cancels out nicely at the end leaving me with just Watts. Thanks a lot!
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