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Intensity of sound and pain level

  1. Nov 18, 2006 #1
    What is the intensity of sound at the pain level of 120 dB? Compare this to that of a whisper at 20 dB?

    I know this should be so simple, but it has me confused.

    I have the formula but I am just not sure how to apply it.

    I(db)=10 log _ 10 (I/I _ 0)
  2. jcsd
  3. Nov 18, 2006 #2
    I would probably just assume that the base level (I_0) is 1... then solve each sound level in dB for the sound level in a linear intensity scale... then compare the two sound levels by saying something like... the loud noise is x times louder than the whisper.
  4. Nov 18, 2006 #3


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    Gold Member

    Wiki has some fascinating information about decibels.

    1 bel is a 10-fold increase in sound level. It is dimensionless (like percent, it is only for comparison). 1 decibel is 1/10th of a bel*.

    *(So, 1 decibel is a 1-fold increase in sound? i.e. no increase at all? :biggrin: )
  5. Nov 19, 2006 #4
    120 dB=10 log (I/1) vs. 20 dB=10 log (I/ 1)
  6. Nov 19, 2006 #5
    b=10 log (I/ I0)
    120 dB=10 log (I/1)
    10^12=(I/ 1)
    I= 10^12 W/m^2

    b=10 log (I/I0)
    20 dB=10 log (I/1)
    I=10^2 W/m^2

    The intensity of 120 dB would be 10^12 W/m^2 compared to the whisper with the intensity at 10^2 W/m^2 which equals 10^10 more intense.

    Sound good?
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