The intensity I of a sound wave is the power per unit area. Because the range of

Question

The intensity I of a sound wave is the power per unit area. Because the range of
intensities is so large and because of the physiology of the ear, it is more convenient to use the intensity level instead. The intensity level is proportional to the log of the intensity. The usual units are decibels (dB).
= 10 log10(I/I0) dB with I0 = 10-12  W/m2, which is near the threshold of hearing. Ordinary conversation is around 60 dB, and loud music is around 120 dB. What is the ratio of the amplitude of that louder sound wave to the amplitude of the quieter one?

Explanation / Answer

intensity level of sound is              = 10 log  ( I / Io )              60 dB =    10 log  ( I / Io )              log ( I / I o ) = 6                  I / I 0   = 403.4271                    I 1 =    403.4271 I o    amplitude of intensity of quiter one is   403.4271 I o   amplitude of intensity of louder one is             log (     I 2 / I o  ) =   12                      I 2 / I o = 162753                     I 2   = 162753 I o   ratio of the amplitude of that louder sound wave to the amplitude of the quieter one              I 2   / I 1    = 162753 I o    / 403.427 I o                                 = 403.43              

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