Why does loudness of sound vary as square of amplitude?

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SUMMARY

The loudness of sound varies as the square of amplitude due to the mathematical relationship between intensity and perceived sound. The intensity of a sound wave is defined by the formula β = log(I/I0)dB, where I0 is 10-12 W/m2. This distinction is crucial as loudness, which relates to human perception, is more complex than mere intensity. Understanding this relationship is essential for accurately measuring and interpreting sound levels.

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  • Understanding of sound wave intensity
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  • Basic knowledge of human auditory perception
  • Mathematical derivation of sound intensity formulas
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Why does loudness of sound vary as square of amplitude? Why not cube of amplitude or just amplitude?
 
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You obtain this result on the mathematical derivation of the intensity.

Edit : This is for the intensity of the sound wave. The loudness(in dB), is measured as β = log(I/I0)dB, where I0 = 10-12W/m2.

You seem to be confused between intensity and loudness:smile:
 
Last edited:
Loudness is a much more complicated thing, as it (usually) refers to what the human ear perceives.
400px-Lindos1.svg.png

See https://en.wikipedia.org/wiki/Loudness for more information.
 

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