Why does loudness of sound vary as square of amplitude?

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The discussion centers on the relationship between loudness and sound amplitude, highlighting that loudness varies with the square of amplitude due to the mathematical derivation of sound intensity. It clarifies that loudness, measured in decibels (dB), is defined as β = log(I/I0)dB, where I0 is a reference intensity. The conversation also distinguishes between intensity and loudness, noting that loudness is a more complex perception influenced by human hearing. For further understanding, a reference to a Wikipedia article on loudness is provided. The key takeaway is that while intensity relates to amplitude mathematically, loudness perception involves additional factors.
Fiona Rozario
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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:
 
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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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