What is Decibel?

The human ear has logarithmic characteristics i.e. the loudness of sound is proportional to log of power which causes it.

Suppose a certain sound power 'P' produces a loudness 'L'. Now let loudness be increased to 'mL' by increasing power to 'kP'.(k, m are constants)

If loudness is again increased by same amount i.e 2mL, it is found that power required is K^2 * P.

If process is repeated 'N' times then

Pn = K^N * P  ---> log(Pn / P) =N*logK

N = [log(Pn/P)] / log K

taking natural log of above equation we get
N = K*log(Pn/P)

but napiers logs are difficult to work.

taking logs to base 10 we arrive at

N = 10 * log10(Pn/P) 

where 'Pn' is power derived and 'P' is power absorbed. 

The unit of above equation is decibel.

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