Search This Blog

Thursday, October 6, 2011

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.