Question

If the intensity is increased by a factor of 20, by how many decibels is the intensity level increased :

Answer 1

The intensity level $L$ of a wave of intensity $I$ is given by ,

$L=10log\left(I/I_0\right)$ , ........................eq1

where $I_0=$ zero level of intensity ,

now if intensity is increased by a factor of 20 , then $I^{\prime }=20I$ ,

and $L^{\prime }=10log\left(I^{\prime }/I_0\right)=10log\left(20I/I_0\right)$ ,...........................eq2 ,

therefore increment in intensity level ,subtracting eq1 from eq2 ,

$L^{\prime }-L=10\left[log\right(20I/I_0)-log(I/I_0\left)\right]=10log20=13dB$