The decibel scale is a logarithmic scale for measuring the sound intensity level. Because the decibel scale is logarithmic, it changes by an additive constant when the intensity as measured in W$/$m$2$W$/$m$2$ changes by a multiplicative factor. The number of decibels increases by $10$ for a factor of $10$ increase in intensity. The general formula for the sound intensity level, in decibels, corresponding to intensity II is

$=10$log$($II$0)$dB$=10$log$($II$0)$dB$,$

where I$0$I$0$ is a reference intensity. For sound waves, I$0$I$0$ is taken to be $1012$W$/$m$21012$W$/$m$2.$ Note that loglog refers to the logarithm to the base $10.$

Part A

What is the sound intensity level $,$ in decibels, of a sound wave whose intensity is $10$ times the reference intensity $($i$.$e$.,$ I$=10$I$0$I$=10$I$0)?$

Express the sound intensity numerically to the nearest integer.

What is the sound intensity level $,$ in decibels, of a sound wave whose intensity is $100$ times the reference intensity $($i$.$e$.$ I$=100$I$0$I$=100$I$0)?$