(Solved): Learning Goal: To understand the decibel scale. The decibel scale is a logarithmic scale for measur ...

Learning Goal: To understand the decibel scale. 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 $\mathrm{W}/{\mathrm{m}}^2$ 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 $I$ is $?=10\log \left(\frac{I}{I_0}\right)\mathrm{dB},$ where $I_0$ is a reference intensity. For sound waves, $I_0$ is taken to be $10^{?12}\mathrm{W}/{\mathrm{m}}^2$. Note that $\log$ refers to the logarithm to the base 10 . Calculate the change in decibels ( $?{?}_2,?{?}_4$, and $?{?}_8$ ) corresponding to $m=2,m=4$, and $m=8$. Give your answers, separated by commas, to the nearest integer--this will give an accuracy of $20\%$, which is good enough for sound.