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 \rm{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 i is \beta = 10\,\log\left(\frac{i}{i_0}\right){ \rm db}, where i_0 is a reference intensity. for sound waves, i_0 is taken to be 10^{-12}\,{\rm w/m^2}. note that \log refers to the logarithm to the base 10. calculate the change in decibels corresponding to m = 2, m = 4, and m = 8.