# You live on a busy street, but as a music lover, you want to reduce th

You live on a busy street, but as a music lover, you want to reduce the traffic noise. (a) If you install special sound-reflecting windows that reduce the sound intensity level (in dB) by 30 dB, by what fraction have you lowered the sound intensity (in W/m2)? (b) If, instead, you reduce the intensity by half, what change (in dB) do you make in the sound intensity level?
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porschomcl

Intensity in decibels is measured by the formula=
$\text{Intensity}\left(dB\right)=10{\mathrm{log}}_{10}\frac{{I}_{o}}{I}.$
part (A)
I=reference intensity which is taken as:
let ${I}_{o}$ = reduction of sound level intensity in $\frac{W}{{m}^{2}}$
$30={\mathrm{log}}_{10}\left(\frac{{I}_{o}}{{10}^{-12}}\right)$
${10}^{3}×{10}^{-12}={I}_{o}$
${I}_{o}=1×{10}^{-9}W{m}^{-2}$
Now in part B
if change in intensity $=\frac{1}{2}{I}_{o}$
then change in decibel, $\gamma =10{\mathrm{log}}_{10}\left[\frac{{10}^{-9}}{2×{10}^{-12}}\right]$