Two sound waves of slightly different frequencies have amplitude ratio $\frac{11}{9} .$ What is the difference of sound levels in decibels of maximum and minimum intensities heard at a point :- ............. $\mathrm{dB}$
Diffcult
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$\mathrm{SL}_{2}-\mathrm{SL}_{1}=10 \mathrm{\,log}$
$\frac{\mathrm{I}_{\max }}{\mathrm{I}_{\min }}=10 \log \frac{(\sqrt{\mathrm{I}_{1}}+\sqrt{\mathrm{I}_{2}})^{2}}{(\sqrt{\mathrm{I}_{1}}-\sqrt{\mathrm{I}_{2}})^{2}}=10 \log \frac{\left(\frac{\mathrm{a}_{1}}{\mathrm{a}_{2}}+1\right)^{2}}{\left(\frac{\mathrm{a}_{1}}{\mathrm{a}_{1}}-1\right)^{2}}$
$=20 \mathrm{\,dB}$
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