Two vibrating tuning forks produce progressive waves given by ${y_1} = 4\,\sin \,\left( {500\pi t} \right)$ and ${y_2} = 2\,\sin \,\left( {506\pi t} \right)$. These tuning forks are held near the ear of a person. The person will hear $\alpha \, beats/s$ with intensity ratio between maxima and minima equal to $\beta $. Find the value of $\beta - \alpha $
Diffcult
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beats $=\alpha=\frac{506 \pi}{2 \pi}-\frac{500 \pi}{2 \pi}$
$\alpha=253-250=3$
$\beta=\frac{\mathrm{I}_{\max }}{\mathrm{I}_{\min }}=\left(\frac{\mathrm{a}_{1}+\mathrm{a}_{2}}{\mathrm{a}_{1}-\mathrm{a}_{2}}\right)^{2}=\left(\frac{4+2}{4-2}\right)^{2}$
$\beta=9$
So $\beta-\alpha=6$
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