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Two vibrating tuning forks producing progressive waves given by; $y_{1} = 4 \sin (500 πt), y_{2} = 2 \sin (506 πt)$ are held near the ear of a person. The person will hear:

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3 beat/s with intensity ratio between maxima and minima equal to 2

3 beat/s with intensity ratio between maxima and minima equal to 9

6 beat/s with intensity ratio between maxima and minima equal to 2

6 beat/s with intensity ratio between maxima and minima equal to 9

answer is B.

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Detailed Solution

$I_{max} = {(A_{1} + A_{2})}^{2}$

$I_{max} = 36$

$I_{min} = {(A_{1} - A_{2})}^{2}$

$I_{\min} = 4$

$I_{max} : I_{\min} = 9 : 1$

$beats = f_{1} - f_{2} = \frac{506 π}{2 π} - \frac{500 π}{2 π} = 3$

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