# Two sources of sound placed close to each other are emitting progressive waves given by y1 = 4 sin 600 t and y2 = 5 sin 608 t. An observer located near these two sources of sound will hear: Option 1) 4 beats per second with intensity ratio 25: 16 between waxing and waning. Option 2) 8 beats per second with intensity ratio 25 : 16 between waxing and waning. Option 3) 8 beats per second with intensity ratio 81 : 1 between waxing and waning. Option 4) 4 beats per second with intensity ratio 81 : 1 between waxing and waning.

P Prateek Shrivastava

As we learnt in

Beat Frequency -

$\Delta \nu = \left | \nu _{1}-\nu _{2} \right |$

module of $\left ( \nu _{1} -\nu _{2}\right )$

- wherein

Where $\nu _{1} \: and\: \nu _{2}$ are frequency of two wave differ slightly  in value of frequency.

Ratio of maximum and minimum intensity -

$\frac{I_{max}}{I_{min}}=\left ( \frac{\sqrt{I_{1}}+\sqrt{I_{2}}}{\sqrt{I_{1}}-\sqrt{I_{2}}} \right )^{2}$

-

$2\pi f_{1}=600 \pi$

$f_{1}=300$                            ....................(i)

$2\pi f_{2}=608 \pi$

$f_{2}=304$                            ....................(ii)

$f_{1}-f_{2}=4\ beats$

$\frac{I_{max}}{I_{min}}=\frac{(A_{1}+A_{2})^{2}}{(A_{1}-A_{2})^{2}}=\frac{(5+4)^{2}}{(5-4)^{2}}=\frac{81}{1}$

Correct option is 4.

Option 1)

4 beats per second with intensity ratio 25: 16 between waxing and waning.

Incorrect

Option 2)

8 beats per second with intensity ratio 25 : 16 between waxing and waning.

Incorrect

Option 3)

8 beats per second with intensity ratio 81 : 1 between waxing and waning.

Incorrect

Option 4)

4 beats per second with intensity ratio 81 : 1 between waxing and waning.

Correct

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