Two sources of sound placed close to each other are emitting progressive waves given by y1 = 4 sin 600 \pi t and y2 = 5 sin 608 \pi 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.

 

Answers (1)
P Prateek Shrivastava

As we learnt in

Beat Frequency -

Delta 
u = left | 
u _{1}-
u _{2} 
ight |

module of left ( 
u _{1} -
u _{2}
ight )

 

- wherein

Where 
u _{1} : and: 
u _{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}}} 
ight )^{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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