Two sounding bodies producing progressive wave given by y_1=4 \sin 400 \, \, pt\, \, and \, \, y_2=4 \sin404\, \, pt are situated very near to the ears of a person who will hear

  • Option 1)

    2 beats per second with intensity ratio (4/3) between maxima and minima

  • Option 2)

    2 beats per second with intensity ratio (49/1) between maxima and minima

  • Option 3)

    4 beats per second with intensity ratio (7/1) between maxima and minima

  • Option 4)

    4 beats per second with intensity ratio (4/3) between maxima and minima

 

Answers (1)

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.

 

 Beat frequency =\left | \nu_{2}-\nu_{1} \right |

                          =\left | \frac{\omega_{2}-\omega_{1}}{2 \pi} \right |\:=\:\left | \frac{404 \pi - 400 \pi}{2\pi} \right |=2                            

Ratio of Intensity maxima and minima

             =\frac{(A_{2}+A_{1})^{2}}{(A_{2}-A_{1})^{2}}=(\frac{4+3}{4-3})^{2}=49:1

In the second equation y_{2}=3sin(404\pi t)

          first equation y_{1}=4sin(400\pi t)

 


Option 1)

2 beats per second with intensity ratio (4/3) between maxima and minima

This option is incorrect.

Option 2)

2 beats per second with intensity ratio (49/1) between maxima and minima

This option is correct.

Option 3)

4 beats per second with intensity ratio (7/1) between maxima and minima

This option is incorrect.

Option 4)

4 beats per second with intensity ratio (4/3) between maxima and minima

This option is incorrect.

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