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  • I have a doubt, kindly clarify. - Oscillations and Waves - JEE Main-8

Sinusodial waves 5 cm in amplitude are to be transmitted along a string having a linear mass density equal to 4\times 10^{-2} \;kg/m. If source deliver maximum power 90 W and tension is 100N then the highest frequency at which the source can operate is

  • Option 1)

    45.3 Hz

  • Option 2)

    50 Hz

  • Option 3)

    30 Hz

  • Option 4)

    62.3 Hz

 

Answers (1)

best_answer

P = \frac{1}{2} \mu \omega ^ {2}A ^ {2} v , v = \sqrt \frac{T}{\mu}

P = \frac{1}{2} \mu \omega ^ {2}A ^ {2} A^{2}\sqrt{T \mu}

f = \frac{\omega}{2\pi} = \frac{1}{2\pi} \sqrt{\frac{2P}{A^{2}\sqrt{T\mu}}} = 30 Hz

 

Intensity of the wave -

I = \frac{1}{2}\rho \omega ^{2}A^{2}V

\rho = mass density

\omega = angular frequency

A = Amplitude

V = Wave speed

 

- wherein

flow of energy per unit area of cross section of the string in the unit time is known as intensity of wave.

 

 

 


Option 1)

45.3 Hz

This is incorrect.

Option 2)

50 Hz

This is incorrect.

Option 3)

30 Hz

This is correct.

Option 4)

62.3 Hz

This is incorrect.

Posted by

divya.saini

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