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  • Can someone help me with this, - Oscillations and Waves - JEE Main-6

If y = 5\sin(30\pi t -\frac{\pi}{7}x + 30\degree), y\rightarrow mm, t \rightarrow second, x\rightarrow m.For given progressive wave equation, phase difference between two vibrating particles having path difference 3.5 m would be

  • Option 1)

    \frac{\pi}{}4

  • Option 2)

    \pi

  • Option 3)

    \frac{\pi}{}3

  • Option 4)

    \frac{\pi}{}2

 

Answers (1)

best_answer

\Delta \phi = \frac{2 \pi}{\lambda} \Delta x

from given equation

k = \frac{\pi}{7} \Rightarrow \frac{2 \pi}{\lambda} = \frac{\pi}{7} \Rightarrow \lambda = 14

\therefore \Delta \phi = \frac{2 \pi}{14} X 3.5 = \frac{\pi}{2}

 

In phase and out of phase -

\Delta x= n\lambda \: \: \: or\: \: \Delta \phi = 2n\pi

i.e. point seprated by distance n\lambda are in same phase.

\Delta x= \frac{m\lambda }{2}\left ( m= 1,3,5,7...... \right )\\\ or \: \Delta \phi = m\pi

Point separated by \frac{m\lambda }{2} are out of phase.

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Option 1)

\frac{\pi}{}4

This is incorrect.

Option 2)

\pi

This is incorrect.

Option 3)

\frac{\pi}{}3

This is incorrect.

Option 4)

\frac{\pi}{}2

This is correct.

Posted by

divya.saini

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