The equation of a progressive wave traveling on a string is y= 4\sin\frac{\pi}{2} \left (8t- \frac{\pi x}{8} \right ) cm. The velocity of the wave is

  • Option 1)

    64 cm/s along + x direction.

  • Option 2)

    64 cm/s along - x direction. 

  • Option 3)

    (\frac{64}{\pi})  cm/s along + x direction

  • Option 4)

    \left ( \frac{64}{\pi} \right )cm/s along - x direction

 

Answers (1)

As we learnt in 

Speed of sinusoidal wave -

Wave Speed

\tfrac{dx}{dt}= V=\frac{\omega }{k}
 

- wherein

\omega = 2\pi \nu

K= \frac{2\pi }{\lambda }

 

 y=4sin(4\pi t-\frac{\pi^{2}}{16}\:x)

\omega =4 \pi    and K=\frac{\pi^{2}}{16}\:\:\:=>V=\frac{\omega}{K}=\frac{4\pi}{\frac{\pi^{2}}{16}}=\frac{64}{\pi}

V=\frac{64}{\pi}\:cm/s along +x direction.

 


Option 1)

64 cm/s along + x direction.

This option is incorrect.

Option 2)

64 cm/s along - x direction. 

This option is incorrect.

Option 3)

(\frac{64}{\pi})  cm/s along + x direction

This option is correct.

Option 4)

\left ( \frac{64}{\pi} \right )cm/s along - x direction

This option is incorrect.

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