A wave equation which gives the displacement along the Y direction is given by y= 10^{-4} \sin (60t + 2x), where x and y are in metres and t is time in seconds. This represents a wave

  • Option 1)

    Traveling with a velocity of 30 m/s in the negative x direction

  • Option 2)

    of wavelength x metre

  • Option 3)

    Of frequency \left ( \frac{30}{\pi} \right )hertz

  • Option 4)

    All of the above

 

Answers (1)

As we learnt in 

Travelling Wave Equation -

y=A \sin \left ( Kx-\omega t \right )
 

- wherein

K=2\pi /\lambda

\omega = \frac{2\pi }{T}

\lambda =  wave length

T = Time period of oscillation

 

This represent a wave whose parameter are given below

\omega =  60

 \Rightarrow frequency\ f=\frac{\omega}{2\pi}=\frac{30}{\pi}\:Hz

K=2

v=\frac{\omega}{K} = 30 m/s,\:\:\:\:wavelength=\frac{2\pi}{K}=\pi

It is moving along - X direction.

All are corrrect.


Option 1)

Traveling with a velocity of 30 m/s in the negative x direction

This option is incorrect.

Option 2)

of wavelength x metre

This option is correct.

Option 3)

Of frequency \left ( \frac{30}{\pi} \right )hertz

This option is incorrect.

Option 4)

All of the above

This option is incorrect.

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