# 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

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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