#### A wave travelling along the x -axis is described by  the equation If the wavelength and the time period of the wave are 0.08 m and 2.0 s, respectively, then in appropriate units are Option 1) Option 2) Option 3) Option 4)

As we learnt in

Relation between phase difference and path difference -

Phase difference

-

Travelling Wave Equation -

- wherein

wave length

Time period of oscillation

The wave travelling along the $x-axis$  is given by

$\dpi{100} y(x,t)=0.005\; cos(\alpha x-\beta t).$

$\dpi{100} Therefore\; \alpha =k=\frac{2\pi }{\lambda }.As\; \lambda =0.08\, m.$

$\dpi{100} \therefore \; \; \alpha =\frac{2\pi }{0.08}=\frac{\pi }{0.04}\Rightarrow \alpha =\frac{\pi }{4}\times 100.00=25.00\, \pi$

$\dpi{100} \omega =\beta \Rightarrow \frac{2\pi }{2.0}=\beta \Rightarrow \pi$

$\dpi{100} \therefore \; \; \alpha =25.00\, \pi ,\beta =\pi$

Correct option is 2.

Option 1)

This is an incorrect option.

Option 2)

This is the correct option.

Option 3)

This is an incorrect option.

Option 4)

This is an incorrect option.