A wave travelling along the x-axis is described by the equation `v(x, t) = 0.005 cos(alpha x - betat)`. If the wavelength and the time period of the wave are `0.08m` and `2.0s`, respectively, then `alpha and beta` in appropriate units are

Options

A. `alpha=12.50pi,beta=(pi)/(2.0)`
B. `alpha=25.00pi,beta=pi`
C. `alpha=(0.08)/(pi),beta=(2.0)/(pi)`
D. `alpha=(0.04)/(pi),beta=(1.0)/(pi)`

Answer

A

Explanation

The wave travelling along the x-axis is given by `y(x,t)=0.005cos(alphax-betat)`
`therefore alpha=k=(2pi)/(lambda)andbeta=omega=(2pi)/(T)`
As `lambda=0.08m and T=2.0s`
`therefore alpha=(2pi)/(0.08)=(pi)/(0.04)=(pi)/(4)xx100.00=25.00piandbeta=(2pi)/(2.0)=pi`