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

Answer

A

Explanation

y(x,t)=0.05 cos (ax-Bt) (given)
Comparing it with the standard equation of wave
`y(x,t)=a cos (kx-omega t)` we get
`k=a and omega =beta`
But `k=(2 pi)/lamda and omega =(2pi)/T`
Given that `lamda=0.08m and T=2.0 s`
`therefore a=(2pi)/lamda=25 pi and beta=(2pi)/2=pi`