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. (a) `alpha = 25.00pi, beta = pi`
B. (b) `alpha = (0.08)/(pi), beta = (2.0)/(pi)`
C. ( c ) `alpha = (0.04)/(pi), beta = (1.0)/(pi)`
D. ( d) `alpha = 12.50(pi), beta = (pi)/(2.0)`

Answer

A

Explanation

(a) `y(x, t) = 0.05 cos(alphax - betat)` (Given)
Comparing it with the standered equation of wave
`y(x, t) = a cos (kx - omegat)` we get
`k = alpha` and `omega = beta`
:. `(2pi)/(lambda) = alpha` and `(2pi)/(T) = beta`
:. `alpha = (2pi)/(0.08) = 25pu` and `beta = (2pi)/(2) = pi`