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

Answer

C

Explanation

We compare the given equation
`y (x,t) = 0.005 cos (alpha x - beta t)`…(I)
with the standard equation of a wave travelling along +x-axis viz.
`:. y (x,t) = A cos ((2pi x)/(lamda) - (2pi t)/(T))`…(II)
Equation the coefficients, of x and t, we get
`alpha = (2pi)/(lamda) = (2pi)/(0.08) = 2pi xx (100)/(8) = 25pi`
and `beta =(2pi)/(T) = (2pi)/(2) = pi`
Thus `[alpha = 25pi and beta = pi]`