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

Options

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

Answer

A

Explanation

y(x,t) = 0.005 `(alpha x - beta t)`
compare it with standard form.
y(x,t) = r cos `((2 pi x)/(lambda) - (2 pi)/(T) t ) `
`alpha = (2pi)/(lambda) = (2pi)/(.08) = 25 pi`
`beta = (2pi)/(T) = (2pi)/(2) = pi `
`rArr ` choice is (a)