A wave travelling in the `+ve` x-direction having displacement along y-direction as 1`m`, wavelength `2pi` m and frequency of `1//pi` Hz is represented by

Options

A. `y = sin (10 pi x - 20 pi t)`
B. `y = sin (2pi x + 2pi t)`
C. `y = sin (x - 2t)`
D. `y = sin (2pi x - 2pi t)`

Answer

C

Explanation

The equation of the wave will be of the form `y = A sin (Kx - omega t)` ….(1)
In this case `lamda = 2pi, n = (1)/(pi)`
`omega = 2pi n = 2pi xx (1)/(pi) = 2`
`K = (2pi)/(lamda) = (2pi)/(2pi) = 1 and A = 1m`
`:.` The equation will be
`y = 1 sin [1 xx x - 2t] = sin (x - 2t)`