A progressive wave having amplitude `5 m` and wavelength `3m`. If the maximum average velocity of particle in half time period is `5 m//s` and waves is moving in the positive x-direction then find which may be the correct equation (s) of the wave ? [wave `x` in meter].

Options

A. `5 sin ((2pi)/(5)t-(2pi)/(3)x)`
B. `4 sin((pit)/(2)-(2pi)/(3))+3 cos ((pi t)/(2)-(2pi)/(3)x)`
C. `5 sin ((pi t)/(2)-(2pi)/(3)x)`
D. `3 cos((2pi)/(5)t-(2pi)/(3)x)-4 sin ((2pi)/(5)t-(2pi)/(3)x)`

Answer

B, C

Explanation

`because lamda = 3 m :. k=(2pi)/(lamda)=(2pi)/(3)`
Maximum displacement in half time period `= 2a = 10 m`
So maximum average velocity `(10)/(.^(T)//_(2))=5 rArr T=4s rArr omega = (2pi)/(T)=(2pi)/(4)=(pi)/(2)`.