The graph shows a wave at t=0 travelling to the right with a velocity of `4 m//s`. The equation that best represents the wave is

Options

A. `y(x,t)=2 sin(pix//4-pit) metres`
B. `y(x,t)=2 sin(16pix-8pit) metres`
C. `y(x,t)=2 sin(pix//4+pit) metres`
D. 4 sin(pix//4-pit) metres`

Answer

a

Explanation

Let equation of the wave is
`y=A sin (omegat-kx +phi_(0))`
the particle at origin is moving downwards (from graph) at t=0, so `phi_(0)=pi`. Also `A=2 m` from graph.
From graph, `lambda=8 m`, so `k=(2pi)/(lambda)=(pi)/(40)`
`omega=vk=(4xxpi)/(4)=(pi)`
putting all the values
`y=2 sin[pit-(pi)/(4)x+pi]implies y=2 sin[(pi)/(4)x-pit]`