A sinusoidal wave is propagating in negative x-direction in a string stretched along x-axis. A particle of string at `x=2` cm is found at its mean position and it is moving in positive y-direction at `t=1` s. the amplitude of the wave, the wavelength and the angular frequency of the wave are `0.1m,pi//4m` and `4pi rad//s`, respectively.
The equation of the wave is

Options

A. `y=0.1 sin(4pi(t-1)+8(x-2))`
B. `y=0.1 sin((t-1)-(x-2))`
C. `y=0.1 sin(4pi(t-1)-8(x-2))`
D. none of these

Answer

a

Explanation

The equation of wave moving in negative `x`-direction, assuming origin of position at `x=2` and origin of time (i.e., initial time) at `t=1 s`.
`y=0.1 sin(4pi t+8x)`
shifting the origin of position to left by `2 m`, to `x=0`. Also shifting the origin of time backwards by `1 s`,that is to `t=0 s`.
`y=0.1 [4pi(t-1)+8(x-2)]`