A sinusoidal wave travels along a taut string of linear mass density `0.1g//cm`. The particles oscillate along `y-` direction and wave moves in the positive `x-` direction . The amplitude and frequency of oscillation are `2mm` and `50Hz` respectively. The minimum distance between two particles oscillating in the same phase is` 4m`.
If at `x=2m` and `t=2s`, the particle is at `y=1 m m ` and its velocity is in positive `y- ` direction, then the equation of this travelling wave is `: ( y` is in `m m, t` is in seconds and `x` is in metres `)`

Options

A. `y=2 sin ((pi x)/(2)-100 pi t + 30^(@))`
B. `y=2 sin ((pi x)/(2) - 100 pi t + 120 ^(@))`
C. `y=2 sin ((pi x)/(2)-100 pi t + 150^(@))`
D. None of these

Answer

D

Explanation

`lambda =4m` and `f=500 Hz.`
`:. V=f lambda=200m//s`
`:' V=sqrt((T)/(mu)):. T=mu v^(2)=(0.1)xx(200)^(2)=400N`
The equation of waves is
`y=A sin (kx-omegat+phi_(0))`
`:.` where `K=(2pi)/(lambda)=(pi)/(2),omega=2pif=100pi` and `A=2`
at `x=2` and `t=2 , y=1 m m`
`:. 1=2 sin (pi-200pi+phi_(0))` solving `phi_(0)=-30^(@)`
`:. y=2 sin ((pix)/(2) -10pit-30^(@))`