A transverse wave travelling along the positive x-axis, given by `y=A sin (kx - omega t)` is superposed with another wave travelling along the negative x-axis given by `y=A sin (kx + omega t)`. The point `x=0` is

Options

A. A standing wave having nodes at `x=(n+(1)/(2))(lamda)/(2),n=0,1,2`
B. A wave travelling along + x direction
C. A wave travelling along -x direction
D. A standing wave having nodes at `x = (n lamda)/(2) , n=0,1,2`

Answer

A

Explanation

`y_(1)=Asin(wt-kx)&y_(2)=Asin(wt-kx)`
By superposition principle
`y = y_(1) +y_(2)`
`=A sin (wt-kx)+A sin (wt +kx)`
`=2A sin wt cos kx`
Amplitude = 2A cos kx
At nodes displacement is minimum
`2A coc kx =0 rArr cos kx =0`
`kx = (2n+1) (pi)/(2) rArr (2pi)/(2)x=(2n+1)(pi)/(2)`
`x =(2n+1)(pi)/(4)` where `n =0,1,2`