Question

A travelling wave represented by
`y=Asin (omegat-kx)`
is superimposed on another wave represented by
`y=Asin(omegat+kx).` The resultant is
A. A standing wave having node at `x=(n+1/2)lambda/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=(nlambda)/2,n=0,1,2`

Answer 1

Correct Answer - a
`y=y_(1)+ y_(2) = a sin (omegat-kx)+a sin (omega t+kx)`
`y= 2a sin omegat cos kx`
Clearly it is equation of standing wave for position of
nodes `y = 0 `
i.e `x=(2n+1)lambda/4`
`= (n+1/2)lambda/2,n=0,1,2,3`