A travelling wave represented by
`y=Asin (omegat-kx)`
is superimposed on another wave represented by
`y=Asin(omegat+kx).` The resultant is

Options

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

Answer

C

Explanation

Equation of standing wave `y = (2a sin kx) cos omega t`
It is seen that the points of maximum or minimum amplitude stay at one position.
The amplitude is zero for values of kx that give sin kx = 0.
`kx = n pi`, for n = 0, 1, 2, 3,....
Substituting `k = 2 pi//lambda` in this equation, we get
`x = (n lambda)/(2)`, for n = 0, 1, 2, 3,....
The positions of zero amplitude are called nodes.