A travelling wave represented by y = A sin `(omega t - kx)` is superimposed on another wave represented by y = A sin `(omega t + 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 a = `(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

D

Explanation

Y = A sin `(omega t - kx) + A sin omega t + kx)`
Y = 2A sin `omega t `cos kx standing wave
For nodes cos kx = 0
`(2pi)/(lambda) x = ( 2n + 1) (pi)/(2) `
`therefore " " x = ((2n + 1)lambda)/(4) . N = 0 , 1,2,3.... `
So, correct choice is d.