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

Answer 1

Correct Answer - 4
`Y = A sin (omegat - kx) + A sin(omegat + kx)`
`Y = 2A sinomegat coskx` standing wave
For nodes `coskx = 0`
`(2pi)/(lambda).x = (2n + 1)(pi)/(2)`
`:. x = ((2n + 1)lambda)/(4), n = 0,1,2,3,….`