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 standing wave
B. a wave travelling along `+x` direction
C. a wave travelling along `-x` direction
D. None of the Above

Answer

A

Explanation

By superposition principle,
`y=y_(1)+y_(2)=Asin(omegat-kx)+Asin(omegat+kx)`
`y=2Asinomegatcoskx`
Clearly, it is equation of standing wave for position of nodes `y=0`.
`x=(2n+1)(lambda)/(4)implies(n+(1)/(2))(lambda)/(2)`, `n=0,1,2,3`