A travelling wave represented by y (x, t) = nsin(kx - `omega`t) is superimposed on another wave represented by y(x, t) = asin(kx + `omega`t). The resultant is a

Options

A. a stainding having nodes at `x=(n+(1)/(2))(lamda)/(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=(nlamda)/(2),n=0,1,2`

Answer

A

Explanation

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