A travelling wave represented by y = A sin (ωt − kx) is superimposed on another wave represented by y = A sin (ωt + kx). The resultant is

A wave travelling along +x direction
A wave travelling along −x direction
A standing wave having nodes at x = nλ/2, n = 0,1,2....
A standing wave having nodes at x = (n + 1/2) λ/2, n = 0,1,2....

Correct answer: A standing wave having nodes at x = (n + 1/2) λ/2, n = 0,1,2....

Solution

sin(wt-kx)+sin(wt+kx) = 2A sin(wt) cos(kx), a standing wave. Nodes occur where cos(kx)=0, i.e. kx = (n+1/2)pi, so x = (n+1/2) lambda/2.

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