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A travelling wave represented by y=a \sin (\omega t-k x) is superimposed on another wave represented by y=a \sin (\omega t-k x),  The resultant is

Option: 1

Standing wave having nodes at x=\left(n+\frac{1}{2}\right) \frac{\lambda}{2} \quad, n=0,1,2


Option: 2

Wave travelling along + x-direction


Option: 3

Wave travelling along -x direction


Option: 4

Standing wave having nodes at x=\frac{n \lambda}{2}, n=0,1,2,


Answers (1)

best_answer

\begin{aligned} &\begin{aligned} & y=y_1+y_2=a \sin (\omega t-k x)+a \sin (\omega t+k x) \\ & y=2 a \sin \omega t \cos k x \end{aligned}\\ &\begin{aligned} y=0, & x=(2 n+1) \frac{\lambda}{4} \\ & x=\left(n+\frac{1}{2}\right) \frac{\lambda}{2} \quad, n=0,1,2,3 \end{aligned} \end{aligned}

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