A travelling wave represented

Question:

A travelling wave represented by $\mathrm{y}=\mathrm{A} \sin (\omega \mathrm{t}-\mathrm{kx})$ is superimposed on another wave represented by $\mathrm{y}=\mathrm{A} \sin (\omega \mathrm{t}+\mathrm{kx})$. The resultant is :-

 

  1. A standing wave having nodes at $\mathrm{x}=\left(\mathrm{n}+\frac{1}{2}\right) \frac{\lambda}{2}, \mathrm{n}=0,1,2$

  2. A wave travelling along $+x$ direction

  3. A wave travelling along $-x$ direction

  4. A standing wave having nodes at $\mathrm{x}=\frac{\mathrm{n} \lambda}{2} ; \mathrm{n}=0,1,2$

Correct Option: , 2

Solution:

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