Q. A travelling wave represented by $y = a\sin(\omega t - kx)$ is superimposed on another wave represented b$y = a\sin(\omega t + kx)$. The resultant is
A) A standing wave having nodes at $x = \left( n + \frac{1}{2} \right)\frac{\lambda}{2},n = 0,1,2$
B) A wave travelling along + x direction
C) A wave travelling along - x direction
D) A standing wave having nodes at $x = \frac{n\lambda}{2};n = 0,1,2$
Explanation
(a) $y = y_{1} + \ y_{2} = a\sin(\omega t - kx) = a\sin(\omega t - kx)$
$y = 2a\sin{\omega t\cos{kx}}$
Clearly it is equation of standing wave for position of nodes y=0.
$i.e.,\ x = (2n + 1)\frac{\lambda}{4}\ $
$\Longrightarrow \left( n + \frac{1}{2} \right)\lambda = 0,1,2,3$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.