Question

Wave $y=asin(\omega t-kx)$ on a string meets with another wave producing a node at x = 0, then the equation of the unknown wave is :

• A. $y=asin(\omega t+kx)$
• B. $y=-asin(\omega t+kx)$
• C. $y=asin(\omega t-kx)$
• D. None of these
  

Answer 1

The correct option is B $y=-asin(\omega t+kx)$

Given equation of wave,

$y=a\sin (wt-kx)$, at $x=0,y=a\sin wt\to \left(1\right)$

This wave form a standing wave which travels in opposite direction

i.e., which is given by : at $x=0$,

$y=a\sin (wt-kx)$ $y=a\sin \left(wt\right)$ $\to \left(2\right)$

or $y=-a\sin (wt+kx)$ $y=-a\sin \left(wt\right)$ $\to \left(3\right)$

From the equation, we conclude : $[y^{\prime }+y_1+y_2]$

If waves $\left(1\right)$ and $\left(2\right)$ superpose, then at $2=0,y=2a\sin wt$, which refers to an anti-node.

But when $\left(1\right)$ and $\left(3\right)$ superpose, thus at $x=0,y^{\prime }=0$ which means a node in formed at $x=0$.

$\therefore$ The unknown wave in $y=-a\sin (wt+kx)$