Question
A wave represented by the equation $$y = a\cos \left( {k\,x - \omega t} \right)$$ is superposed with another wave to form a stationary wave such that point $$x = 0$$ is a node. The equation for the other wave is
A.
$$a\sin \left( {k\,x + \omega t} \right)$$
B.
$$ - a\cos \left( {k\,x - \omega t} \right)$$
C.
$$ - a\cos \left( {k\,x + \omega t} \right)$$
D.
$$ - a\sin \left( {k\,x - \omega t} \right)$$
Answer :
$$ - a\cos \left( {k\,x + \omega t} \right)$$
Solution :
NOTE : Stationary wave is produced when two waves travel in opposite direction.
Now, $$y = a\cos \left( {k\,x - \omega t} \right) - a\cos \left( {k\,x + \omega t} \right)$$
$$\therefore \,\,y = 2\,a\sin k\,x\sin \omega t$$ is equation of stationary wave
which gives a node at $$x = 0.$$