find the resultant of the amplitude in the form of

Dear Student,
To have a node of 0 amplitude, the amplitudes of the two superimposing waves must be same, i.e., a
The stationary wave formed by the superposition can be of the following form:
$$\begin{gathered} Y=2a\cos \left(kx\right)\sin \left(\omega t\right) \\ or \\ Y=2a\sin \left(kx\right)\cos \left(\omega t\right) \\ or \\ Y=2a\cos \left(kx\right)\cos \left(\omega t\right) \\ or \\ Y=2a\sin \left(kx\right)\sin \left(\omega t\right) \end{gathered}$$

For having a node at x = 0., the amplitude of the standing wave must be 0 at x = 0, which is possible for
$\sin \left(kx\right)=\sin \left(0\right)=0$.
So, the equation of the standing wave must be
$$\begin{gathered} Y=2a\sin \left(kx\right)\cos \left(\omega t\right) \\ or \\ Y=2a\sin \left(kx\right)\sin \left(\omega t\right) \end{gathered}$$

This we get from the following superposition:
$$\begin{gathered} Y=a\cos \left(kx-\omega t\right)-a\cos \left(kx+\omega t\right) \\ Y=2a\sin \left(kx\right)\sin \left(\omega t\right) \\ So, \\ Y(at x=0)=0 \end{gathered}$$

Ans (2)

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