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  4. Two simple harmonic waves of the same frequency and amplitude and a phase difference of (π/2) superimpose on each other at right angles to each other. The resultant motion will be

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Q. Two simple harmonic waves of the same frequency and amplitude and a phase difference of $\frac {\pi}{2}$ superimpose on each other at right angles to each other. The resultant motion will be

Oscillations

Solution:

This is a case of the formation of $Lissajous\, figures$. They are straight line for $\theta$ = 0$^\circ$ and 180$^\circ$, and ellipse for other values of $\theta$. If amplitudes are equal, the Lissajous figure for $\theta$ = 90$^\circ$ is a circle.