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

Question

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 (A) linear (B) circular (C) elliptical (D) none of the above

Tardigrade Admin · Accepted Answer

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

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

linear

circular

elliptical

none of the above

This is a case of the formation of $L i ss aj o u s f i gu res$ . They are straight line for $θ$ = 0 $^{\circ}$ and 180 $^{\circ}$ , and ellipse for other values of $θ$ . If amplitudes are equal, the Lissajous figure for $θ$ = 90 $^{\circ}$ is a circle.

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