Tíwo simple harmonic waves of the same amplitude and frequency differ by a phase π / 2 When they are fed simultaneously to the X and Y-plates of a CRO, the screen would display the trace of :

Question

Tíwo simple harmonic waves of the same amplitude and frequency differ by a phase π / 2 When they are fed simultaneously to the X and Y-plates of a CRO, the screen would display the trace of : (A) a circle (B) an ellipse (C) a straight line (D) a square

Tardigrade Admin · Accepted Answer

Two simple harmonic waves of same amplitude and frequency with phase difference

\frac{π}{2}

in

x

and

y -

directions respectively are written as:

x = a sin ω t

...(i)

y = a sin (ω t + \frac{π}{2})

... (ii)
From Eqs.(i) and (ii),

sin ω t = \frac{x}{a}

... (iii)

sin (ω t + \frac{π}{2}) = cos ω t = \frac{y}{a}

.... (iv)
Squaring and adding Eqs. (iii) and (iv), we have

x^{2} + y^{2} = a^{2}

This is an equation of a circle.

Q. Tíwo simple harmonic waves of the same amplitude and frequency differ by a phase π/2 When they are fed simultaneously to the X and Y-plates of a CRO, the screen would display the trace of :

a circle

an ellipse

a straight line

a square

Q. Tíwo simple harmonic waves of the same amplitude and frequency differ by a phase $π /2$ When they are fed simultaneously to the $X$ and $Y$ -plates of a CRO, the screen would display the trace of :