question_answer

Two simple harmonic waves of the same amplitude and frequency differ by a phase\[\pi /2\]. 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

Correct Answer: A

Solution :

Two simple harmonic waves of same amplitude and frequency with phase difference \[\frac{\pi }{2}\] in x and y-directions respectively are written as :                 \[x=a\sin \omega \,t\] ... (i)                 \[y=a\sin \left( \omega \,t+\frac{\pi }{2} \right)\] ... (ii) From Eqs. (i) and (ii),                 \[\sin \omega \,t=\frac{x}{a}\] ... (iii)                 \[\sin \left( \omega \,t+\frac{\pi }{2} \right)=\cos \,\omega \,t=\frac{y}{a}\] ... (iv) Squaring and adding Eqs. (iii) and (iv), we have                 \[{{x}^{2}}+{{y}^{2}}={{a}^{2}}\] This is an equation of a circle.