question_answer

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