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.You need to login to perform this action.
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