| \[{{y}_{1}}=\frac{1}{2}\sin \omega \,t+\frac{\sqrt{3}}{2}\cos \omega \,t\] |
| \[{{y}_{2}}=\sin \omega \,t+\cos \omega \,t\], is |
A) \[\frac{7\pi }{12}\]
B) \[\frac{\pi }{12}\]
C) \[-\frac{\pi }{6}\]
D) \[\frac{\pi }{6}\]
Correct Answer: B
Solution :
\[{{y}_{1}}=\frac{1}{2}\sin \omega t+\frac{\sqrt{3}}{2}\cos \omega t\] \[=\cos \,\frac{\pi }{3}\,\sin \omega t\,+\frac{\sqrt{3}}{2}\,\cos \omega t\] Similarly, \[{{y}_{2}}=\sqrt{2}\,\sin \,\left( \omega t\,+\frac{\pi }{4} \right)\] \[\therefore \] Phase difference \[\Delta f=\frac{\pi }{3}\,-\frac{\pi }{4}\,=\frac{\pi }{12}\]
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