A) \[\frac{\lambda }{2\pi }[\phi +\pi /2]\]
B) \[\frac{\lambda }{2\pi }[\phi ]\]
C) \[\frac{\lambda }{2\pi }[\phi -\pi /2]\]
D) \[\frac{2\pi }{\lambda }[\phi ]\]
Correct Answer: A
Solution :
Given, \[{{y}_{2}}={{a}_{2}}\cos \left[ \omega t-\frac{2\pi x}{\lambda }+\phi \right]\] Or \[{{y}_{2}}={{a}_{2}}\sin \left[ \frac{\pi }{2}+\left( \omega t-\frac{2\pi x}{\lambda }+\phi \right) \right]\] and \[{{y}_{1}}={{a}_{1}}\sin \left( \omega t-\frac{2\pi x}{\lambda } \right)\] We have phase difference between two waves \[=\left[ \frac{\pi }{2}+\phi \right]\] Path difference = \[\frac{\lambda }{2\pi }\times \] phase difference \[\therefore \] Path difference \[=\frac{\lambda }{2\pi }\left[ \frac{\pi }{2}+\phi \right]\]
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