A) \[\pi \]
B) \[\frac{2\pi }{3}\]
C) \[\frac{2\pi }{3}\]
D) \[3\pi \]
Correct Answer: B
Solution :
Let\[{{A}_{R}}\]be the amplitude of resultant disturbance. \[{{A}_{R}}=\sqrt{A_{1}^{2}+A_{2}^{2}+2{{A}_{1}}{{A}_{2}}\cos \Phi }\] But, \[{{A}_{R}}=A\] \[\therefore \]\[A=\sqrt{2{{A}^{2}}(1+cos\Phi )}=\sqrt{4{{A}^{2}}{{\cos }^{2}}\frac{\Phi }{2}}=2A\cos \frac{\Phi }{2}\] or \[\Phi =\frac{2\pi }{3}.\] Hence, the correction option is [b].
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