A) \[\frac{\pi }{3}\]
B) \[\frac{2\pi }{3}\]
C) \[\frac{\pi }{6}\]
D) \[\frac{\pi }{4}\]
Correct Answer: B
Solution :
| The given progressive waves are |
| \[{{y}_{1}}=a\sin \,(\omega t+{{\phi }_{1}})\] |
| \[{{y}_{2}}=a\sin \,(\omega t+{{\phi }_{2}})\] |
| The resultant of two waves is |
| \[y={{y}_{1}}+{{y}_{2}}\] |
| \[=a\,[\sin \,(\omega t+{{\phi }_{1}})+\sin \,(\omega t+{{\phi }_{2}})]\] |
| If A is the amplitude of resultant wave, then |
| \[A=a\] (given) |
| \[\therefore \] \[{{A}^{2}}={{a}^{2}}+{{a}^{2}}+2{{a}^{2}}\cos \phi \] |
| or \[{{a}^{2}}={{a}^{2}}+{{a}^{2}}+2{{a}^{2}}\cos \phi \] |
| or \[\cos \phi =-\frac{1}{2}=\cos {{120}^{o}}\] |
| \[\therefore \] \[\phi ={{120}^{o}}=\frac{2\pi }{3}\] |
| Thus, \[{{\phi }_{1}}-{{\phi }_{2}}=\frac{2\pi }{3}\] |
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