A) 10 cm
B) 20 cm
C) \[5\sqrt{2}\]cm
D) 50 cm
Correct Answer: A
Solution :
\[x=5\sqrt{2}\left( \sin 2\pi \,t+\cos 2\pi \,t \right)\] \[=5\sqrt{2}\sin 2\pi \,t+5\sqrt{2}\cos 2\pi \,t\] \[x=5\sqrt{2}\sin 2\pi t+5\sqrt{2}\sin \,\left( 2\pi \,t+\frac{\pi }{2} \right)\] Phase difference between constituent waves \[\varphi =\frac{\pi }{2}\] \[\therefore \] Resultant amplitude\[A=\sqrt{{{(5\sqrt{2})}^{2}}+{{(5\sqrt{2})}^{2}}}\]=10 cm.
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