A) \[\frac{a+b}{ab}\]
B) \[\frac{\sqrt{a}+\sqrt{b}}{ab}\]
C) \[\frac{\sqrt{a}\pm \sqrt{b}}{ab}\]
D) \[\sqrt{\frac{a+b}{ab}}\]
Correct Answer: D
Solution :
\[y=\frac{1}{\sqrt{a}}\sin \omega t\pm \frac{1}{\sqrt{b}}\sin \left( \omega t+\frac{\pi }{2} \right)\] Here phase difference =\[\frac{\pi }{2}\]\[\therefore \] The resultant amplitude = \[\sqrt{{{\left( \frac{1}{\sqrt{a}} \right)}^{2}}+{{\left( \frac{1}{\sqrt{b}} \right)}^{2}}}=\sqrt{\frac{1}{a}+\frac{1}{b}}=\sqrt{\frac{a+b}{ab}}\]
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