A) \[a/\sqrt{2}\]
B) \[a\sqrt{2}\]
C) \[2a\]
D) \[a/2\]
Correct Answer: A
Solution :
Here: Equation of first wave, \[{{y}_{1}}=a\sin \omega t\] Equation of second wave, \[{{y}_{2}}=a\cos \omega t\] Hence, the amplitude of first wave\[{{a}_{1}}\] = amplitude of second wave\[{{a}_{2}}\] The resultant amplitude is given by, \[\sqrt{a_{1}^{2}+a_{2}^{2}+2{{a}_{1}}{{a}_{2}}\cos \phi }\] \[=\sqrt{{{a}^{2}}+{{a}^{2}}+2a.a\cos \frac{\pi }{2}}\] \[=\frac{a}{\sqrt{2}}\]
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