A) \[5\,cm\]
B) \[7\,cm\]
C) \[1\,cm\]
D) \[0\,cm\]
Correct Answer: A
Solution :
Equations of the waves is \[{{y}_{1}}=4\,\sin \,\omega t\], \[{{y}_{2}}=3\sin \left( \omega t+\frac{\pi }{2} \right)\] Comparing these equations with \[y=a\,\sin \,(\omega t+\phi )\] \[{{a}_{1}}=4,\,{{a}_{2}}=3,\,\phi =\frac{\pi }{2}\] Resultant amplitude \[R=\sqrt{{{a}_{1}}^{2}+{{a}_{2}}^{2}+2{{a}_{1}}{{a}_{2}}\,\cos \phi }\] \[=\sqrt{{{4}^{2}}+{{3}^{2}}+2\times 4\times 3\cos \frac{\pi }{2}}\] \[=\sqrt{16+9+24\times 0}\] \[=5cm\]
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