Question

The displacement equation for two waves undergoing superposition are $ {{y}_{1}}=4\,\sin \,\omega t,{{y}_{2}}=3\sin \,(\omega t+\pi /2), $ then resultant amplitude will be:

• A. $ 5\,cm $
• B. $ 7\,cm $
• C. $ 1\,cm $
• D. $ 0\,cm $

Answer 1

Answer: (A)

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 $