A) \[\sqrt{A_{1}^{2}+A_{2}^{2}+2{{A}_{1}}{{A}_{2}}\cos ({{\beta }_{1}}-{{\beta }_{2}})}\]
B) \[\sqrt{A_{1}^{2}+A_{2}^{2}+2{{A}_{1}}{{A}_{2}}\sin ({{\beta }_{1}}-{{\beta }_{2}})}\]
C) \[{{A}_{1}}+{{A}_{2}}\]
D) \[|{{A}_{1}}+{{A}_{2}}|\]
Correct Answer: A
Solution :
Phase difference between the two waves is \[\varphi =(\omega t-{{\beta }_{2}})=(\omega t-{{\beta }_{1}})=({{\beta }_{1}}-{{\beta }_{2}})\] \Resultant amplitude \[A=\sqrt{A_{1}^{2}+A_{2}^{2}+2{{A}_{1}}{{A}_{2}}\cos ({{\beta }_{1}}-{{\beta }_{2}})}\]
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