Two waves \[{{y}_{1}}={{A}_{1}}\sin (\omega t-{{\beta }_{1}})\], \[{{y}_{2}}={{A}_{2}}\sin (\omega t-{{\beta }_{2}})\] Superimpose to form a resultant wave whose amplitude is [CPMT 1999]

• 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.            \[|{{A}_{1}}+{{A}_{2}}|\]