Two waves $y_{1}=A_{1} \sin \left(\omega t-\beta_{1}\right)$ and $y_{2}=A_{2} \sin \left(\omega t-\beta_{2}\right)$ superimpose to form a resultant wave whose amplitude is

• A

  $A_{1}+A_{2}$
• B

  $\left|\mathrm{A}_{1}+\mathrm{A}_{2}\right|$
• C

  $\sqrt{A_{1}^{2}+A_{2}^{2}-2 A_{1} A_{2} \sin \left(\beta_{1}-\beta_{2}\right)}$
• Correct answer
  D

  $\sqrt{A_{1}^{2}+A_{2}^{2}+2 A_{1} A_{2} \cos \left(\beta_{1}-\beta_{2}\right)}$

Hence, the correct answer is option: 'D'.