Two waves are represented by ${y}_{1}=a\mathrm{sin}\left(\omega \text{\hspace{0.17em}}t+\frac{\pi }{6}\right)$ and ${y}_{2}=a\mathrm{cos}\omega \text{\hspace{0.17em}}t$. What will be their resultant amplitude

(1) a

(2) $\sqrt{2}\text{\hspace{0.17em}}a$

(3) $\sqrt{3}\text{\hspace{0.17em}}a$

(4) 2a

(3) $A=\sqrt{\left({a}_{1}^{2}+{a}_{2}^{2}+2{a}_{1}{a}_{2}\mathrm{cos}\varphi \right)}$

Putting a1 = a2 = a and $\varphi =\frac{\pi }{3}$, we get $A=\sqrt{3}a$

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