The resultant amplitude of waves {y_1} = a si | vedclass

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(D) The resultant amplitude $A$ of two waves with amplitudes $a_1$ and $a_2$ and phase difference $\phi$ is given by the formula: $A = \sqrt{a_1^2 + a

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$\sqrt{3} a$

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(D) The resultant amplitude $A$ of two waves with amplitudes $a_1$ and $a_2$ and phase difference $\phi$ is given by the formula: $A = \sqrt{a_1^2 + a_2^2 + 2 a_1 a_2 \cos \phi}$.Here,$a_1 = a$,$a_2 = a$,and the phase difference $\phi = \frac{\pi}{3} - 0 = \frac{\pi}{3}$.Substituting these values into the formula:$A = \sqrt{a^2 + a^2 + 2(a)(a) \cos(\frac{\pi}{3})}$Since $\cos(\frac{\pi}{3}) = \frac{1}{2}$,we get:$A = \sqrt{a^2 + a^2 + 2a^2(\frac{1}{2})}$$A = \sqrt{2a^2 + a^2} = \sqrt{3a^2} = \sqrt{3} a$.

The resultant amplitude of waves ${y_1} = a \sin \left( \omega t + \frac{\pi}{3} \right)$ and ${y_2} = a \sin \omega t$ is:

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