Three waves of equal frequency having amplitu | vedclass

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(C) Let the amplitudes be represented as vectors: $\vec{A}_1 = 10\hat{i}$,$\vec{A}_2 = 4\hat{j}$,and $\vec{A}_3 = -7\hat{i}$ (since the phase differen

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$5$

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(C) Let the amplitudes be represented as vectors: $\vec{A}_1 = 10\hat{i}$,$\vec{A}_2 = 4\hat{j}$,and $\vec{A}_3 = -7\hat{i}$ (since the phase difference is $\pi/2$ between successive waves).The resultant amplitude vector $\vec{A}_R = \vec{A}_1 + \vec{A}_2 + \vec{A}_3$.$\vec{A}_R = (10 - 7)\hat{i} + 4\hat{j} = 3\hat{i} + 4\hat{j}$.The magnitude of the resultant amplitude is $A_R = \sqrt{3^2 + 4^2} = \sqrt{9 + 16} = \sqrt{25} = 5\, \mu m$.

Three waves of equal frequency having amplitudes $10\, \mu m, 4\, \mu m$ and $7\, \mu m$ arrive at a given point with successive phase difference of $\pi/2$. The amplitude of the resulting wave in $\mu m$ is given by

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