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(A) The amplitudes of the waves are $a_{1} = 10 \, \mu m$,$a_{2} = 4 \, \mu m$,and $a_{3} = 7 \, \mu m$.The phase difference between the $1^{st}$ and

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$5$

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(A) The amplitudes of the waves are $a_{1} = 10 \, \mu m$,$a_{2} = 4 \, \mu m$,and $a_{3} = 7 \, \mu m$.The phase difference between the $1^{st}$ and $2^{nd}$ wave is $\phi_{12} = \pi / 2$,and the phase difference between the $2^{nd}$ and $3^{rd}$ wave is $\phi_{23} = \pi / 2$. Thus,the phase difference between the $1^{st}$ and $3^{rd}$ wave is $\phi_{13} = \pi$.First,we combine the $1^{st}$ and $3^{rd}$ waves. Since they are in opposite phase $(\pi)$,their resultant amplitude $A_{13}$ is:$A_{13} = |a_{1} - a_{3}| = |10 - 7| = 3 \, \mu m$.Now,we combine this resultant $A_{13}$ with the $2^{nd}$ wave. The phase difference between the $2^{nd}$ wave and the resultant of the $1^{st}$ and $3^{rd}$ waves is $\pi / 2$ (since the resultant $A_{13}$ is in the direction of the $1^{st}$ wave).The final resultant amplitude $A$ is given by:$A = \sqrt{A_{13}^{2} + a_{2}^{2} + 2 A_{13} a_{2} \cos(\pi / 2)}$$A = \sqrt{3^{2} + 4^{2} + 0} = \sqrt{9 + 16} = \sqrt{25} = 5 \, \mu m$.

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

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