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(B) 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 $2^{nd}$ wav

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(B) 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 $\frac{\pi}{2},$ and between the $2^{nd}$ and $3^{rd}$ wave is $\frac{\pi}{2}.$ Therefore,the phase difference between the $1^{st}$ and $3^{rd}$ wave is $\pi.$ Combining the $1^{st}$ and $3^{rd}$ waves,their resultant amplitude $A_1$ is given by: $A_1 = \sqrt{a_1^2 + a_3^2 + 2a_1a_3 \cos(\pi)} = \sqrt{10^2 + 7^2 + 2(10)(7)(-1)} = \sqrt{100 + 49 - 140} = \sqrt{9} = 3 \mu m.$ This resultant $A_1$ is in the direction of the $1^{st}$ wave. Now,combining this resultant $A_1$ with the $2^{nd}$ wave (which has a phase difference of $\frac{\pi}{2}$ relative to the $1^{st}$ wave),the final resultant amplitude $A$ is: $A = \sqrt{A_1^2 + a_2^2 + 2A_1a_2 \cos(\frac{\pi}{2})} = \sqrt{3^2 + 4^2 + 2(3)(4)(0)} = \sqrt{9 + 16} = \sqrt{25} = 5 \mu m.$

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

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