Explanation

(b) The amplitudes of the waves are
$a_{1} = 10\ \mu m,a_{2} = 4\ \mu m$ and $a_{3} = 7\mu m$
and the phase difference between 1$^{st}$ and 2$^{nd}$ wave is $\frac{\pi}{2}$ and that between 2$^{nd}$ and 3$^{rd}$ is $\frac{\pi}{2}$. Therefore, phase difference between 1$^{st}$ and 3$^{rd}$ is $\pi$. Combining 1$^{st}$ with 3$^{rd}$, their resultant amplitude is given by
$A_{1}^{2} = a_{1}^{2} + a_{3}^{2} + 2a_{1}a_{3}\cos\phi$
Or $A_{1} = \sqrt{10^{2} + 7^{2} + 2 \times 10 \times 7\cos\pi} = \sqrt{100 + 49 - 140}$
$= \sqrt{9} = 3\mu m$ in the direction of first
Now combining this with 2$^{nd}$ wave we have, the resultant amplitude
$A^{2} = A_{1}^{2} + a_{2}^{2} + 2A_{1}a_{2}\cos\frac{\pi}{2}$
Or $A = \sqrt{3^{2} + 4^{2} + 2 \times 3 \times 4\cos{90{^\circ}}} = \sqrt{9 + 16} = 5\mu m$