Explanation

(b) Given that, two waves
$y = a\sin(\omega t - ka)$
And y = a cos (ωt-kx)
Here, the phase difference between the two waves is $\frac{\pi}{2}$.
So, the resultant amplitude
$A = \sqrt{a_{1}^{2} + a_{2}^{2} + 2a_{1}a_{2}\cos\Phi}$
$\left( Here\ a_{1} = a,a_{2} = a,\Phi = \frac{\pi}{2} \right)$
$\therefore A = \sqrt{a^{2} + a^{2} + 2a\ a\cos\frac{\pi}{2}}\ $
$or\ \ A = \sqrt{a^{2} + a^{2} + 0}$
$\Longrightarrow A = \sqrt{2}a$