Answer
The amplitude of the resultant wave is $~~1.41~y_m$
Work Step by Step
We can find the amplitude of the resultant wave:
$y_m' = (2 y_m) cos \frac{\phi}{2}$
$y_m' = (2 y_m) cos \frac{\pi/2}{2}$
$y_m' = (2 y_m) cos \frac{\pi}{4}$
$y_m' = (2 y_m) (\frac{\sqrt{2}}{2})$
$y_m' = 1.41~y_m$
The amplitude of the resultant wave is $~~1.41~y_m$
