Answer
The amplitude of the resultant wave is $~~5.0~cm$
Work Step by Step
We can find the horizontal component of the resultant wave's amplitude:
$y_{mh}' = (y_{m1}) cos ~(0) + (y_{m2}) cos~(\frac{\pi}{2})$
$y_{mh}' = (3.0~cm) cos ~(0) + (4.0~cm) cos~(\frac{\pi}{2})$
$y_{mh}' = 3.0~cm$
We can find the vertical component of the resultant wave's amplitude:
$y_{mv}' = (y_{m1}) sin ~(0) + (y_{m2}) sin~(\frac{\pi}{2})$
$y_{mv}' = (3.0~cm) sin ~(0) + (4.0~cm) sin~(\frac{\pi}{2})$
$y_{mv}' = 4.0~cm$
We can find the amplitude of the resultant wave:
$y_m' = \sqrt{(3.0~cm)^2+(4.0~cm)^2}$
$y_m' = 5.0~cm$
The amplitude of the resultant wave is $~~5.0~cm$
