Two waves, each of amplitude 3 mm, with the same frequency and wavelength, move together along a…

We use $A = 2a\cos(\phi/2)$ with $a = 3\ \text{mm}$.

(a) $A = 2 \times 3\ \text{mm} \times \cos 0 = 6\ \text{mm}$.

(b) $A = 6\ \text{mm} \times \cos(\pi/4) = 4.24\ \text{mm}$.

(c) $A = 6\ \text{mm} \times \cos(\pi/3) = 3\ \text{mm}$. The sum is no bigger than one wave alone.

(d) $A = 6\ \text{mm} \times \cos(\pi/2) = 0\ \text{mm}$. The waves cancel.