Answer
(a) $A = 8.0~cm$
(b) $A = 2.0~cm$
(c) The amplitude for constructive interference is larger than the amplitude for destructive interference by a factor of 4.
Work Step by Step
(a) If the two waves interfere constructively, the amplitude of the resulting wave is the sum of $A_1$ and $A_2$:
$A = A_1+A_2 = 5.0~cm+3.0~cm = 8.0~cm$
(b) If the two waves interfere destructively, the amplitude of the resulting wave is the difference of $A_1$ and $A_2$:
$A = A_1-A_2 = 5.0~cm-3.0~cm = 2.0~cm$
(c) Note that $8.0~cm = 4\times 2.0~cm$
The amplitude for constructive interference is larger than the amplitude for destructive interference by a factor of 4.
