Answer
(a) $A = 9.0~cm$
(b) $A = 3.0~cm$
(c) The intensity for constructive interference is larger than the intensity for destructive interference by a factor of 9.
Work Step by Step
(a) If the two waves interfere constructively, the amplitude of the resulting wave is the sum of $A_1$ and $A_2$:
$A = A_1+A_2 = 6.0~cm+3.0~cm = 9.0~cm$
(b) If the two waves interfere destructively, the amplitude of the resulting wave is the difference of $A_1$ and $A_2$:
$A = A_1-A_2 = 6.0~cm-3.0~cm = 3.0~cm$
(c) Note that $9.0~cm = 3\times 3.0~cm$
The amplitude for constructive interference is larger than the amplitude for destructive interference by a factor of 3. The intensity of a wave is proportional to the square of the amplitude. Therefore, the intensity for constructive interference is larger than the intensity for destructive interference by a factor of 9.
