Walker, Halliday & Resnick — Waves-I: Problem 16

16 Two sinusoidal waves of the same frequency are to be sent in the same direction along a taut string. One wave has an amplitude of 5.50 mm, the other 12.0 mm. (a) What phase difference \(\phi_1\) between the two waves results in the smallest amplitude of the resultant wave? (b) What is that smallest amplitude? (c) What phase difference \(\phi_2\) results in the largest amplitude of the resultant wave? (d) What is that largest amplitude? (e) What is the resultant amplitude if the phase angle is \((\phi_1 - \phi_2)/2\)?