Halliday, Resnick & Walker — Waves-I: Problem 50

50 Four waves are to be sent along the same string, in the same direction: \[ y_1(x, t) = (5.00 \text{ mm}) \sin(4\pi x - 400\pi t) \] \[ y_2(x, t) = (5.00 \text{ mm}) \sin(4\pi x - 400\pi t + 0.8\pi) \] \[ y_3(x, t) = (5.00 \text{ mm}) \sin(4\pi x - 400\pi t + \pi) \] \[ y_4(x, t) = (5.00 \text{ mm}) \sin(4\pi x - 400\pi t + 1.8\pi) \] What is the amplitude of the resultant wave?