Question

Two waves traveling on a string in the same direction both have a frequency of 150 Hz, a wavelength of 2 cm, and an amplitude of 0.06 m. What is the amplitude of the resultant wave if the original waves differ in phase by each of the following values?

(a) pi/6
(b) pi/3

I am terribly lost.

Answer 1

If both waves have the same amplitude (0.06 m) and frequency, when they are in phase the resultant amplitude is
0.12 m.
When they are pi radians out of phase, the resultant amplitude is zero.

(a) When they are pi/6 radians out of phase, and of the same amplitude, the resultant amplitude is 2*0.06*cos(pi/12) = 0.116 m

(b) When they are pi/3 radians out of phase, and of the same amplitude, the resulatant amplitude is 2*0.06*cos(pi/6) = 0.104 m