Question

These two waves travel along the same string: y1 = (4.17 mm) sin(2.24?x - 300?t), y2 = (5.96 mm) sin(2.24?x - 300?t + 0.727?rad). What are (a) the amplitude and (b) the phase angle (relative to wave 1) of the resultant wave? (c) If a third wave of amplitude 5.20 mm is also to be sent along the string in the same direction as the first two waves, what should be its phase angle in order to maximize the amplitude of the new resultant wave?

Answer 1

The superpostion of the waves can be written as

which can be simplified to

Let

and

then

and

Therefore

a) The amplitude is

b) the phase angle of the resultant wave is

c) If another wave is sent along the string its phase angle should be

relative to the first wave in order to maximise the amplitude of the resultant wave