Two sinusoidal waves of the same frequency are to be sent in the same direction

Question

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 5.0 mm, the other 10.6 mm. (a) What phase difference ?1 between the two waves results in the smallest amplitude of the resultant wave? (b) What is that smallest amplitude? (c) What phase difference ?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 (?1 - ?2)/2?
Give your answers in mm, where applicable.

Explanation / Answer

(b) the resultant of both ym = ym2 ~ym1 = 8-5 = 3mm

(e) resultant amplitude if phase angle =(?1-?2)/2

                                                        = ?(8)2+ (5)2

                                                =9.4mm( resultant amplitude )

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