The diagram shows two sources of waves S1 and S2. The sources oscillate with a phase difference of 180°.

Question 23

The diagram shows two sources of waves S1 and S2. The sources oscillate with a phase difference of 180°.

The sources each generate a wave of wavelength 2.0 cm. Each source produces a wave that has amplitude x0 when it reaches point P.

What is the amplitude of the oscillation at P?

A 0                  B x0 / 2                        C x0                       D 2x0

Reference: Past Exam Paper – June 2018 Paper 11 Q26

Solution:

Answer: A.

The wave from each source travels along a different path to reach point P.

path difference between S₁P and S₂P = 13 – 5 = 8 cm

The wavelength of the wave is 2.0 cm.

The path difference of 8 cm is equivalent to (8 / 2 =) 4 wavelengths.

If the waves from the sources were in phase, this phase difference would imply that constructive interference occurs at P.

Recall the conditions for interference when waves are emitted in phase.

Constructive interference: path difference = nλ         (where n = 0, 1, 2, 3 …)

Destructive interference: path difference = nλ / 2

However, the question tells us that the waves from the sources are out of phase (that is, there is a phase difference of 180° between the oscillations of the two sources). This reverse the conditions for interference.

 
Thus, in this case, destructive interference occurs at P. The waves are out of phase at P, and the resultant displacement is 0.