Explain why two coherent sources of waves are necessary to observe a stable interference pattern.

IB DP Physics Standard Level (2023 syllabus) — C.3 Wave phenomena · Explain · 4 marks · View as Markdown

Written & reviewed by James Millett — Biology (Imperial College London), PGCE Science (University of Cambridge).

Two loudspeakers are connected to the same signal generator and placed a small distance apart. A student walking along a line parallel to the loudspeakers notices alternating regions of loud and quiet sound.

Model answer (4 marks)

Two coherent sources keep a constant phase difference, so the waves from each source arrive at a point with a fixed relative phase. For constructive interference the path difference must be an integer multiple of the wavelength (nλ), giving a maximum. For destructive interference the path difference must be a half‑integer multiple ((n+½)λ), giving a minimum. If the sources were not coherent the phase difference would change randomly with time, so the positions of maxima and minima would move and no stable interference pattern would be seen.

Examiner tips

Show that coherence gives a fixed phase difference
Explain the conditions for constructive and destructive interference
Mention that without coherence the pattern would shift
Use the terms ‘stable pattern’ and ‘constant phase difference’

Common mistakes

Confusing coherence with identical frequency only
Ignoring the need for a fixed phase difference
Not linking the path‑difference conditions to constructive/destructive interference

Mark scheme (4 marks)

Coherent sources maintain a constant phase difference (which may be zero) between the two waves.
For constructive interference to occur, the path difference from the two sources to a given point must equal a whole number of wavelengths (nλ), resulting in a maximum.
For destructive interference to occur, the path difference must equal a half-integer number of wavelengths ((n + ½)λ), resulting in a minimum.
If the sources were not coherent, the phase difference would vary randomly over time, so the positions of maxima and minima would shift continuously and no stable pattern would be observed.

Key terms in this question

coherent sources · stable interference pattern