(c) interference, coherence, path difference and phase difference

The idea

Interference is the superposition of waves from two or more sources, producing regions of maximum and minimum resultant displacement. Coherence means waves have a constant phase difference and the same frequency, which is needed for a stable interference pattern. Path difference is the difference in distance travelled by two waves from their sources to a point; when it equals a whole number of wavelengths the waves arrive in phase and interfere constructively, and when it equals an odd number of half wavelengths they arrive in antiphase and interfere destructively. Phase difference describes how far one wave is ahead of another in its cycle, measured in degrees or radians; a phase difference of 360° or 2π rad corresponds to one whole cycle.

What earns the marks

• Defines interference as the superposition of waves producing maxima and minima of resultant displacement.
• States that coherent waves have the same frequency and a constant phase difference.
• Defines path difference as the difference in distance travelled by two waves to a given point.
• Relates constructive interference to a path difference of a whole number of wavelengths.
• Relates destructive interference to a path difference of an odd number of half wavelengths.
• Defines phase difference as the fraction of a cycle by which one wave leads or lags another, measured in degrees or radians.

Common mistakes and how to put them right

• Confusing path difference with phase difference.

  Put it right: Path difference is a distance, while phase difference is an angle or fraction of a cycle.

• Thinking any two waves of the same frequency are coherent.

  Put it right: Coherence also requires a constant phase difference, which independent sources do not maintain.

• Using path difference equal to a half wavelength for constructive interference.

  Put it right: Constructive interference needs a whole number of wavelengths, while an odd number of half wavelengths gives destructive interference.

• Treating phase difference as always measured in degrees.

  Put it right: It may be measured in degrees or radians, and 360° equals 2π rad.

Exam tips

• Convert path difference to phase difference using the fraction of a wavelength, then express it in degrees or radians as required.
• Check whether the question asks for constructive or destructive conditions before substituting numbers.
• Remember that coherence requires both the same frequency and a constant phase difference.