A line or surface joining points on a wave that are in phase, such as all the crests.

What does it mean for two sources to be coherent?

They emit waves of the same frequency with a constant phase difference.

State the principle of superposition.

When waves meet, the resultant displacement is the sum of the displacements of the individual waves.

Define path difference.

The difference in the distances travelled by two waves from their sources to the same point.

What condition for path difference gives constructive interference (sources in phase)?

Path difference = nλ, where n is a whole number.

What is the phase difference when waves are in antiphase?

π rad (180°), or an odd multiple of π.

State the relationship between phase difference and path difference.

φ = 2π × (path difference) / λ, in radians.

What happens at a point of constructive interference?

The waves arrive in phase and the resultant amplitude is a maximum.

Why can two filament lamps not produce a stable interference pattern?

Their light has randomly changing phase differences, so the sources are not coherent and any pattern keeps moving.

Does coherent mean in phase?

No. Coherent means a constant phase difference, which need not be zero.

Superposition, interference and path differenceEdexcel International A Level Physics: Flashcards

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What is a wavefront?: A line or surface joining points on a wave that are in phase, such as all the crests.
What does it mean for two sources to be coherent?: They emit waves of the same frequency with a constant phase difference.
State the principle of superposition.: When waves meet, the resultant displacement is the sum of the displacements of the individual waves.
Define path difference.: The difference in the distances travelled by two waves from their sources to the same point.
What condition for path difference gives constructive interference (sources in phase)?: Path difference = nλ, where n is a whole number.
What condition for path difference gives destructive interference (sources in phase)?: Path difference = (n + ½)λ.
What is the phase difference when waves are in antiphase?: π rad (180°), or an odd multiple of π.
State the relationship between phase difference and path difference.: φ = 2π × (path difference) / λ, in radians.
What phase difference corresponds to a path difference of λ/4?: π/2 rad (90°).
What happens at a point of constructive interference?: The waves arrive in phase and the resultant amplitude is a maximum.
Why can two filament lamps not produce a stable interference pattern?: Their light has randomly changing phase differences, so the sources are not coherent and any pattern keeps moving.
Does coherent mean in phase?: No. Coherent means a constant phase difference, which need not be zero.

Exam questions on Superposition, interference and path difference

Two small loudspeakers, X and Y, are connected to the same signal generator and emit sound of wavelength 0.40 m in phase. A listener stands at a point P that is 3.00 m from X and 3.60 m from Y.
Explain, using ideas of path difference and phase, why the sound at P is not loud.2 marks
A progressive wave has a wavelength of 0.90 m and a frequency of 120 Hz. Two points A and B lie along the direction of travel of the wave, 0.15 m apart.
Calculate the minimum separation of two points on the wave that are exactly in antiphase.2 marks
Two identical dippers, S₁ and S₂, vibrate in phase at 8.0 Hz in a ripple tank, each producing circular waves of wavelength 2.5 cm. A point Q on the water surface is 20.0 cm from S₁ and 25.0 cm from S₂.
State what is meant by superposition, and explain why the dippers must be coherent to produce a stable interference pattern.3 marks

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Written by the Exaim team, led by Shaun Daswani (Head of Upper Secondary, Improve ME Institute; MSc Financial Mathematics, Imperial College London; BSc, UCL) and Jason Daswani (operational lead, Improve ME Institute; LSE).