H2 Physics Interference: Include the Starting Phase Before Choosing a Maximum

In a public SGExams question, a student asks how to improve at superposition after revision and practice still leave the topic unfamiliar. A manageable starting point is two-source interference: decide the phase relationship at the observation point before choosing a formula for a maximum or minimum.

The 2026 SEAB H2 Physics 9478 syllabus includes superposition, coherence, phase difference, path difference and two-source interference. This article uses that revised syllabus as its reference. The original student discussion predates it; the discussion supplies the learning question, while the official document supplies the scope.

Add displacements, with their signs

Superposition combines the instantaneous displacements contributed by overlapping waves at the same point. If one wave contributes +3 mm and another contributes −2 mm at an instant, the resultant displacement is +1 mm. Adding their magnitudes would miss the direction information.

That instantaneous result is not automatically the resultant amplitude. Amplitude describes the maximum displacement over a cycle. To predict the repeating interference pattern, we need the relative phase of the arriving waves, as well as their individual amplitudes.

Convert extra distance into part of a cycle

For waves of wavelength λ, a path difference Δr corresponds to a propagation phase difference with magnitude 2πΔr/λ. One extra wavelength corresponds to a full cycle, while half a wavelength corresponds to half a cycle. Work with Δr/λ first if that makes the physical meaning easier to see.

For an original example, let two coherent, in-phase sources have wavelength 0.40 m. Their distances to point P are 1.20 m and 1.40 m. The path difference is 0.20 m, or half a wavelength. The waves therefore arrive in antiphase. With equal amplitudes at P, they cancel completely in the ideal model.

Include how the sources started

The familiar rule that an integer-wavelength path difference gives a maximum assumes the sources are in phase. If the sources begin in antiphase, a half-wavelength path difference can compensate for that initial difference. The waves can then arrive in phase.

Use the same distances and wavelength as before, but change the initial source phase difference to π radians. The additional half-cycle from propagation changes the relative phase by another half-cycle, giving an arrival phase equivalent to zero modulo 2π. This is constructive interference. The geometry has stayed the same; the source condition has changed the result.

Use a signed convention consistently

One explicit convention is to define the phase of wave i at P as ωt + φᵢ − krᵢ, where k = 2π/λ. Then the phase of wave 2 minus wave 1 at P is (φ₂ − φ₁) − k(r₂ − r₁). This makes both the initial source phase and the travel distances visible.

For maxima and minima, compare the resulting phase modulo 2π. A phase difference of zero modulo 2π gives in-phase arrival; π modulo 2π gives antiphase arrival. A different sign convention is equally usable if every term follows it. Do not mix an unsigned distance difference with a signed phase statement halfway through the working.

Check amplitude before claiming complete cancellation

Antiphase arrival gives a minimum, but zero resultant amplitude requires equal arriving amplitudes. If the amplitudes are A and 0.6A, the minimum amplitude is 0.4A, while the maximum is 1.6A. The waves can oppose each other without cancelling completely.

Where intensity is proportional to amplitude squared under the same physical conditions, an in-phase combination of two equal amplitudes A gives resultant amplitude 2A and intensity four times that of either wave alone. Simply adding the two individual intensities would give the wrong maximum for coherent waves.

Build a short decision routine

For each question, write the source phase condition, the two path lengths, their difference and the arriving amplitudes if supplied. Calculate the arrival phase, classify the interference, then answer the actual request about displacement, amplitude or intensity. Those quantities are related but are not interchangeable.

For practice, take one interference question from the JC H2 Physics collection. After solving it, change only the source phase or one amplitude and explain which conclusion changes. Check older papers against your syllabus. The numerical examples here are ideal wave calculations, not measurements from a speaker or optical experiment.