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Physics OscillationsIntermediateStarter track

Concept module

Wave Interference

Superpose two coherent sources, trace their path difference to phase difference, and watch bright and dark regions emerge on the same live screen.

Interactive lab

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Starter track

Step 7 of 90 / 9 complete

Waves

Earlier steps still set up Wave Interference.

1. Simple Harmonic Motion2. Wave Speed and Wavelength3. Sound Waves and Longitudinal Motion4. Pitch, Frequency, and Loudness / Intensity+5 more steps

Previous step: Doppler Effect.

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Why it behaves this way

Explanation

Wave interference is what happens when two oscillating disturbances reach the same place at the same time. The result is not decided by one wave alone. It depends on how their amplitudes and phases combine at that point.

This lab keeps the source spacing and screen distance fixed so you can focus on one honest chain of ideas: geometry sets path difference, path difference sets phase difference, and phase difference controls whether the screen point brightens, dims, or lands somewhere in between.

Key ideas

01Constructive interference happens when the total phase difference is close to a whole-number multiple of 2π, so the arrivals reinforce.

02Destructive interference happens when the total phase difference is close to an odd multiple of π, so equal-amplitude arrivals can nearly cancel.

03Changing wavelength or probe position changes the path-difference phase term, while changing source phase shifts the whole pattern without moving the geometry.

Frozen walkthrough

Step through the frozen example

Frozen walkthrough

These examples read the current probe geometry and source settings directly from the live state, so the steps stay tied to the same bright or dark region you are inspecting.

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Frozen valuesUsing frozen parameters

For the current probe position at y = 0.8\,\mathrm{m}, what total phase difference reaches the screen point?

y_{p}

Probe height

0.8 m

Δ r

Path difference

0.26 m

λ

Wavelength

1.6 m

ϕ_{0}

Source phase offset

0 rad

1. Identify the relation

Use

Δ ϕ = \frac{2 π Δ r}{λ} + ϕ_{0}

2. Substitute the live geometry

Δ ϕ = \frac{2 π ( 0.26 )}{1} .6 + 0

3. Wrap it to the useful comparison angle

That gives a wrapped phase difference of

1.02 rad

, or about 0.16 wavelengths of extra travel before the source phase offset is added.

Current phase difference

Δ ϕ = 1.02 rad

The phase difference is between the bright and dark limits, so the probe shows only partial reinforcement.

Common misconception

If the path lengths are different, the interference must always be destructive.

Different path lengths only matter through the phase they produce relative to the wavelength.

A nonzero path difference can still be constructive if it equals one wavelength, two wavelengths, or another whole-number multiple.

Mini challenge

You are sitting on a bright region and you are not allowed to change either source amplitude. What is one reliable way to turn that same probe point dark?

Make a prediction before you reveal the next step.

Decide whether changing probe position, wavelength, or source phase would work and why.

Check your reasoning against the live bench.

Shift the total phase difference by about π, either by moving the probe so the path difference changes by roughly λ/2 or by adding a source phase offset of π.

Destructive interference depends on the total phase difference, not on one control in isolation. Geometry and source phase both feed the same phase sum.

Quick test

Graph reading

Question 1 of 4

Use geometry, phase, and amplitude together. Each question asks what the screen point must do, not what a formula looks like in isolation.

A bright peak on the screen pattern means which condition is most nearly true at that screen height?

Use the live bench to test the result before moving on.

Accessibility

The simulation shows two coherent sources on the left, a shared screen on the right, and one adjustable probe point on that screen. Two wavy paths run from the sources to the probe so the user can compare the path lengths, the local phase split, and the resulting probe motion in the same picture.

The probe point also appears on a vertical screen strip that brightens or darkens according to the time-averaged resultant amplitude. Optional overlays label the path difference, the resultant envelope, and a phasor-style phase map.

Graph summary

The probe-motion graph plots Source A, Source B, and the live resultant at one selected screen point as functions of time.

The screen-pattern graph plots relative intensity against screen height, so it stays position-based even while the time rail continues to inspect the instantaneous probe motion.

Keep this idea moving

Open the next concept, route, or track only when you want the current model to widen into a larger branch.

Single-slit spreadOptics