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Wave Interference

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What you learned

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Key takeaway

  1. Bright and dark regions come from two waves overlapping at the same screen point, not from one wave disappearing.
  2. Path difference and Source phase offset both feed the total phase difference that decides whether arrivals reinforce or cancel.
  3. Complete cancellation needs opposite phase and matched amplitudes; unequal sources leave leftover motion.

Common misconception

A dark band means one source stopped reaching that point.

A dark fringe is produced by two waves arriving at the same point with nearly opposite phase.

Use path difference first, then convert that extra travel into the phase difference that decides bright or dark.

  1. Path difference

    Read as: path difference equals distance from source two minus distance from source one

    The extra distance one arrival travels before the two waves meet at the same screen point.

  2. Total phase difference

    Read as: total phase difference equals two pi times path difference over wavelength, plus source phase offset

    How far out of step the two arrivals are at the screen point, combining path difference with any source phase offset.

Why it behaves this way

Explanation

Keep the Path-difference guide and Combined-amplitude guide visible, and fix the probe at one screen height. The probe graph traces Source A, Source B, and their combined wave at that one point over time, while the pattern graph shows the long-run brightness at every screen height. A bright band is not one frozen crest in time. It is a position where the combined wave stays large cycle after cycle.

The key quantity is the total phase difference: how far out of step the two arrivals are when they meet. The Path-difference guide shows where part of it comes from. When you move the probe, r1 and r2 change, so the extra distance Delta r changes too. If Delta r is 0, one wavelength, two wavelengths, and so on, equal sources reinforce. If Delta r is about half a wavelength, one and a half wavelengths, and so on, equal sources arrive nearly opposite in phase and the screen becomes dark.

The source controls let you test which part of that phase difference changed. Source phase offset can turn the center from bright to dark without changing the geometry at all, because it adds phase directly. Changing Wavelength also leaves the geometry alone, but it changes how much phase each meter of path difference represents, so the fringes squeeze together or spread apart on the pattern graph.

One last check matters before you trust a dark band: destructive phase does not guarantee a perfect zero unless the source amplitudes are matched. If Source A and Source B are unequal, the combined-amplitude guide—the outline of how large the added wave can get—does not fully close. The same idea later reappears in standing waves, noise cancellation, and optical interference. Next, make a dark band by moving Probe height, return to the center and darken it again with Source phase offset alone, then unbalance the amplitudes and watch the null fill back in.

Key ideas

01The pattern graph shows brightness across the whole screen, while the probe graph traces the wave at one chosen point over time.
02A bright or dark band depends on total phase difference: whole-wavelength path differences reinforce, while half-wavelength differences cancel for equal sources.
03A perfect dark fringe needs both destructive phase and equal source amplitudes.

Worked examples

Worked examples

Open examples when you want to see the same idea walked through step by step.

Frozen walkthrough

Step through the frozen example

Frozen walkthrough
These examples use the live probe position and source settings, so each calculation stays tied to the bright or dark region you are actually inspecting.

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Example 1 of 2
Frozen valuesUsing frozen parameters

For the current probe position at y = 0\,\mathrm{m}, what total phase difference reaches this screen point?

Probe height

0 m

Path difference

0 m

Wavelength

1.6 m

Source phase offset

0 rad

1. Identify the relation

Use .

2. Substitute the live path difference

.

3. Reduce it to an equivalent comparison angle

That gives a wrapped phase difference of , or about 0 wavelengths of extra travel before the source phase offset is added.

Current phase difference

The phase difference is close to a whole-number multiple of 2pi, so the probe sits on a bright region where the two arrivals reinforce.

Quick test

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Accessibility

Accessibility

Open the text-first descriptions when you need the simulation and graph translated into words.

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 combined amplitude. Optional overlays label the path difference, the combined-amplitude guide, and an arrow diagram for phase addition.

Graph summary

The probe graph plots Source A, Source B, and their combined wave at one selected screen point as functions of time.

The screen-pattern graph plots average brightness against screen height, so it stays position-based even while the time rail is used to inspect the instantaneous probe motion.

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Starter track

Step 7 of 9

Waves

Wave Interference appears later in this track, so it is cleaner to start from the beginning first.

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