Interference Pattern
Make the pattern two or more sets of circular waves draw where they overlap, like ripples from two stones dropped in a pond. Place 1 to 6 point sources in a row or on a circle, set their spacing in wavelengths, the wavelength on the page, a phase step between them and the strength of the second source. The tool adds the waves exactly at every point: where they arrive in step the pattern is bright, where they arrive half a wave apart it is dark. Show the brightness in six shades or two colours, the wave crests at one moment, or line drawings: for two sources the darkest and brightest lines, which are hyperbolas around the sources. Download a PDF with the wavelength printed at the length you type, a 300 DPI PNG or an SVG. Nothing is uploaded.
100% private — everything runs in your browser. Everything runs in your browser; nothing is uploaded.
Print at 100% (Actual size): the wavelength is printed at the length you type, and the pattern fills the page. The SVG holds the shades as rectangles and every line as a path.
Sources
Look
Page
Runs in your browser with our own code: nothing you type is uploaded or saved. Every shade and line is worked out from the sum of the waves by our own code. You may use what you make here, including commercially, with no credit needed.
How to make and print an interference pattern
- Pick a preset, or set the number of sources, their spacing and the wavelength.
- Add a phase step or make the second source weaker if you like.
- Choose brightness shades, two colours, lines or wave crests, and the colours.
- Check the line count and the settings under the preview.
- Download the PDF and print at 100% (Actual size), or the PNG or SVG.
What you can use it for
- Physics lessons on two-source interference and path difference
- Worksheets: find the bright and dark lines
- Posters, cards and wall art
- Laser, plotter and vinyl art from the SVG lines
- Pattern ideas for textiles and backgrounds
- Comparing with a ripple tank demonstration
The 16 presets
| Preset | Sources | Spacing | Wavelength | Phase step | Strengths | Look | Darkest lines (two sources) |
|---|---|---|---|---|---|---|---|
| Two sources in step, 4 wavelengths apart: brightness | 2, row | 4 λ | 8 mm | 0° | equal | brightness, 6 shades | 8 |
| Two sources: the darkest lines (hyperbolas) | 2, row | 4 λ | 8 mm | 0° | equal | lines | 8 |
| Two sources: darkest and brightest lines | 2, row | 4 λ | 8 mm | 0° | equal | lines | 8 |
| Two sources 8 wavelengths apart: brightness | 2, row | 8 λ | 6 mm | 0° | equal | brightness, 6 shades | 16 |
| Two sources 1.5 wavelengths apart: brightness | 2, row | 1.5 λ | 10 mm | 0° | equal | brightness, 6 shades | 2 |
| Two sources half a wave out of step (180°) | 2, row | 4 λ | 8 mm | 180° | equal | lines | 7 |
| Two sources a quarter wave out of step (90°) | 2, row | 4 λ | 8 mm | 90° | equal | brightness, 6 shades | 8 |
| Two sources, second at half strength | 2, row | 4 λ | 8 mm | 0° | 1 : 0.5 | brightness, 6 shades | 8 |
| Two sources: bright and dark in two colours | 2, row | 5 λ | 8 mm | 0° | equal | two colours | 10 |
| Two sources: wave crests at one moment | 2, row | 4 λ | 8 mm | 0° | equal | wave crests | 8 |
| One source: wave crests (rings) | 1 | – | 10 mm | 0° | equal | wave crests | – |
| Three sources in a row, 3 wavelengths apart | 3, row | 3 λ | 8 mm | 0° | equal | brightness, 6 shades | – |
| Four sources in a row, 2 wavelengths apart | 4, row | 2 λ | 7 mm | 0° | equal | brightness, 6 shades | – |
| Three sources on a circle (radius 3 wavelengths) | 3, circle | 3 λ | 8 mm | 0° | equal | brightness, 6 shades | – |
| Six sources on a circle: half-brightness lines | 6, circle | 3 λ | 8 mm | 0° | equal | lines | – |
| Six sources in a row, phase step 60° | 6, row | 1 λ | 8 mm | 60° | equal | brightness, 6 shades | – |
Spacing is between neighbouring sources in a row, or the radius of the circle. Line counts are worked out by the tool and checked against the lines it traces.
Darkest and brightest lines for two sources
| Spacing (wavelengths) | Darkest lines, in step | Brightest lines, in step | Darkest lines, 180° apart | Brightest lines, 180° apart |
|---|---|---|---|---|
| 0.5 | 0 | 1 | 1 | 0 |
| 1 | 2 | 1 | 1 | 2 |
| 1.5 | 2 | 3 | 3 | 2 |
| 2 | 4 | 3 | 3 | 4 |
| 3 | 6 | 5 | 5 | 6 |
| 4 | 8 | 7 | 7 | 8 |
| 5 | 10 | 9 | 9 | 10 |
| 8 | 16 | 15 | 15 | 16 |
| 12 | 24 | 23 | 23 | 24 |
| 20 | 40 | 39 | 39 | 40 |
In step, the line straight between the two sources is always a brightest line; half a wave out of step, it is a darkest line.
Where the fringes are (two sources in step, 8 mm wavelength)
| m | Brightest where the paths differ by | Darkest where the paths differ by | Brightest, distance from the midpoint along the line between the sources | Darkest, distance from the midpoint |
|---|---|---|---|---|
| 0 | 0 λ | 0.5 λ | 0 mm | 2 mm |
| 1 | 1 λ | 1.5 λ | 4 mm | 6 mm |
| 2 | 2 λ | 2.5 λ | 8 mm | 10 mm |
| 3 | 3 λ | 3.5 λ | 12 mm | 14 mm |
| 4 | 4 λ | 4.5 λ | 16 mm | 18 mm |
Along the line between the sources the path difference is twice the distance from the midpoint, so bright and dark places alternate every quarter wavelength (2 mm here).
What prints
| Download | What is in it |
|---|---|
| The pattern filling the page at real size, vector, with the settings, the line count and a check bar | |
| PNG 300 DPI | The same sheet as a picture |
| SVG | The shades as rectangles and every line as a path, at the printed size |
For a cutter that needs DXF, use SVG to DXF.
Which tool to use
| You want | Use |
|---|---|
| Fringes from waves spreading out of one to six points | Interference Pattern (this page) |
| Still lines of a vibrating square plate | Chladni Pattern |
| Two line or dot screens laid over each other | Moiré Pattern Generator |
| Wavy section dividers for a website | SVG Wave Generator |
| Plain grid paper for your own drawings | Graph Paper |
Other tools: the Moiré Pattern Generator overlays two screens, the SVG Wave Generator makes website dividers and Graph Paper prints grids.
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Frequently asked questions
What is an interference pattern?
When two waves of the same kind and frequency meet, they add up. Where they arrive in step they make a bigger wave (constructive interference); where one arrives half a wave after the other they cancel (destructive interference). Seen from above, two sets of circular waves make a fan of bright and dark lines between and around the sources.
How does the tool work it out?
Each source sends out a circular wave. At every point the tool adds the waves from all sources as complex numbers, using the distance to each source, the wavelength, the phase and the strength, and takes the squared size of the sum as the brightness (1 = brightest possible). Our tests check the shades and lines against a separate calculation and, for two equal sources, against the exact formula brightness = cos² of half the phase difference.
Where are the bright and dark lines?
For two sources in step, a point is brightest where its distances to the two sources differ by a whole number of wavelengths (0, 1, 2 …) and darkest where they differ by a whole number and a half (½, 1½ …). On the line between the sources the bright and dark places alternate every quarter of a wavelength. The table below lists them for an 8 mm wavelength.
Why are the lines curved like that?
All the points whose distances to two fixed points differ by the same amount lie on a hyperbola, with the two sources as its foci. So every darkest and brightest line is one branch of a hyperbola, and far from the sources they straighten out into a fan.
How many dark lines are there?
For two sources in step d wavelengths apart, there is one darkest line for every value (m + ½) smaller than d: 8 lines at 4 wavelengths apart. A phase step shifts the whole fan sideways; at 180° bright and dark swap places. The table below gives the counts, and our tests count the lines actually traced.
What does the second source strength do?
If one source is weaker, the waves never fully cancel: the darkest lines stay in the same places, but they are only as dark as the difference between the two waves allows. With a strength of 0.5 the darkest lines are at one ninth of full brightness.
Is this the same as a moiré pattern?
No. A moiré pattern comes from laying two sets of printed lines or dots over each other, and the stripes you see come from where the lines cover each other. This tool adds waves, with their phase, so the fringes follow the path difference to the sources. The two can look alike, but they are made in different ways.
What is left out?
The tool keeps every wave at full strength everywhere, a simplified picture: real waves fade as they spread. It draws point sources only, not slits.
Is it free?
Yes. There is no sign-up, no watermark and no limit.
Is anything uploaded?
No. Every line, dot and shade is worked out by JavaScript in your browser. Nothing you type is sent anywhere or saved when you close the page.