Wave simulator

A wave simulator lets you see waves spread out, overlap and interfere. Our Wave Interference Simulator is a ripple tank: send waves from two sources, through a double slit or through a single slit, and watch bright and dark bands form where the waves add up or cancel. It reads the path difference at any point, and gives the fringe spacing and the angle of the first minimum.

It opens on two sources 6 cm apart making waves 2 cm long, with the nodal lines, where the waves cancel, drawn on.

Try it

Wave Interference Simulator

Overlap waves in a ripple tank to see interference and diffraction

Open the simulatorGo to its page

How to use the wave simulator

1. Under Tank, choose Two sources, Double slit or Single slit.
2. Set the Wavelength (1 to 6 cm), the Separation of the sources or slits, the Slit width, the Phase difference between the sources, and the Distance to screen.
3. Show the tank as Ripples or as Intensity, and turn the Nodal lines on or off.
4. Press play under Run to watch the waves move.
5. Drag the probe to read the distances r₁ and r₂ to the two sources, the path difference, and whether the waves meet constructively or destructively there.

The readouts also give the frequency, the fringe spacing (or, for a single slit, the width of the central maximum) and the angle of the first minimum. Waves in the tank travel at 4 cm/s, so a 2 cm wavelength has a frequency of 4 ÷ 2 = 2 Hz, from v = fλ. Practice and help sets interference and diffraction questions with worked solutions.

Interference and path difference

Where two waves meet, they add. If they arrive in step, crest on crest, they reinforce: constructive interference. If they arrive half a wavelength out of step, crest on trough, they cancel: destructive interference. Which happens depends on the path difference, r₂ − r₁:

Example 1: reading the probe

In the opening set-up, put the probe at (10, 0), straight ahead of the midpoint. Both sources are the same distance away, so the path difference is 0 and the simulator says constructive. Move it to (10, 3.7) and the path difference is 0.986 cm, 0.493 wavelengths, close to ½λ, so it says destructive: the probe is on a nodal line.

Try the wave equation in the course, then press Mark:

Double slit and fringe spacing

Light or water waves through two narrow slits make evenly spaced bright fringes on a screen. For slits a distance d apart, a screen L away and wavelength λ, the fringe spacing is:

Example 2: fringe spacing

With λ = 2 cm, d = 6 cm and L = 22 cm, the opening set-up gives w = 2 × 22 ÷ 6 = 7.33 cm, as the simulator shows. Choose Double slit with λ = 3 cm and d = 8 cm, and it gives 3 × 22 ÷ 8 = 8.25 cm. Longer waves or closer slits spread the fringes further apart. Our diffraction grating guide covers many slits at once.

Single slit diffraction

Waves spread out after passing through a gap. The narrower the gap compared with the wavelength, the more they spread. For a single slit of width a, the first dark band is at sin θ = λ/a.

Example 3: the first minimum

Choose Single slit with λ = 2 cm and a slit 4 cm wide. Then sin θ = 2 ÷ 4 = 0.5, so the first minimum is at θ = 30.0°, and the central maximum is 22.0 cm wide on the screen. Make the slit 2 cm wide with λ = 3 cm and λ/a is more than 1: there is no minimum at all, and the simulator says the waves spread over the whole tank.

Phase difference

If the two sources are out of step, the whole pattern shifts. Set the phase difference to 180° and the point straight ahead, where the path difference is 0, becomes destructive instead of constructive. Back at the probe from the opening set-up, 1.04 wavelengths of path difference now gives destructive interference. The first-minimum readout moves with the phase: 9.59° at 0°, 4.78° at 90°, and 0° at 180°, where the minimum sits straight ahead.

What the simulator does not show

• A ripple tank only. It shows waves spreading over water from sources and slits. It has no single wave travelling along a rope, and no sound waves as compressions and rarefactions. Our transverse and longitudinal waves guide and sound waves guide cover those.
• No reflection off walls or standing waves. Waves leave the tank without reflecting back.
• Water-wave scale. Wavelengths are in centimetres, but the same rules apply to light and sound.

Common mistakes

• Using the wrong path difference for destructive interference. It is an odd number of half wavelengths, ½λ, 1½λ, not 1λ.
• Forgetting the phase. The rules above are for sources in phase. Sources in antiphase swap constructive and destructive.
• Thinking a wider slit spreads waves more. Narrower gaps diffract more, most when the gap is about one wavelength.
• Mixing units in w = λL/d. Use the same unit for λ, L and d, or convert to metres.

Practise waves in a short timed paper

Interference, path difference and the double slit come up in A-level Physics: Year 1 practice in the UK, and in College Physics (Calculus Based) in the US. Each daily paper is a short timed paper of 8 questions worth 25 to 35 marks, and the papers mix topics. For v = fλ on its own, use the Wave Speed Calculator.

Read next

Physics · Waves and lightWhat is a wave? Types, amplitude, frequency and wavelengthA wave carries energy from place to place without carrying matter. Learn the types of wave, amplitude, frequency, wavelength, v = fλ and how to draw one.