Why are there still lines behind a double slit?

Each slit acts as a new source (Huygens’ principle) and their waves add. Where the path difference to the two slits is an odd number of half wavelengths, crests always meet troughs and the water barely moves: these are nodal lines. Where it is a whole number of wavelengths the waves reinforce. Neighbouring bright directions satisfy sinθ = λ/d, so smaller spacing or longer wavelength spreads the pattern. The time-averaged intensity view makes it easiest to see.

How does slit width affect diffraction?

When the slit width a is close to or below the wavelength, the wave spreads out in almost every direction behind it; when the slit is much wider, the wave mostly goes straight through with slight bending at the edges. The first minimum is at sinθ = λ/a, and for a < λ there are no minima at all. That is why sound (wavelengths in meters) bends around doorways while light (under a micrometer) seems to travel in straight lines.

Why do water waves refract over shallow water?

In shallow water the wave speed is about √(gh), so shallower water is slower. When a wave enters shallow water at an angle, the part that enters first slows first and the wavefront turns toward the normal, following the same Snell’s law as light: sinθ₁/sinθ₂ = c₁/c₂. Going from slow to fast water beyond the critical angle, the wave is reflected completely: total internal reflection.

How does a Mach cone form?

When the source moves faster than the waves (v > c), it keeps outrunning its own wavefronts, and the circles emitted at different times are enveloped by a cone (a V shape in 2D) with half-angle sinα = c/v. Boat wakes and supersonic shock waves work the same way. For v < c you get the ordinary Doppler effect: shorter wavelength ahead, longer behind.

What numerical method does the simulation use?

The water height u obeys the 2D wave equation ∂²u/∂t² = c²∇²u − γ∂u/∂t. The tool advances it on a grid with an explicit centered-difference (leapfrog FDTD) scheme at Courant number 0.5 for stability. Walls are reflecting (∂u/∂n = 0) and the edges use a first-order Mur absorbing boundary to mimic open water. Sources drive a small Gaussian patch using the time derivative of an envelope so no DC offset builds up.

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🌊Ripple Tank Simulator - Double Slit, Diffraction, Refraction, Doppler, Standing Waves

Q: Why do water waves refract over shallow water?

In shallow water the wave speed is about √(gh), so shallower water is slower. When a wave enters shallow water at an angle, the part that enters first slows first and the wavefront turns toward the normal, following the same Snell’s law as light: sinθ₁/sinθ₂ = c₁/c₂. Going from slow to fast water beyond the critical angle, the wave is reflected completely: total internal reflection.

Q: How does a Mach cone form?

When the source moves faster than the waves (v > c), it keeps outrunning its own wavefronts, and the circles emitted at different times are enveloped by a cone (a V shape in 2D) with half-angle sinα = c/v. Boat wakes and supersonic shock waves work the same way. For v < c you get the ordinary Doppler effect: shorter wavelength ahead, longer behind.

Q: What numerical method does the simulation use?

The water height u obeys the 2D wave equation ∂²u/∂t² = c²∇²u − γ∂u/∂t. The tool advances it on a grid with an explicit centered-difference (leapfrog FDTD) scheme at Courant number 0.5 for stability. Walls are reflecting (∂u/∂n = 0) and the edges use a first-order Mur absorbing boundary to mimic open water. Sources drive a small Gaussian patch using the time derivative of an envelope so no DC offset builds up.

A virtual ripple tank that solves the 2D wave equation in real time in your browser. Choose single slit, double slit, grating, two point sources, refraction into a shallow region, a shallow-water lens, total internal reflection, standing waves in a pool, a moving source or a parabolic reflector, or draw and erase walls and place sources with your finger or mouse. The edges absorb waves; the time-averaged intensity view shows nodal lines clearly, and a probe plots the water height at one point over time.

Free · No sign-up · Runs in your browserLast updated: 2026-10-29

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How to use Ripple Tank Simulator

1Pick an experiment preset and adjust frequency, slit width, spacing or the shallow-region index
2Watch the live surface or switch to time-averaged intensity to see interference fringes
3Choose the wall, erase, source or probe tool and drag or tap in the tank
4Pause, step or reset the simulation and compare with the theory shown above (e.g. sinθ = λ/d)

FAQ

Why are there still lines behind a double slit?: Each slit acts as a new source (Huygens’ principle) and their waves add. Where the path difference to the two slits is an odd number of half wavelengths, crests always meet troughs and the water barely moves: these are nodal lines. Where it is a whole number of wavelengths the waves reinforce. Neighbouring bright directions satisfy sinθ = λ/d, so smaller spacing or longer wavelength spreads the pattern. The time-averaged intensity view makes it easiest to see.
How does slit width affect diffraction?: When the slit width a is close to or below the wavelength, the wave spreads out in almost every direction behind it; when the slit is much wider, the wave mostly goes straight through with slight bending at the edges. The first minimum is at sinθ = λ/a, and for a < λ there are no minima at all. That is why sound (wavelengths in meters) bends around doorways while light (under a micrometer) seems to travel in straight lines.
Why do water waves refract over shallow water?: In shallow water the wave speed is about √(gh), so shallower water is slower. When a wave enters shallow water at an angle, the part that enters first slows first and the wavefront turns toward the normal, following the same Snell’s law as light: sinθ₁/sinθ₂ = c₁/c₂. Going from slow to fast water beyond the critical angle, the wave is reflected completely: total internal reflection.
How does a Mach cone form?: When the source moves faster than the waves (v > c), it keeps outrunning its own wavefronts, and the circles emitted at different times are enveloped by a cone (a V shape in 2D) with half-angle sinα = c/v. Boat wakes and supersonic shock waves work the same way. For v < c you get the ordinary Doppler effect: shorter wavelength ahead, longer behind.
What numerical method does the simulation use?: The water height u obeys the 2D wave equation ∂²u/∂t² = c²∇²u − γ∂u/∂t. The tool advances it on a grid with an explicit centered-difference (leapfrog FDTD) scheme at Courant number 0.5 for stability. Walls are reflecting (∂u/∂n = 0) and the edges use a first-order Mur absorbing boundary to mimic open water. Sources drive a small Gaussian patch using the time derivative of an envelope so no DC offset builds up.

Features

Leapfrog FDTD solution of the 2D wave equation with Mur absorbing edges and a thin sponge
11 classic experiment presets with the matching formulas and values
Draw and erase walls, add or remove sources and move the probe, all touch-friendly
Slow shallow regions for refraction, lens focusing and total internal reflection
Moving source for the Doppler effect and supersonic Mach cone
Grid size adapts to screen width and measured frame rate, so it stays smooth on phones

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