Fluid dynamics · water-wave diffraction

Ripple Tank

Why does narrowing an opening spread the transmitted wave through a wider angle? How far a wave spreads depends on the width of the opening compared with the wavelength. A wide gap lets a nearly straight beam through. As the gap shrinks toward one wavelength, the wave that gets through spreads out from it almost like a new wave from a single point.

Rotate around the water surface, drawn with its height exaggerated, then look at the same field from above and read the probe history. Compare one or two point sources, one or two slits, a disk obstacle, walls that hold the height fixed, rigid walls and outgoing boundaries. You can pause, step or switch off the drive without erasing the waves.

Wave-equation energy proxy (not joules) $0\,\mathrm{m^4\,s^{-2}}$

Simulation time $0.0000\,\mathrm{s}$

Nominal wavelength

\lambda_0

$0.50\,\mathrm{m}$

Resolved slit ratio

a_h/\lambda_0

$1.04$

Grid opening

a_h

$0.522\,\mathrm{m}$

Probe height

\eta

$0.000\,\mathrm{mm}$

Field height RMS

\eta_{\mathrm{rms}}

$0.000\,\mathrm{mm}$

Probe position

(x_p,y_p)

$(3.94,\,1.52)\,\mathrm{m}$

Courant number

C

$0.102$

Controls

Shape the diffraction field

Drive the sourceSwitch off to observe existing waves without clearing the field.Probe historyThe trace covers a fixed eight-second window, sampled at every solver step.Solver gridReveal the numerical mesh behind the field.Source: plane / single / double

\text{plane}

Geometry: single slit / double slit / open / disk

\text{single slit}

Wall: fixed height / rigid / outgoing

\text{outgoing}

Source amplitude

A

3\,\mathrm{mm}

Requested double-slit separation

d

1.20\,\mathrm{m}

Outgoing-boundary absorption

s

1

Source frequency

f

1.50\,\mathrm{Hz}

Wave speed

c

0.75\,\mathrm{m\,s^{-1}}

Damping

\beta

0.30\,\mathrm{s^{-1}}

Requested slit width

a

0.55\,\mathrm{m}

Each double-slit opening is at most 0.9 m wide. The separation is limited so that a solid divider stays between the slits and both fit in the tank. The opening readout gives the actual width of one slit on the grid. At zero absorption the edges fall back to an approximate reflecting boundary that copies the edge values. The energy shown is a stand-in computed from the wave equation, not a calibrated fluid energy.

To move the probe, click in the transmitted field, or focus the canvas and use the arrow keys. Moving it restarts only the probe trace. Reset and presets keep the probe where it is and leave playback running or paused as before.

This Lab solves the damped, linear two-dimensional wave equation $\frac{\partial^2\eta}{\partial t^2}+2\beta\frac{\partial\eta}{\partial t}=c^2\nabla^2\eta$ . A Dirichlet wall fixes the height, and a Neumann wall fixes its normal gradient. In absorbing mode, the outer walls use first-order Mur outgoing conditions and a sponge layer, while internal obstacles have zero normal flux. Some reflection remains for waves that arrive at an angle and at the corners. The 3D display exaggerates the same height 25 times. Wave breaking, viscosity, dispersion and three-dimensional free-surface motion are not modeled.

Physics tutorial

Ripple Tank: how one opening redraws a wavefront

BackgroundIn the linear, small-amplitude limit, water height is a signed scalar field. A driven line launches an approximately plane wave. Barrier nodes are pinned to zero height except at the opening; this is not the no-through-flow boundary of a full fluid tank.

Why it mattersWater waves, sound and light all diffract in the same way. A ripple tank lets you see the wavelength, the boundaries and the shape of the wavefronts directly.

Start with the essentials

Focus question: Why does narrowing an opening make the transmitted wave spread through a wider angle?
One-sentence intuition: How far the wave spreads depends on the ratio of the slit width $a$ to the wavelength $\lambda$ , not on the width alone.

Core mathematical model

Damped wave equation

\frac{\partial^2\eta}{\partial t^2}+2\beta\frac{\partial\eta}{\partial t}=c^2\nabla^2\eta

Wherever the surface is curved, it is pulled back toward flat, and damping makes the amplitude shrink as the wave travels.

Frequency, speed, and wavelength

\lambda_0=\frac{c}{f}

The readout gives the nominal wavelength of the undamped model; damping and the finite grid change how the waves actually travel. At fixed wave speed, a higher frequency shortens this wavelength.

Opening width on the grid

a_h=N_{\mathrm{open}}\Delta y,\qquad \Delta y=\frac{3}{69}\,\mathrm{m}

The opening can only change by whole grid nodes. The drawing and the readout use the same mask as the solver. The width counts the intervals covered by open nodes, and the wall position is not resolved more finely than the grid.

How the probe keeps time

t_n=n\Delta t,\qquad \Delta t=\frac{1}{240}\,\mathrm{s}

Each solver step records the height with a timestamp, and the plot always spans eight seconds. The screen frame rate does not change the sampling. When the display stalls, each frame advances only a limited amount, so simulation time can fall behind real time.

How widely a single slit spreads the wave

\sin\theta\sim\frac{\lambda}{a}

An opening about one wavelength wide spreads the wave strongly sideways. This is a rough scaling rule; the full wave field gives the details.

Common difficulties

Color shows height above or below the flat surface

Typical misconceptionThe brighter color always means more energy and the darker color means no wave.

Better mental modelThe two colors mark crests and troughs. Energy depends on the square of the amplitude, so you cannot read it from which color you see.

A narrow slit does not create energy

Typical misconceptionWider spreading means the slit amplified the transmitted wave.

Better mental modelThe barrier spreads the transmitted energy over more angles and reflects part of the incoming wave. Spreading wider does not mean more total energy.

Run the experiment

01
Start with a wide slit
Choose Wide slit and wait for the wavefront to cross.
What to observe: The middle of the transmitted front stays mostly flat, and it bends strongly only near the two edges.
02
Narrow the slit to about one wavelength
Choose Narrow slit and compare the $a_h/\lambda_0$ readout.
What to observe: Nearly circular fronts spread out behind the opening, and a probe placed far to the side starts recording an oscillation.
03
Measure while paused
Pause, then press Advance half a second until the transmitted waves reach the probe. Move the probe, switch off Drive the source and keep advancing.
What to observe: Moving the probe starts a new trace at the new spot without clearing the waves. After the drive stops, the waves already in the tank keep travelling and fading. One step advances the solver by exactly one step.
04
Shorten only the wavelength
Keep the opening fixed and choose Short waves.
What to observe: The same opening is now wider compared with the wavelength, so the wave spreads less to the sides.

Conceptual inspiration: FluidMotion. Original simulations and graphics; the model limits are described above.