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Sandbox Physics

Fluid dynamics · water-wave diffraction

Ripple Tank

A driven edge launches plane water waves from the left. Change wave speed, frequency, damping, and slit width to compare broad transmission with narrow-slit diffraction, then tap the transmitted field to move a local height probe.

Interactive modelRipple Tank
Simulation time0.00 s0.00\,\mathrm{s}
Wavelength λ\lambda0.50 m0.50\,\mathrm{m}
Slit ratio a/λa/\lambda1.101.10
Probe height η\eta0.00 mm0.00\,\mathrm{mm}
Courant number CC0.1020.102

Physics tutorial

Ripple Tank: how one opening redraws a wavefront

BackgroundIn the linear, small-amplitude limit, water height acts as a signed scalar field. A driven edge produces an approximately plane wave while a fixed barrier transmits only through its central opening.

Why it mattersThe same diffraction logic connects water, sound, and light; a ripple tank makes wavelength, boundaries, and wavefront geometry directly visible.

Start with the essentials

Focus question
Why does narrowing an opening make the transmitted wave spread through a wider angle?
One-sentence intuition
Spreading is controlled not by slit width aa alone, but by its ratio to wavelength λ\lambda.

Core mathematical model

Damped wave equation

∂2η∂t2+2β∂η∂t=c2∇2η\frac{\partial^2\eta}{\partial t^2}+2\beta\frac{\partial\eta}{\partial t}=c^2\nabla^2\eta

Spatial curvature restores the surface toward equilibrium while damping reduces amplitude during propagation.

Frequency, speed, and wavelength

λ=cf\lambda=\frac{c}{f}

At fixed wave speed, increasing drive frequency shortens wavelength and changes the relative size of the same opening.

Single-slit spreading scale

sin⁡θ∼λa\sin\theta\sim\frac{\lambda}{a}

An opening comparable to one wavelength spreads strongly sideways. This is a scaling guide, not a replacement for the full field.

Common difficulties

Color is signed water height

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

Better mental modelThe two colors represent crests and troughs. Energy depends on squared amplitude and cannot be read directly from the sign of the color.

A narrow slit does not create energy

Typical misconceptionWider spreading means the slit amplified the transmitted wave.

Better mental modelThe barrier redistributes transmitted energy by angle and reflects part of the incident wave; wider spreading does not mean larger total energy.

Run the experiment

  1. 01

    Begin with the wide opening

    Choose Wide slit and wait for the wavefront to cross.

    What to observe: The central transmitted front remains mostly plane, with strong bending confined near the two edges.
  2. 02

    Shrink the opening toward one wavelength

    Choose Narrow slit and compare the a/λa/\lambda readout.

    What to observe: Nearly circular fronts emerge behind the opening, and probes far to the side begin recording an oscillation.
  3. 03

    Shorten only the wavelength

    Keep the opening fixed and choose Short waves.

    What to observe: The same opening becomes wider relative to wavelength, so sideways spreading weakens.