---
title: "How One Opening Redraws a Water Wave Interactive Lab | Sandbox Physics"
description: "Change the source, open two slits, and compare reflecting with outgoing walls. Why does narrowing an opening spread the transmitted wave through a wider angle?"
canonical_url: "https://sandboxphysics.com/labs/ripple-tank/"
language: "en"
page_type: "lab"
alternate_languages:
  zh-CN: "https://sandboxphysics.com/zh/labs/ripple-tank/"
---

Fluid dynamics · water-wave diffraction

# Ripple Tank

Orbit the exaggerated height surface, then inspect the same field from above and sample its probe history. Compare one or two point sources, one or two slits, a disk obstacle, fixed-height reflection, rigid-wall reflection, and outgoing boundaries. Pause, step, or switch off the drive without erasing the waves.

> Interactive simulation: open this page in a web browser to change the parameters and run the model.

This Lab solves the damped, linear two-dimensional wave equation $\frac{\partial^2\eta}{\partial t^2}+2\beta\frac{\partial\eta}{\partial t}=c^2\nabla^2\eta$. Dirichlet fixes height and Neumann fixes its normal gradient. Absorbing mode uses first-order Mur outgoing conditions and a sponge at the outer walls, with zero-normal-flux internal obstacles. Oblique incidence and corners still reflect. The 3D display exaggerates the same height by 25 times; no breaking, viscosity, dispersion, or three-dimensional free-surface dynamics are solved.

Physics tutorial

## Ripple Tank: how one opening redraws a wavefront

**Background** In 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 matters** The 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 $a$ alone, but by its ratio to wavelength $\lambda$.

### Core mathematical model

#### Damped wave equation

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

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

#### Frequency, speed, and wavelength

$$
\lambda_0=\frac{c}{f}
$$

The readout is the nominal wavelength of the undamped model; damping and the finite grid alter actual propagation. At fixed speed, higher frequency shortens this reference scale.

#### Grid-resolved opening

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

The opening changes in discrete nodes. Its drawing and readout share the solver mask; the width describes the intervals represented by open nodes, not a sub-grid wall location.

#### The physical probe clock

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

Every solver step records a timestamped height in a fixed eight-second plot. Display frame rate does not change sampling. Per-frame advancement is capped during stalls, so simulation time need not follow wall-clock time.

#### Single-slit spreading scale

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

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 misconception** The brighter color always means more energy and the darker color means no wave.

**Better mental model** The 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 misconception** Wider spreading means the slit amplified the transmitted wave.

**Better mental model** The 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 $a_h/\lambda_0$ readout.

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

3. 03

   #### Measure while paused

   Pause and advance half a second at a time until transmitted waves reach the probe. Move the probe, switch off Drive the source, and keep advancing.

   **What to observe:** Moving starts a trace at the new location without clearing waves. After the drive stops, existing waves continue travelling and decaying. One step advances exactly one solver step.

4. 04

   #### 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.

Physical conclusion

Diffraction is not a ray turning at an edge; it is the whole restricted wavefront propagating anew beyond an opening.

Conceptual inspiration: [FluidMotion](http://www.bugman123.com/FluidMotion/index.html). Original simulations and graphics; the model limits are described above.

Waves & optics · Starter path

## From one ray to interference measurement

Start with refraction, find where the ray picture stops working, then use interference to measure tiny distances.

[Start here → **Optical Boundary Explorer** Turn the incident angle and watch reflected and transmitted power trade off. Then switch to the critical-angle scene. Observe · 11 min](https://sandboxphysics.com/labs/optical-boundary-explorer/)

1. [1 Optical Boundary Explorer](https://sandboxphysics.com/labs/optical-boundary-explorer/)
2. [2 Rainbow Caustic Observatory](https://sandboxphysics.com/labs/rainbow-laboratory/)
3. [3 Camera Obscura](https://sandboxphysics.com/labs/camera-obscura/)
4. [4 Coherent Wave Composer](https://sandboxphysics.com/labs/coherent-wave-composer/)
5. [5 Young Double-Slit Bench](https://sandboxphysics.com/labs/young-double-slit-bench/)
6. [6 Michelson Precision Lab](https://sandboxphysics.com/labs/michelson-precision-lab/)

[View the full path →](https://sandboxphysics.com/topics/waves-and-optics/#starter-path)