Find a still point.
Two equal sources, opposite timing, and a probe equally far from both. Compare each source’s trace with their sum. Then move the probe away from the centre line.
FIELD NOTE 10 / WAVE PLAYGROUND
Where waves meet.
Make a ripple. Find a pattern. Discover a quiet place.
0.0 s
Crests & troughs right now
TroughCrestDark = still-water level
Move
Drag A, B or P, or choose an item and tap the water. The tank is 12 × 8 m. Colours show computed displacement; wave height is exaggerated.
- Wavelength · λ
- 1.76 m
- Period · T
- 1.18 s
- Wave speed · c
- 1.50 m/s
Try a scene
AT THE MOVABLE PROBE
One place. Every passing wave.
x 8.0 m · y 4.0 m
Height 0.000
Recent RMS 0.000
Relative unitsFrom AFrom BA + B
The white trace is the sum of both contributions, including their reflections. Moving the probe starts a new local trace.
Optional sound turns the probe’s recent RMS height into the loudness of a soft tone. It is a sonification, not the sound of water at this frequency.
The tank opens with ripples already travelling. All controls work while it runs.
Make a prediction. Change one thing. See what happens.
Model notes & references ↗FOLLOW THE SCIENCE
Motion everywhere.
Stillness in between.
A ripple is a travelling disturbance. The surface at one place rises and falls while the pattern travels across the tank. Two small waves can pass through one another: at each point, their displacements add.
If two crests arrive together, the surface rises farther. If a crest meets an equal trough, their displacements cancel at that place and time. The result can be a quiet band surrounded by moving water. This is interference. OpenStax: interference and superposition ↗
A FEW QUESTIONS TO TRY
Follow the ripples.
Let a wave turn a corner.
Send waves through one opening. Compare a narrow gap with a wide one, then change the frequency. Watch the region beyond the barrier fill with ripples.
One source. Two paths.
A single source illuminates two openings. Switch to Activity and move the probe through bright and dark bands beyond the barrier. What changes if you narrow the openings?
These scenes change the current settings without pausing or rewinding. Existing ripples remain. Use Reset tank if you want to watch a scene begin from still water.
Timing at the source. Timing at the destination.
RELATIVE PHASE
Are the sources moving together?
One cycle is 360°. At 0°, the two drivers move together. At 180°, they oppose each other. That difference travels outward with the waves.
PATH DIFFERENCE
Did the waves travel equally far?
A longer path delays a wave’s arrival. For equal-frequency sources, each extra wavelength adds a full cycle of travel phase. Source phase and path difference both determine the local result.
A dark patch is not always a quiet place.
In Surface view, a point is dark whenever its displacement crosses zero—even if it is oscillating strongly. Activity shows recent root-mean-square (RMS) height. A persistent dark band there identifies small displacement over time. Neither view directly measures energy flux; a displacement node does not mean every form of wave energy vanishes.
Frequency, wavelength and speed belong together.
c = fλ · T = 1/f
Frequency f counts cycles per second; period T is the time for one cycle; wavelength λ is the distance between successive crests along the direction of travel. Here the medium has a fixed wave speed, so raising the frequency shortens the wavelength. Changing frequency preserves the driver’s accumulated phase and leaves earlier waves travelling through the tank. OpenStax: the mathematics of waves ↗
An opening does not make a sharp wave-shaped shadow.
Waves spread beyond an opening and into regions behind its edges. This is diffraction. Compare the gap width with the wavelength: an opening comparable to or narrower than a wavelength produces broad spreading. A wider opening produces a more forward-directed pattern, with diffraction still present at its edges. The incoming wavefront also matters.
With two openings, each transmitted wave spreads, and the two contributions interfere beyond the wall. In this scene, “From A” includes everything produced by source A, including both openings and all reflections; the plot does not assign one trace to each slit. OpenStax: diffraction through an opening ↗
Where does the quiet come from?
The probe records the two computed source contributions independently. At a quiet point, they can remain substantial while their sum becomes small. Cancellation concerns the combined displacement. In other places, the same pair of sources can reinforce one another. Changing the geometry changes where those places are.
From ripples to sound and light.
Superposition and diffraction appear in many wave systems. The oscillating quantity changes: surface height here, pressure for sound, and electric and magnetic fields for light. This playground uses one scalar wave field. It does not simulate light’s polarization, photons or the full motion of water.
The mathematics, assumptions & references
A linear ripple tank
∂²h/∂t² + 2γ ∂h/∂t = c²∇²h + SA + SB
h = hA + hB
h = hA + hB
The model solves the two-dimensional, constant-speed scalar wave equation on a 12 × 8 m domain. c = 1.50 m/s. Displacement h and source strength use a fixed relative scale, not calibrated water heights or actuator power. The two additive source terms are compact Gaussian drivers, about 0.09 m in standard deviation, with equal strength and a common adjustable frequency. Source B has the selected phase offset. A short startup ramp reduces a sharp initial transient.
Two independent fields are evolved and summed, so the probe can display their separate contributions even after diffraction and reflection. Turning a source off stops its forcing; its existing waves continue. Moving a source changes where new forcing is applied. Frequency changes keep the accumulated oscillator phase. Phase changes deliberately change B’s driver phase and can launch a transient.
Boundaries and openings
The vertical barrier is centred at x = 6 m. A solid face uses zero normal displacement gradient, representing a reflecting boundary for this scalar surface-height model. A single opening is centred at y = 4 m. Two openings are centred at y = 2.4 m and y = 5.6 m. Widths are resolved on the grid, so effective edges are quantized by about one cell. Adding a barrier zeros the fields in solid cells. Removing a wall or widening an opening fills newly exposed cells by averaging the neighbouring water at both stored time levels. This avoids an artificial flat strip that would launch short grid-scale ripples, while leaving existing water untouched. The wave field still adjusts when previously separated regions meet. Water displaced by construction and the work of moving the barrier are not modelled.
The outer 1.1 m has smoothly increasing damping, reaching about 8 s⁻¹ at the edge; a small background damping of 0.008 s⁻¹ is also applied. A first-order outgoing-wave condition closes the outside edge. Together, these absorb most outgoing waves, but some reflection remains, especially for oblique incidence or long wavelengths. Drivers and the probe stay at least 1.2 m from the outside edges. This is an idealized linear, nondispersive wave experiment: water depth variations, surface tension, viscosity-driven frequency dependence, currents, breaking waves, nonlinear interactions and material transport are omitted.
Time stepping and measurements
A centred finite-difference update uses 169 × 113 points, spacing 1/14 m, and a fixed 1/60 s step. The two-dimensional Courant number cΔt/Δx = 0.35 is below the 1/√2 stability bound. A wall substitutes the local value for a blocked neighbour. Live edits preserve time and the propagating fields except at cells occupied or exposed by a changed barrier. Reset tank explicitly clears the field and returns time to zero while retaining settings and positions. Pause and Play retain the same state.
dM/dt = (h² − M)/τ · RMS = √M · τ = 3/f
Activity uses an exponential average of squared displacement with a three-period time constant. It starts at zero and takes time to settle, especially after a change. It is a local displacement measure, not a calibrated wave-energy or power map. The plot retains up to 20 s of local samples and displays the most recent 12 s, with an automatically scaled vertical axis. A probe move starts a new trace at its new position; it does not reset the tank. Thin dashed traces distinguish the source contributions from their solid white sum.
Surface colours use a fixed nonlinear display scale: cyan is positive displacement and violet is negative. Activity brightness increases with recent RMS. Neither colour map rescales itself as source strength changes. The optional 220 Hz tone uses probe RMS to control loudness; it is muted while paused or when the page is hidden. Simulation frequencies of 0.3–1.5 Hz are not presented as audible water sounds. The global sound preference is shared with the other experiments.