READ THE RELATIONSHIP
Reinforcement
- Frequency difference
- Beat period
- Local phase at t = 0
THE ART OF ADDING THINGS UP
Make waves.
Find the quiet.
Two sources. One shared space.
Mix a signal, move a probe, and discover what happens when waves meet.
A
FIRST OSCILLATOR
Source A
SIGNAL MIXER
Two signals. One result.
A · cyanB · pinkSum · orange
ELAPSED
Field & probeShape the field. Measure any point.
Probe PDrag in the field or set its position. Arrow keys move a focused field.
At one point, displacement adds instant by instant. Dashed curves show the envelope.
B
SECOND OSCILLATOR
Source B
What probe P experiences
Same clock · same wave fieldSource A now0.000relative displacement
Source B now0.000relative displacement
Combined now0.000A + B at this point
Combined amplitude1.400Peak relative displacement
Ready. Try a preset or tune either source.
CHANGE ONE THING
Keep a reference.
Capture the current experiment, then change a frequency, phase, or probe position. The dashed white trace preserves your reference.
No baseline captured. Export includes the current time window.
BASELINE AMPLITUDE
CURRENT AMPLITUDE
MAKE IT AUDIBLE
Hear the source mix.
Sound uses 120× the source frequencies. In Ripple field, Listen at probe applies local wave levels and travel phases. Switch it off to compare the source mix. Visual speed does not change audio pitches.
Enable sound, mute and adjust the volume from the bar above the visualization.
PREDICT → TEST → EXPLAIN
Can two waves make zero?
Start with two 2 Hz sources, each with amplitude 0.70. Predict the combined amplitude at a 180° phase offset.
Use the time trace. Then reduce just one source’s amplitude to test whether the cancellation survives.
A MODEL YOU CAN INSPECT
Add displacement. Follow phase.
y = A sin(2πft + φ)
λ = v / f · fbeat = |fA − fB|
At equal frequencies, the phase relationship is fixed. At different frequencies, it changes with time, creating a moving envelope. In the ripple field, travel distance changes phase too.
Assumptions, controls & references
Linear sine-wave superposition in a uniform, unbounded medium. Ripple speed is adjustable; radial amplitude uses the illustrative factor 1/√(1 + distance). There are no boundaries, reflections, obstacles or fluid dynamics. Displacement is relative, not calibrated pressure or sound level.
Traces recompute the current settings across the displayed window, including negative model time after Restart. A baseline preserves a setup, not a recorded history. The CSV samples this analytic trace; it is not microphone data.
Source controls surround the plot on desktop. On smaller screens, use the Source A, Source B and Field & probe tabs; Left/Right arrow keys change the selected tab. Quick actions match B to A without restarting time or replacing a baseline. Full screen expands the complete workbench; Escape exits. Field controls: drag the probe, tap a point, or focus the field and use arrow keys (0.1 m; Shift for 0.5 m). Exact X/Y inputs are also available. Step pauses and advances 0.05 s. Saved setups stay on this device.
OpenStax: interference of waves · OpenStax: beats · PhET: wave interference