Interactive Wave Generator - See & Hear Sine Waves Add Up - Simple Number Tools<br>Skip to content Search tools

Interactive Wave Generator

A point going round a circle at a steady speed traces a sine wave - its height<br>over time is the wave. Add more waves to see them combine, view the spinning point as a 3D<br>spiral, and turn on sound to hear them.

Pause Sound: off Speed Volume

+ Add wave Circle to wave<br>Each circle's spinning dot is one wave; its height draws the matching coloured curve. The bold curve is the sum.<br>In 3D: the wave is a spiral<br>Spin the circle through time and it becomes a helix ; its shadow on the back wall is the flat wave. One spiral per wave.

Three waves, one point<br>Let wave 1 drive the X axis, wave 2 the Y axis, and wave 3 the Z axis. The single point at (x, y, z) traces a 3D Lissajous figure - simple frequency ratios (like 1:2:3) close into a neat loop. Uses the first three waves.<br>You have more than three waves - only the first three drive this view.

This is a playground for seeing where a sine wave comes from and what happens when you add<br>waves together. A point moving steadily around a circle traces a sine wave: its height at each<br>moment is the wave. Add a second or third wave and watch them stack into a new shape, view the<br>spinning point as a 3D spiral, and turn on sound to hear them.

How to Use It

Three waves are already running (frequencies 1x, 2x, and 3x). Drag any wave’s frequency ,<br>amplitude , and phase sliders and watch the circles and the curve respond.

Press + Add wave to layer another one, or remove waves you do not want. Each wave gets its<br>own colour, its own circle, and its own animated point. The bold curve is the sum .

Use Pause , Speed , and Sound as you like. Sound starts only when you turn it on.

Where the Wave Comes From

A point going round a circle of radius A at a steady rate has a height that rises and falls as a<br>sine wave. If the point completes f turns per second and starts at angle φ, its height at time t is:

y(t)=Asin⁡(2πft+φ)y(t) = A \sin(2\pi f t + \varphi)y(t)=Asin(2πft+φ)<br>That is exactly what the spinning dot draws: amplitude A is the circle’s radius, frequency<br>f is how fast it spins, and phase φ is where it started. This is the honest, exact version of<br>“simple harmonic motion” - the projection of steady circular motion.

Adding Waves (Superposition)

When two or more waves overlap, the combined wave is just their values added at every instant:

y(t)=A1sin⁡(2πf1t+φ1)+A2sin⁡(2πf2t+φ2)+⋯y(t) = A_1 \sin(2\pi f_1 t + \varphi_1) + A_2 \sin(2\pi f_2 t + \varphi_2) + \cdotsy(t)=A1​sin(2πf1​t+φ1​)+A2​sin(2πf2​t+φ2​)+⋯<br>Small changes in frequency or phase can produce very different combined shapes - this is the idea<br>behind everything from music chords to noise cancellation.

The 3D Spiral

Take the spinning point and stretch it out along a time axis and the circle becomes a helix (a<br>spiral). Its shadow on the back wall is the flat wave you see above - projecting the helix onto that<br>wall drops the depth and leaves a pure sine curve. The 3D view draws one spiral per wave you add.

Three Waves, One Point

Instead of stacking the waves, you can let each one drive a different direction in space: wave 1<br>moves a point left and right (X), wave 2 moves it up and down (Y), and wave 3 moves it toward and<br>away from you (Z). Plotting that single point over time traces a 3D Lissajous figure :

Two waves give a flat Lissajous curve - the looping shapes seen on oscilloscopes.

Three waves give a 3D Lissajous knot .

When the frequencies are simple whole-number ratios (like 1:2:3) the curve closes into a steady<br>repeating loop; off-ratios drift and slowly fill a box. This view uses the first three waves.

Related Tools

The circle behind it all: the circle calculator.

Another step-by-step visual: square roots, step by step.

The right-triangle identity behind sine and cosine: the Pythagorean theorem calculator.

Related Tools<br>Calculators Circle Calculator Find a circle's radius, diameter, circumference, and area from any one of them. Shows the formulas. Calculators Square Root, Step by Step See how to find a square root by hand, revealed step by step. Choose the regular long-division method or a fast approximation, and play the working through. Calculators Pythagorean Theorem Calculator Find the hypotenuse or a missing leg of a right triangle using the Pythagorean theorem. Shows the steps.

Math results are exact for the numbers you enter. Financial calculators give estimates, so verify important decisions independently. Worksheet and problem answers are educational aids, and children should use them with a parent, teacher, or caregiver when needed.

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