The two sounds (pure sine waves) are at the bottom of the screen in black and blue. The resulting wave, showing beats, is in heavier black above that.

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How does changing one of the frequencies (actually the 2πf, the ω values) affect the pattern of the combined wave?

How does changing one of the amplitudes (the a values) affect the beat pattern?

How does changing the relative phase of the two waves ( the φ values) affect the combined wave?

Lenore Horner, Created with GeoGebra