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Change the frequencies, amplitudes and phase, and watch interference and beats appear in the sum.
Two sine waves are drawn at the top over two seconds, and their sum at the bottom, with a dashed envelope showing how big the sum can get at each moment. Sliders set each wave's amplitude and frequency and the phase of the second wave. With equal frequencies the sum is a single sine wave whose size depends on the phase: up to double in step, zero half a turn apart with equal amplitudes. With different frequencies the sum swells and fades: beats, at the difference of the two frequencies.
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InteractiveThe math, with your numbers
The dashed envelope is √(A₁² + A₂² + 2A₁A₂ cos(2π(f₂ − f₁)t + φ)): it stays put when the frequencies match and swells and fades |f₂ − f₁| times a second when they don't.
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Want to know why it behaves like this?
The lesson “Trig Identities: Sums, Doubles & Beats” explains it step by step: Why does a ball thrown at 45° go farthest?