What you're seeing

Three graphs share one time axis. The top two are Wave 1 and Wave 2 on their own. The bottom one is the two added together — what reaches your ear when both play.

Why beats happen

When crests line up with crests, the waves add and the sound is loud. A little later one wave has pulled ahead by half a cycle, crests meet troughs, and the waves cancel — the sound is quiet. Then they line up again. This happens |f₁ − f₂| times each second.

Things to try

Listen to Wave 1, then Wave 2, then Both. Each note alone is steady; together they pulse. Nudge Wave 2 toward Wave 1 — the beats slow down. Make them equal and the beats stop. Spread them far apart: past about 15 beats per second the pulsing blurs into a rough, buzzy sound, and farther apart you hear two separate notes.

The two views

Beat pattern shows two beats. Real notes wiggle hundreds of times a second — far too many to see — so the wiggles are drawn slowed down. The beats are not slowed: the time axis, the beat length, and the white line sweeping along with the sound are all true.

Close-up shows just four cycles. Wave 1 is held still so you can watch Wave 2 slowly slide past it, in and out of step.

Sound

Laptop speakers work; headphones are better. On a phone, check the volume and the silent switch.