Play two guitar strings that are almost in tune and you hear something odd: not two notes, but one note that swells and fades, wah-wah-wah, like a slow tremolo. Neither string is wobbling. Each one rings steadily. The throb only exists when the two sounds meet.
Musicians call this beating, and it is one of the most useful things in music. It is how piano tuners tune a piano by ear, how orchestras settle on a shared pitch, and why some organ stops are put out of tune on purpose.
The teal string plays a steady 440 Hz, the A that orchestras tune to. The red string is a little off. Drag sideways on the picture (or use the slider) to retune it, and watch the black line, which is what actually reaches your ear. Tap Listen to hear it.
A sound is a pressure wave: the air is pushed, then pulled, hundreds of times a second. When two waves arrive together, their pushes and pulls simply add up.
If the two notes had exactly the same frequency, their peaks would stay lined up forever and you would just hear one louder note. But 446 cycles a second and 440 cycles a second slowly slide past each other. For a moment the peaks coincide and the sound is loud. A little later one wave's push meets the other's pull, they cancel, and the sound almost vanishes. Then they drift back into step.
How often does that happen? Once for every cycle one string gains on the other. The rule is beautifully simple:
beats per second = difference between the two frequencies
So 446 Hz against 440 Hz gives 6 beats a second. 441 against 440 gives one slow swell per second. At exactly 440 against 440, the beating stops completely, and that silence is the target.
Your ear is quite bad at saying whether a note is one hertz too high. It is excellent at hearing a wobble. So instead of judging pitch, a tuner listens for the beats and turns the peg until they slow down and disappear.
A piano makes this essential. Most of its notes use two or three strings struck by the same hammer, and those strings have to agree exactly. A piano that has drifted gives the warbling "honky-tonk" sound precisely because those strings beat against each other.
The same trick works beyond unisons. A string also vibrates at 2, 3, 4… times its main frequency (its harmonics). When two notes form a fifth, the third harmonic of the lower note lands right next to the second harmonic of the upper one, and those two beat too.
On a modern piano the fifths are deliberately tuned a hair narrow (that compromise is what lets every key sound acceptable). In the middle of the keyboard it shows up as a very slow beat, somewhere between one every two seconds and about one a second. For the fifth A3 to E4 the numbers work out to 660 Hz against 659.26 Hz: about 0.74 beats per second. Tuners set those slow wobbles one interval at a time, sometimes timing them against a metronome.
Push the red string further away in the demo and listen. At a few beats per second you hear one note pulsing. Past roughly ten to fifteen a second the pulses blur into a harsh, buzzy roughness: the texture we hear as dissonance. Pull the notes far enough apart and the roughness smooths out again into two separate notes. The exact boundaries shift with pitch and from person to person, so treat these as rough zones rather than hard lines.
That buzzy middle zone is a big part of why some chords sound tense: their harmonics sit close enough to rub against each other.
Beating is not always a fault. Many pipe organs have a stop called the voix céleste ("heavenly voice"): a row of pipes detuned slightly so that, played with a normally tuned row, the sound gently undulates, warm and shimmering. Accordions do the same with their "musette" setting, where two or three reeds per note are tuned slightly apart for that bright, wavering café sound. The chorus effect on guitar pedals and synthesizers borrows the same idea.
One strange twist: play 520 Hz into one ear and 530 Hz into the other with headphones, and many people still hear a 10 Hz wobble. Those two sounds never mix in the air, so this binaural beat is built by your brain, not by the waves.
Next time a band tunes up, listen for that slow wah… wah… fading into stillness. That is the sound of two waves learning to march in step.