What it does
Strike two tuning forks that are almost, but not quite, the same, and you hear a single note whose loudness swells and fades, “wah, wah, wah”. These swells are beats. They happen because the two waves add up (superposition): at one moment their crests line up and the sound is loud; a little later the crest of one meets the trough of the other and they cancel. The number of swells each second is the difference between the two frequencies.
This tool draws a few milliseconds of each wave, then their sum over two beats with the swelling envelope dashed in red. It plays the sound so you can hear it, and gives the beat frequency, the time between swells and the pitch you actually hear. The second mode is the classic school puzzle: an unknown fork gives some beats with a known fork; work out its frequency, using wax to decide between the two possible answers.
It follows the school topics on the principle of superposition and beats (Class 11 Physics, waves). For a single moving wave see travelling wave, for waves trapped on strings and in pipes standing waves calculator, and for measuring the speed of sound with a tuning fork resonance tube practical.
How to use it
- In Two tones, set the two frequencies and the loudness of the second tone. The big number is the beats per second.
- Tap Play the sound to hear it for 6 seconds (turn the volume down first). Moving a slider while it plays retunes it.
- In Find the unknown fork, read the beats, tap Put wax on the unknown fork, see whether the beats rise or fall, and type your answer. New unknown fork gives you another.
Worked example
Open the page: 256 Hz and 260 Hz. The beat frequency is 260 − 256 = 4 Hz, so the sound swells 4 times a second, once every 0.25 s. The pitch you hear is the average, 258 Hz. With both tones equally loud the sum falls to silence between swells; set the second tone to 50 % and the quietest point is still half as loud as one tone.
The fork puzzle: a 256 Hz fork and an unknown fork give 4 beats per second, so the unknown is 252 Hz or 260 Hz. With wax (which lowers it by 1 Hz here), suppose the beats drop to 3: the unknown moved closer to 256 Hz, so it was above it: 260 Hz. If the beats had risen to 5, it would have been 252 Hz.
Tips
- Musicians tune two strings by adjusting one until the beats slow down and stop.
- Beats faster than about 15 a second are no longer heard as swells, only as roughness.
- Filing the prongs of a fork makes it vibrate faster; wax makes it slower.
FAQ
Is the beat frequency a new tone? No. No new sound wave is made; the loudness of the average-pitch tone simply goes up and down.
Why does the graph look like a solid band? At hundreds of hertz there are many waves in each beat; the shape of the band is the envelope you hear as loudness.
Is anything stored or recorded? No. The tool only plays sound; it never uses the microphone, and nothing leaves your browser.
Where the numbers come from
- Superposition of two waves, sin a + sin b = 2 cos((a − b)/2) sin((a + b)/2), the beat frequency |f₁ − f₂| and the tuning-fork wax-loading method: standard school physics found in any textbook.
- Checked against the product formula at 2000 times, the envelope bound for unequal loudness, and every case of the wax puzzle with 2 to 6 beats.
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Last updated 2026-11-09.