What this calculator does
When two notes of slightly different pitch sound together, they alternately reinforce and cancel, producing a slow throbbing in the volume. The rate of that throbbing is the beat frequency, and it is simply the difference between the two frequencies.
Musicians use it constantly. Tuning by ear means adjusting one string until the beats slow down and stop, which happens precisely when the two frequencies match, and it is far more sensitive than judging pitch directly.
The formula
Subtract the smaller frequency from the larger and take the absolute value. The beat period is the reciprocal of that figure, and the pitch actually perceived is the average of the two frequencies.
| Term | Meaning |
|---|---|
| Beat frequency | The number of loudness pulses per second, equal to the difference between the two source frequencies. |
| Beat period | The time between successive pulses, the reciprocal of the beat frequency. |
| Constructive and destructive interference | The alternate reinforcement and cancellation of the two waves that produces the beating. |
The inputs explained
| Field | What to enter |
|---|---|
| Frequency 1 (Hz) | The first frequency in hertz. |
| Frequency 2 (Hz) | The second frequency in hertz. Beats are only perceptible when the two are reasonably close. |
When to use it
Tuning an instrument by ear
Adjusting until the beats slow to nothing gives a match far more precise than judging the pitches separately.
Checking a reference against a standard
Sounding an unknown against a known frequency turns a small difference into an audible, countable rate.
Understanding a wobble in a sound
Two sources slightly out of tune, such as a twin-engine aircraft, produce the same effect on a larger scale.
Worked examples
Every figure in the tables below is produced by this page’s own calculator at build time, so the numbers and the tool always agree. Select any row to load that scenario.
How fast do the beats go as the second note moves away?
A 440 Hz reference against notes of increasing difference.
| Second frequency | Beat frequency | Beat period |
|---|---|---|
| 441 Hz | 1.000 Hz | 1.000 s |
| 443 Hz | 3.000 Hz | 0.333 s |
| 445 Hz | 5.000 Hz | 0.200 s |
| 450 Hz | 10.000 Hz | 0.100 s |
Questions
Why does tuning by beats work so well?
Because the ear is poor at judging small pitch differences directly but excellent at noticing a slow pulse. A one hertz error at 440 Hz is under a quarter of a per cent, yet it produces an obvious once-per-second throb.
What pitch do you actually hear?
The average of the two frequencies, with the loudness varying at the beat rate. Two notes at 440 and 444 Hz are heard as roughly 442 Hz pulsing four times a second.
Why do fast beats stop sounding like beats?
Above roughly 15 to 20 hertz the pulses blur together and are perceived as roughness rather than as a countable rhythm. Push the difference further and the two notes separate into distinct pitches.
Does this happen with light?
The same mathematics applies to any waves, and optical beating is used in interferometry and laser measurement. It is not visible directly because optical frequencies are far too high for the eye to follow.
For the pitch shift caused by motion instead, see the Doppler effect calculator. For loudness rather than pitch, see the decibel calculator.