Beat Frequency Calculator
When two tones of slightly different frequency sound together, their waves alternately reinforce and cancel, producing a slow throb in loudness called beats. The number of throbs per second is the beat frequency, equal to the difference between the two source frequencies. This calculator takes two frequencies and returns the beat frequency, the beat period and the average tone you actually hear. It is a staple of instrument tuning, ultrasonic measurement, radio heterodyning and any situation where two near-equal frequencies combine.
Beat frequency formula
Beat frequency: f_beat = |f1 - f2|
Beat period: T_beat = 1 / f_beat
Average tone: f_avg = (f1 + f2) / 2
Two superposed sinusoids of frequencies f1 and f2 produce a carrier at the average frequency whose amplitude is modulated at the difference frequency. The ear perceives one loudness cycle per beat period.
Beat phenomenon context
- The standard orchestral tuning reference A is 440 Hz; a second tone at 444 Hz gives a 4 Hz beat.
- Beats vanish when the two frequencies are exactly equal, which is the basis of zero-beat tuning.
- Beats apply to all waves: sound, radio and light alike obey the same difference rule.
- Radio receivers mix an incoming signal with a local oscillator and use the beat (intermediate frequency) for processing.
- If the two frequencies differ by more than about 15 Hz the throb is heard instead as a rough or dissonant combined tone.
Beat frequency: frequently asked questions
What is beat frequency?
Beat frequency is the rate at which the loudness of a combined sound rises and falls when two tones of slightly different frequency are played together. It equals the absolute difference between the two frequencies. If you play 440 Hz and 444 Hz together you hear 4 beats per second.
What is the formula for beat frequency?
The beat frequency f_beat equals the absolute value of f1 minus f2, where f1 and f2 are the two source frequencies in hertz. The perceived combined tone oscillates at the average frequency, (f1 + f2) / 2, while its amplitude is modulated at the beat frequency.
How is beat period related to beat frequency?
The beat period is the time between successive peaks in loudness and equals one divided by the beat frequency. A beat frequency of 4 hertz gives a beat period of 0.25 seconds, meaning the sound swells and fades once every quarter second.
Why do musicians use beats to tune instruments?
When two strings are slightly out of tune you hear beats. As you adjust one string toward the other the beats slow down, and when the beat frequency reaches zero the two pitches match exactly. Listening for the disappearance of beats is one of the most precise tuning methods available by ear.
Does beat frequency apply to light and radio waves?
Yes. Any two waves of nearly equal frequency produce beats, a phenomenon used in radio heterodyne receivers and laser interferometry. The mathematics is identical: the beat frequency is the difference of the two frequencies regardless of whether the waves are sound, radio or light.
Official sources
- NASA Glenn Research Center: Sound and waves.
- U.S. National Institute of Standards and Technology: Physical Measurement Laboratory.
Reviewed by the CalculatorHub team, edited by James Graham, 16 June 2026. See our methodology.