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Acoustic Beat Period Calculator

Enter two frequencies to find their acoustic beat frequency and period.

Result

3.00 Hz
0.3333 s
180 beats/min

How it is calculated

When two tones sound together, the loudness swells and fades at the difference of their frequencies. The tool computes beat frequency = |f1 − f2| in hertz, period = 1 ÷ beat frequency in seconds, and beats per minute = beat frequency × 60. Enter both frequencies in hertz; the order does not matter because the difference is taken as an absolute value. Beat frequency is shown with two decimals, the period with four decimals, and the beats per minute as a whole number, all calculated from the unrounded difference. If the two frequencies are exactly equal there is no beat, so no result is given. The tool does not check whether the tones are close enough to be heard as a beat.

Worked example

A piano string sounds at 443 Hz against a reference tone of 440 Hz. The beat frequency is |440 − 443| = 3.00 Hz. The period is 1 ÷ 3 = 0.3333 s, so the loudness pulses roughly once every third of a second. In beats per minute that is 3 × 60 = 180 beats/min. Tuning the string down until the beat slows and finally disappears brings it to 440 Hz.

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Common mistakes

  • Entering the tone names or note numbers instead of frequencies in hertz: the tool needs the actual frequencies, such as 440 for the A above middle C.
  • Using the tool for tones that are far apart: 440 and 880 Hz give a difference of 440 Hz, which is just a mathematical difference and not a slow, audible pulse.
  • Confusing the beat period with the wave period: the period given is that of the loudness pulse, not of either tone.
  • Expecting a result when both frequencies are equal: with no difference there is no beat, and the tool returns nothing, which is the goal when tuning a unison.

About this calculator

When two tones of slightly different frequencies (f₁ and f₂) sound together, their amplitudes periodically reinforce and cancel, producing an audible pulsing called a beat. The beat frequency equals the absolute difference between the two tones, |f₁ − f₂|, the beat period is its reciprocal (1 ÷ beat frequency), and beats per minute is simply the beat frequency multiplied by 60.

Piano and instrument tuners use audible beats as their primary tuning reference: when tuning a unison or octave, they adjust a string or pipe until the beat frequency slows to zero (or to a specific target rate for tempered intervals), since a trained ear can judge beat rate far more precisely than pitch alone. The same phenomenon explains the throbbing “wah-wah” sound of two closely tuned musical instruments playing together, and physicists use it to demonstrate wave interference.

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Comments (1)

  • Editorial team

    For octaves the beat does not come from the two fundamentals. Compare the upper note with the lower note's second harmonic instead: enter 441 Hz for an A4 string and 440 Hz, which is twice a 220 Hz A3, and the tool reports a 1.00 Hz beat. Much past a dozen or so hertz the pulsing blends into roughness rather than a countable beat. Do you tune by ear, with a tuner, or both, and which intervals give you trouble?

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