Beat Frequency Calculator
Calculate beat frequency from two sound waves. Find beat rate |f₁−f₂|, beat period, tuning correction in cents, musical interval ratios, and harmonic beats for instrument tuning.
Hz
Hz
Beat Frequency
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Beat Period —
Beats per Minute —
Extended More scenarios, charts & detailed breakdown ▾
Hz
Hz
Beat Frequency
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Beat Period —
Beats per Minute —
Frequency Ratio —
Professional Full parameters & maximum detail ▾
Hz
Hz
Tuning Analysis
Cents Deviation —
Beat Rate at A4 —
Harmonic Beats
Harmonic of Reference —
Harmonic of Observed —
Beat at Harmonic —
How to Use This Calculator
- Enter Frequency 1 and Frequency 2 to get beat frequency and beat period.
- Use Tuning tab — enter target pitch and observed beat rate to find corrected frequencies in Hz and cents.
- Use Musical Intervals tab to see octave, fifth, fourth, and third relationships.
- Switch to Professional for cents deviation, A4 tuning analysis, and harmonic beats.
Formula
Beat Frequency = |f₁ − f₂|
Beat Period = 1 / Beat Frequency
Cents = 1200 × log₂(f_obs / f_ref)
Example
Example: Two strings at 440 Hz and 444 Hz → Beat frequency = 4 Hz (4 pulses/second). Beat period = 0.25 s.
Frequently Asked Questions
- Beat frequency is the audible pulsation heard when two sound waves of slightly different frequencies interfere. Beat frequency = |f₁ − f₂|. The beats per second equals the frequency difference.
- When two notes are slightly out of tune, beats slow as the pitch converges. At zero beats the notes match. Tuning to eliminate beats is one of the most precise aural tuning methods available.
- A cent is 1/100 of a semitone (1/1200 of an octave). Cents deviation = 1200 × log₂(f_observed / f_reference). The human ear can detect deviations of 5–10 cents.
- A just perfect fifth has a 3:2 frequency ratio. In equal temperament (12-TET), it is 2^(7/12) ≈ 1.4983, which is 1.96 cents lower than the pure 3:2 ratio — this small difference produces slow, pleasant beats.
- Beats occur not just at the fundamental frequency but also at each harmonic. The nth harmonic of two close pitches produces beats at n × |f₁ − f₂|. Higher harmonics produce faster, more audible beats.
Related Calculators
Sources & References (5) ▾
- Beats — HyperPhysics — Georgia State University HyperPhysics
- University Physics Vol 1, Ch 17.6: Beats — OpenStax
- Acoustical Society of America — Sound Beats — Acoustical Society of America
- MIT OCW 8.03: Physics III — Vibrations and Waves — MIT OpenCourseWare
- Stanford CCRMA — Music Acoustics — Stanford Center for Computer Research in Music and Acoustics