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
Beat Period
Beats per Minute
Extended More scenarios, charts & detailed breakdown
Hz
Hz
Beat Frequency
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

  1. Enter Frequency 1 and Frequency 2 to get beat frequency and beat period.
  2. Use Tuning tab — enter target pitch and observed beat rate to find corrected frequencies in Hz and cents.
  3. Use Musical Intervals tab to see octave, fifth, fourth, and third relationships.
  4. 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)
  1. Beats — HyperPhysics — Georgia State University HyperPhysics
  2. University Physics Vol 1, Ch 17.6: Beats — OpenStax
  3. Acoustical Society of America — Sound Beats — Acoustical Society of America
  4. MIT OCW 8.03: Physics III — Vibrations and Waves — MIT OpenCourseWare
  5. Stanford CCRMA — Music Acoustics — Stanford Center for Computer Research in Music and Acoustics