2. Wave Interaction & Interference · Concept 7 of 10
Beat Frequency
A slow throbbing or wobble you hear when two notes are almost but not quite the same pitch.
Two near-identical tones drift in and out of step, swinging the combined loudness from LOUD (peaks add) to SILENT (peak cancels trough); the throb rate equals the frequency difference.
What it is
A slow throb in loudness you hear when two tones are nearly the same pitch, pulsing at the rate of their frequency difference.
Key facts
Beat frequency formula: f_beat = |f1 - f2|, where f1 and f2 are the two tone frequencies in hertz (Hz) and the bars mean absolute value (always positive)
Example: 440 Hz + 443 Hz = 3 Hz beat = 3 throbs per second
Closer pitches = slower beat: 440 vs 441 Hz gives 1 throb per second; 440 vs 440 Hz gives ZERO beats (perfectly in tune)
Beat PERIOD (seconds per throb) = 1 / f_beat, so a 2 Hz beat throbs once every 0.5 s
Loudness swings between SUM (constructive, both peaks add) and ZERO (destructive, peak cancels trough)
Ear hears distinct beats roughly below 15-20 Hz; above ~20 Hz the throb blurs into a rough buzz then a separate difference tone
Speed of sound in air = 343 m/s at 20 degrees C (about 1235 km/h)
Doubling SPL pressure = +6 dB; doubling acoustic POWER (or two equal uncorrelated sources) = +3 dB
Halving power = -3 dB (the half-power point); two identical correlated tones in phase = +6 dB
How it works
Two tones start in step, peaks aligning, so they ADD and the sound is LOUD (constructive)
Because pitches differ slightly, one tone slowly creeps ahead of the other
They drift fully out of step, peak meets trough, and CANCEL to silence (destructive)
They drift back into step, loud again; this loud-soft cycle IS the beat
Number of full loud-soft cycles per second equals the frequency difference in Hz
To tune by ear, adjust one source until the throb slows to a stop (zero beats)
Real examples
Tuning a guitar: fret the low E at the 5th fret and play the open A, slow the wobble to zero and they match
Two synths both set to 'A' but one drifts to 441 Hz, giving an unwanted 1 Hz throb across the PA
Piano tuners deliberately leave a few beats per second to spread the temperament
Aircraft propellers slightly out of sync produce the audible wow-wow drone passengers hear
Tuning timpani or a bass to the kick drum, you hear the beat slow as the pitches converge
How it helps in live sound
Hearing a slow wow-wow on a sustained note? Suspect two sources slightly detuned, not an effect, check both first
Tune backing tracks, samplers and synths to the same reference (A=440 Hz unless the act specifies 442)
Stack two of the same synth patch and detune ~1-3 Hz on purpose for a fat chorus, but keep it OFF lead vocals or it sounds drunk
Use a tuner or RTA tone to set bass and keys to identical pitch; zero beats = locked in
Beats can expose a flat battery-powered wireless IEM drifting in pitch, swap the pack
Two subs fed the same signal but wired out of polarity wont beat, theyll just lose low end, check polarity separately
Everyday analogy
Like two car indicators blinking at almost the same rate, drifting in and out of sync so they flash together then opposite, over and over.
Watch out
Myth: a beat means the room or speaker is faulty. Truth: it is two near-identical pitches interfering; fix the tuning and the throb vanishes.
Fun fact
Your brain can detect beats so fine that musicians tune to better than 1 Hz, hearing a throb of one cycle every few seconds that no cheap meter would flag.
Key takeaways
Beat rate = the difference between the two frequencies, in Hz
Closer the pitches, slower the throb; identical pitches, no throb
The throb is loudness swinging between add (loud) and cancel (silent)
Tune by ear by slowing the beat to zero
A slow wobble on a held note usually means two sources are slightly out of tune