Interference
Interference means that two sound waves overlap and their displacements add. If wave crests meet crests, the sound is reinforced; if crests meet troughs, it is cancelled wholly or in part. From the interference of two almost equal notes the beat arises.
- Principle
- superposition: the displacements add
- Reinforcement
- waves in step (same phase)
- Cancellation
- waves out of step (opposite phase)
- Beat
- difference of the two frequencies in hertz
- Related
- vibration, wave, resonance
Waves add up
Sound consists of pressure fluctuations of the air that travel as waves from the instrument to the ear. If two waves meet at the same place, their displacements add. That is called interference. If both are in step, so in the same phase, a larger wave results: constructive interference. If they are out of step, one displacement cancels the other: destructive interference. With two equally loud notes of the same frequency this can lead to complete silence at that spot.
This cancellation is used technically in noise-cancelling headphones, which pick up the noise and overlay it with sound in opposite phase. It is also the reason why two loudspeakers with reversed polarity can sound thin at low notes.
From interference to beats
If two notes have almost but not exactly the same frequency, they slowly drift out of step. Sometimes the wave crests lie on top of each other, sometimes against each other. The ear therefore hears a regular swelling and fading of the volume, the beat. Its frequency is simply the difference of the two notes in hertz: 440 Hz and 442 Hz pulse twice a second, as the page Cent also notes. The table works through four cases and gives the distance in cents for comparison.
| Two notes | Frequency difference | Beats per second | Distance in cents |
|---|---|---|---|
| 440 Hz and 441 Hz | 1 Hz | 1 | about 4 |
| 440 Hz and 442 Hz | 2 Hz | 2 | about 8 |
| 440 Hz and 444 Hz | 4 Hz | 4 | about 16 |
| 440 Hz and 448 Hz | 8 Hz | 8 | about 31 |
The cent values follow from the frequency ratio: 442 to 440 gives 1200 times the base-2 logarithm of 442/440, so a good 7.8 cents. You hear two beats per second clearly. When you tune a guitar, you use the beat: you turn until the pulsing of two strings gets ever slower and finally disappears.
Interference in tuning
You meet it in tuning too. On a piano tuned in equal temperament major thirds audibly beat, because they are not quite pure. There it is not two notes but their overtones that lie close together and interfere with each other. More on this is in the article Equal, meantone, just — why your piano is slightly out of tune.
Common mistakes
- Confusing beats with vibrato: vibrato is a deliberate pitch fluctuation of a single note. A beat arises from two notes.
- Assuming cancellation destroys energy: it only moves it to other places in the room.
- Counting beats in cents instead of hertz: the pulses per second correspond to the frequency difference in hertz, not to the distance in cents.
Continue on Maikstrings
Related terms
BeatingVibrationWaveResonanceCentCombination toneHarmonic seriesStandard pitchTuning fork
Editor: Maik Krohm · reviewed on 3 October 2026
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