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Beats in oscillators
Intermediate
Two close frequencies produce periodic amplitude variation.
f_beat = ∣f₁−f₂∣Two oscillations with nearby frequencies f₁ and f₂ interfere to give an amplitude that varies at the beat frequency |f₁ − f₂|.
440 Hz and 444 Hz: 4 beats per second.
Beat frequency is the difference, not the average.
In more detail
Beats occur when two oscillations of slightly different frequencies combine, producing a slow variation in amplitude. The beat frequency equals the difference of the two frequencies.
Real-world uses
- Piano tuners listen for beats between strings to tune them.
- Radio receivers use beats to convert high frequencies to audible ones.
- A piano tuner listens for beats between two nearly identical notes and adjusts one until the beats disappear.
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Frequently asked questions
How do I calculate the beat frequency?
Subtract the two frequencies and take the absolute value.
What do I hear?
A pulsing sound at the beat frequency, with loudness rising and falling.
How does a tuner use beats?
When two strings are exactly in tune, the beats vanish, so slowing the beat rate tells the tuner they are close to matching.
Related topics in Oscillations & SHM
Analogy between mechanical and electrical oscillators · Coupled oscillators · Normal modes · Superposition of SHMs · Lissajous figures · Anharmonic oscillation