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Beats
Intermediate
Two close frequencies produce loud–soft pulsing.
f_b = ∣f₁−f₂∣Two waves of slightly different frequencies produce amplitude variations at the beat frequency f_b = |f₁ − f₂|. Musicians use beats to tune instruments.
Tuning a guitar string against a reference: beats slow down as they match.
The perceived pitch is the average frequency.
In more detail
Beats occur when two waves of close frequencies overlap, producing a periodic variation in loudness at the difference frequency. They are heard when two notes are nearly in tune.
Real-world uses
- Tuning instruments by listening for beats between two strings.
- Pilots and engineers use beats to detect slightly mismatched engines.
- A guitarist tunes two strings by listening for beats, which slow down as the frequencies become closer.
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Frequently asked questions
How many beats per second?
The difference between the two frequencies.
What do beats sound like?
A pulsing wah-wah effect whose rate matches the frequency difference.
How fast should the beats be for a good tune?
They should be slow or absent, since a beat frequency of zero means the two notes are exactly the same.
Related topics in Waves & Sound
Principle of superposition · Constructive and destructive interference · Path difference and phase · Standing waves · Nodes and antinodes · Modes of a stretched string