Physics·TPC

Beats

Tsokos Ch. 11.3

Overview

When two waves of slightly different frequencies f₁ and f₂ are superimposed, they alternately interfere constructively and destructively. The result is a wave whose amplitude pulses at the beat frequency: f_beat = |f₁ − f₂|. You hear a throbbing sound |f₁ − f₂| times per second. As f₁ → f₂, beats slow and disappear. Used by musicians to tune instruments: when beats disappear, the frequencies are equal. Note: beats occur when f₁ ≈ f₂ — if the difference is too large, you hear two separate notes.

Beats — interference of slightly different frequencies

When two waves with slightly different frequencies f₁ and f₂ superpose, they periodically come in and out of phase. The result is a wave whose amplitude oscillates: the envelope 'beats'. Beat frequency = |f₁ − f₂|. Beats are heard as a pulsing sound. Musicians use beats to tune instruments: when two strings are perfectly in tune, beats disappear (f₁ − f₂ = 0).

Worked Examples
Common Mistakes
  • Confusing beat frequency with the actual frequencies of the waves
  • Thinking beats only occur with sound — beats occur for any two superposing waves with different frequencies