Key Concepts: Beats & Harmonics

Beats

• Beats occur when two waves with slightly different frequencies interfere.
• The result is a periodic variation in loudness (throbbing sound).
• Beat frequency: f_beat = |f₁ − f₂|.
• Used in tuning instruments — beats disappear when frequencies match.

Harmonics

• Harmonics are integer multiples of the fundamental frequency: f₁, 2f₁, 3f₁, ...
• The 1st harmonic = fundamental. 2nd harmonic = 1st overtone. 3rd harmonic = 2nd overtone.

Harmonic Series

• Strings and open tubes produce all harmonics.
• Closed tubes produce only odd harmonics (1st, 3rd, 5th, ...).
• The mix of harmonics gives each instrument its unique timbre.