The Physics of Musical Instruments
Music is organized vibration. Whether it's a guitar string, a flute's air column or a drumhead, instruments work by trapping standing waves at specific frequencies — and your ear reads those frequencies as pitch.
Standing waves set the pitch
A guitar string fixed at both ends vibrates in standing-wave modes; the fundamental is f = v/2L. Pressing a fret shortens L, raising the frequency — that's all frets do.
Harmonics make timbre
Real strings vibrate at the fundamental plus integer multiples (harmonics). The mix of harmonics is why a violin and a flute playing the same note sound different — same pitch, different recipe.
Resonance amplifies
The guitar's hollow body is a resonant cavity tuned to reinforce the strings' frequencies. Without it, an electric guitar unplugged is whisper-quiet.
Beats tune instruments
Two nearly identical frequencies produce beats at the difference frequency. Tuners listen for the beats to vanish — zero beats means zero difference, perfect tuning.
Try this yourself
- Pluck a rubber band stretched over a box, then shorten it with a finger — hear the pitch rise as L shrinks.
- Play two slightly detuned tones (phone apps can) and count the beats per second.