How Musical Instruments Make Notes

Turning a wiggle into a tune

Pluck a string, blow across a bottle, bang a drum — each makes a sound, but only some instruments make a clear musical note. The difference comes down to one idea from wave physics: resonance. Understanding it explains pianos, flutes, drums and your own singing voice. A quick look at sound and how we hear sets the scene.

It all starts with a vibration

Sound is a vibration of air. So every instrument needs something that vibrates fast enough to make air ripple:

• a string on a guitar, violin or piano
• a column of air in a flute, trumpet or organ pipe
• a stretched skin on a drum
• a metal bar or block on a xylophone or chime

The vibration pushes the nearby air into compressions and rarefactions — a longitudinal sound wave — which travels to your ears.

Resonance: the secret to a strong note

Tap any object and it prefers to vibrate at certain natural frequencies, just as a swing prefers a particular rhythm. Push a swing at exactly that rhythm and the swings grow huge; push at the wrong rhythm and nothing builds up.

Resonance is the same idea: when an instrument is driven at one of its natural frequencies, the vibration grows large and steady, producing a clear, sustained note. A flute player blows a stream of air that excites the air column's natural frequency; a guitar's wooden body resonates with the strings to make them loud. Without resonance you would get only a dull thud.

Standing waves: why only certain pitches fit

When a vibration is trapped between two ends — the two ends of a string, or the two ends of a pipe — the wave reflects back and forth and overlaps itself. The result is a standing wave: a pattern that appears to stay still, with points that never move (nodes) and points that swing the most (antinodes).

The key rule is that only wavelengths that fit neatly into the length survive. The longest one that fits — half a wavelength on a string fixed at both ends — gives the lowest and loudest note, the fundamental. Shorter wavelengths that also fit give the higher harmonics layered on top. This is why a given string or pipe plays definite pitches rather than a smear of noise.

What controls the pitch?

For a vibrating string, three things set the note:

• Length — shorter string → higher note. Pressing a guitar fret shortens the string to raise the pitch.
• Tension — tighter string → higher note. You tune by turning the pegs to change tension.
• Thickness (mass) — thinner string → higher note. The thick low strings give the deep notes.

For a pipe or air column, the main control is length: a longer tube holds a longer wavelength, so it plays a lower note. A piccolo is tiny and shrill; a tuba is long and deep.

Worked example: tuning a string

A guitar string is 0.65 m long and plays a fundamental note. On a string fixed at both ends, the fundamental wavelength is twice the length:

λ = 2 × 0.65 = 1.3 m

If the wave travels along the string at about 260 m/s, the frequency is:

f = v / λ = 260 ÷ 1.3 = 200 Hz

Now press a fret halfway, halving the length to 0.325 m. The wavelength halves to 0.65 m, so:

f = 260 ÷ 0.65 = 400 Hz

Half the length gives double the frequency — exactly one octave higher. The maths of the wave equation is doing the music.

Try it yourself! 🧪

Build a one-octave bottle organ.

1. Line up several identical glass bottles and pour different amounts of water into each.
2. Tap the bottles gently with a spoon. The bottle with the most water has the least glass-and-water to vibrate quickly... actually the air and glass vibrate — the fuller bottle gives a lower tap-note.
3. Now blow across the tops instead. This time the emptier bottle (longer air column) gives the lower note, and the fuller bottle gives the higher note.
4. Add or pour off water to tune neighbouring bottles a clear step apart, and you can play a simple scale.

Notice that tapping and blowing vibrate different things (the glass-plus-water versus the air column), so they respond to the water level in opposite ways — a neat demonstration of resonance in action.