Sound begins with vibration
Every sound starts with something vibrating: a guitar string, a drumhead, vocal cords, a speaker cone. The vibrating object pushes and pulls on the nearby air, creating regions where molecules are squeezed together (compressions) and regions where they are spread apart (rarefactions). Those pressure changes travel outward as sound waves.
Sound waves are longitudinal, meaning the air moves back and forth along the direction the wave travels. The air itself does not stream from the instrument to your ear. The pattern of pressure moves, while each molecule just jiggles around its position. Because sound needs a medium, it cannot travel through a vacuum. In air at room temperature, it moves at roughly 343 meters per second, faster in water and faster still in solids such as steel.
Pitch and frequency
Pitch is how high or low a sound seems, and it is determined mainly by frequency: the number of vibration cycles per second, measured in hertz (Hz). A faster vibration gives a higher pitch.
Young, healthy human ears can typically detect frequencies from about 20 Hz to 20,000 Hz, with the upper limit generally dropping with age. The standard tuning note most orchestras use, the A above middle C, is 440 Hz. That means the air pressure completes 440 cycles every second.
Shorter or tighter strings vibrate faster, which is why a guitarist presses a string against a fret to shorten it and raise the pitch. Thicker, heavier strings vibrate more slowly and sound lower.
Loudness and amplitude
Loudness is related to the amplitude of the wave, which is how large the pressure variations are. A harder pluck makes a bigger vibration, which carries more energy and sounds louder. Perceived loudness also depends on frequency and on the listener, because our ears are more sensitive to some pitches than others.
Sound level is usually measured in decibels (dB), a logarithmic scale. A rise of 10 dB corresponds to a tenfold increase in sound intensity, although it is usually heard as only roughly twice as loud. Because very loud sound can damage hearing, prolonged exposure to high levels is something to take seriously, and anyone with concerns should consult a hearing professional.
Timbre: why instruments sound different
If a piano and a trumpet play the same note at the same volume, you can still tell them apart. That quality is called timbre, or tone color. It comes from the mix of frequencies present in the sound, not just the main one.
Most instruments do not vibrate at a single frequency. A string vibrates as a whole, producing the lowest pitch, called the fundamental. At the same time, it vibrates in halves, thirds, quarters and so on, producing higher frequencies called overtones. When those overtones are whole-number multiples of the fundamental, they are called harmonics. A string with a fundamental of 220 Hz, for instance, also produces harmonics at 440, 660 and 880 Hz. The relative strengths of the harmonics, along with how the sound starts and fades, give each instrument its character.
Resonance: how instruments get their volume
Resonance happens when an object is driven at a frequency close to one of its natural vibration frequencies, so it responds strongly. A bare guitar string makes very little sound on its own because it moves little air. The string’s vibration is passed to the wooden body, which resonates and pushes much more air, making the sound louder and richer.
Wind instruments rely on resonance in the air column. The length of the tube sets which frequencies fit inside it. A longer tube resonates at lower frequencies, which is why a tuba sounds lower than a trumpet. Opening and closing finger holes or valves changes the effective length of the column and therefore the note.
A familiar demonstration is blowing across the top of a bottle. The air inside resonates, and pouring in water shortens the air column and raises the pitch. Singers also use resonance, shaping the throat and mouth to emphasize certain harmonics.
From frequencies to musical notes
Western music divides the octave into twelve notes. An octave is the interval between a note and another with exactly double its frequency, so the A at 440 Hz and the A above it at 880 Hz sound like the “same” note at different heights. The brain seems to treat notes related by simple whole-number ratios as blending well together. A frequency ratio of 3 to 2, for example, gives the interval called a perfect fifth, which most listeners find stable and pleasant.
Modern keyboards are usually tuned in equal temperament, where each of the twelve steps in an octave has the same frequency ratio, about 1.059 (the twelfth root of two). This is a compromise: it makes every key playable but slightly adjusts the pure ratios. The result works well enough that most listeners accept it, though some musicians prefer other tuning systems for particular music.
Our habits of reading sheet music give each of these pitches a position on the staff, translating physics into written symbols.
Standing waves and strings
On a string fixed at both ends, certain wave patterns fit exactly, with the ends staying still and the middle moving. These are standing waves. The wavelength of the fundamental is twice the length of the string, and each higher harmonic fits one more half-wavelength. This explains why touching a string lightly at its midpoint, then plucking it, produces a ringing note exactly one octave higher: the touch suppresses the fundamental and leaves the second harmonic.
Why music affects us
Physics describes the signals, but not the whole experience. The brain interprets patterns of frequency, rhythm and expectation, and that interpretation connects to memory, which is part of why music and emotion are so closely linked. Why certain combinations feel tense or calm is a subject of ongoing research, and the physical ratios are only part of the story.
Different traditions use these same physical ingredients in different ways. The classical music periods each favored particular ensembles and harmonies, and the jazz origins story is partly one of musicians bending pitch and rhythm beyond what written notation captures. On a piano, each key strikes strings tuned to a fixed frequency, while a violin player decides the pitch with finger placement, so violin technique involves continually adjusting the vibrating length of the string. Guitar chords, meanwhile, combine several strings at once, so their harmonics blend into one composite sound.
Key ideas
- Sound is a pressure wave carried by a medium.
- Frequency sets pitch, amplitude sets loudness, and the mix of harmonics sets timbre.
- Resonance amplifies sound in instruments.
- Doubling a frequency produces an octave, and simple ratios give pleasant intervals.