Understanding Sound: Pitch and Amplitude
At its root, sound is movement. When something vibrates - a string, a speaker cone, your vocal cords - it pushes on the air (or water, or a solid) around it, sending out a travelling wave. Waves in physics are disturbances in space that transfer energy, and sound waves are a type of mechanical wave. That wave reaches your ear, your brain decodes it, and you experience it as sound. Sound is our perception of a wave. Of all the physical properties a sound has, music cares about three above the rest: how fast it vibrates (frequency), how strongly (amplitude) and for how long (duration).
The Relationship Between Frequency and Pitch in Sound
In physics and psychoacoustics (psychoacoustics is the scientific study of how humans perceive sound), the relationship between frequency and pitch is that frequency is the objective, measurable physical property of a sound wave, while pitch is the subjective, psychological perception of that sound by the human ear.
They are directly proportional - as frequency increases, perceived pitch gets higher - but the relationship is not perfectly linear.
Physical vs. Perceptual
- Frequency (f): This is the number of sound wave vibrations (cycles) that occur per second. It is measured objectively in Hertz (Hz). For example, a standard tuning fork vibrates exactly 440 times per second (440 Hz).
- Pitch: This is how "high" or "low" a sound feels to a listener. You cannot measure pitch with a physical tool; it happens entirely inside the human brain.
(Where f is frequency and T is the time period of one wave cycle).
The Logarithmic Nature of Hearing
The human ear does not perceive changes in frequency on a straight, linear scale. Instead, our perception of pitch is logarithmic.
This is most obvious in music through octaves:
- If you play a note at 220 Hz and want to hear the exact same note one octave higher, you must double the frequency to 440 Hz (a difference of 220 Hz).
- To go up another octave, you must double it again to 880 Hz (a difference of 440 Hz).
- To go up a third octave, it jumps to 1760 Hz (a difference of 880 Hz).
Even though the musical distance (the pitch interval) feels exactly the same to your brain each time, the physical gap between the frequencies grows exponentially larger.
Human Hearing Limits
The standard range of human hearing is generally accepted to be between 20 Hz and 20,000 Hz (20 kHz).
| Frequency Range | Perceived Pitch | Examples |
|---|---|---|
| Below 20 Hz | Infrasound (Unhearable) | Earthquakes, elephant rumbles (felt rather than heard). |
| 20 Hz – 250 Hz | Low / Bass | Sub-bass drops, thunder, the lowest notes on a piano or bass guitar. |
| 250 Hz – 4,000 Hz | Midrange | Human speech, a violin, most musical melodies. The ear is most sensitive here. |
| 4,000 Hz – 20,000 Hz | High / Treble | Whistles, sizzling cymbals, the "air" or crispness in a recording. |
| Above 20,000 Hz | Ultrasound (Unhearable) | Dog whistles, bat echolocation. |
Note: As humans age, the tiny hair cells in the cochlea that detect high frequencies naturally degrade. While a child might hear up to 20 kHz, most adults lose the ability to hear pitches above 15 kHz or 16 kHz.
Other Factors That Affect Pitch
While frequency is the main driver of pitch, our brains can be tricked by other physical properties of sound:
- Intensity/Volume: If a low-frequency sound (below 2,000 Hz) gets significantly louder, our brains actually perceive it as dropping slightly lower in pitch, even if the frequency stays exactly the same.
- The "Missing Fundamental": If a complex sound wave is stripped of its fundamental lowest frequency, the brain can look at the remaining overtones (harmonics) and mathematically "fill in the blank," causing you to still hear the low pitch even though the physical frequency is completely absent.
Press Play sound for a sustained tone you can sweep with the sliders, or play the keyboard below - pointer, touch, computer keys, or a connected MIDI device. Whatever you play, the highest note you're holding sets the oscillator's frequency.
…or play the keyboard below - the highest note you hold sets the frequency.
The flip side of frequency is wavelength - the distance from one crest of the wave to the next. A long, stretched-out wave fits fewer cycles into each second (low frequency, a lower and bassier pitch), while a short, tight wave packs in more (high frequency, a higher and brighter pitch).
Low frequency - long wavelength
High frequency - short wavelength
Try this on the tone above: drag the frequency slider to the very bottom or top and the sound fades into silence as you cross out of the audible range - into infrasound below 20 Hz or ultrasound above 20 kHz.
Amplitude and loudness
Amplitude is how far the wave swings - its height - and that is what we hear as loudness. A speaker driven harder pushes the air more forcefully, making a taller wave and a louder sound. Crucially, amplitude and frequency are independent: turning a sound up or down changes its loudness but never its pitch, and vice versa. Watch the graph above - the amplitude knob stretches the wave taller without changing how tightly the cycles are packed.
Low amplitude - quiet
High amplitude - loud
What carries the sound
A sound wave is a mechanical wave: it travels by jostling the particles of whatever it passes through - air, water, wood, your eardrum. That means it always needs a medium to move through. This sets it apart from electromagnetic waves like light and radio, which stream happily through empty space. It's why the vacuum of space is utterly silent, however enormous the explosion looks on screen: with no particles to pass the vibration from one to the next, the wave has nothing to travel on.
Sound and noise
Not every sound has a pitch. When a vibration is orderly - a single, steady, repeating frequency your ear can lock onto - you hear a clear musical tone, like a plucked string or a sung vowel. When it's a jumble of many frequencies with no stable pattern, you hear noise: a cymbal crash, radio static, a slammed door. Physically these are the same kind of mechanical wave; the difference is simply whether there's a steady frequency there to be perceived as a pitch.
A pitched sound - a steady, repeating wave
Noise - no single repeating frequency
A pitch on its own, though, is just a number on a dial. Music really lives in the distances between pitches - those gaps are called intervals, and stacking and sequencing them is what builds melody and harmony.