2.1 Frequency and pitch

Frequency and Pitch in Acoustics

Frequency and pitch sit at the foundation of how we understand and describe sound. Frequency is the physical measurement of a sound wave's oscillations, while pitch is the perceptual experience your brain creates from that frequency. Understanding both, and how they relate, is essential for everything else in acoustics.

Frequency and Pitch Perception

Frequency measures the number of complete oscillations (cycles) a sound wave completes per second, expressed in Hertz (Hz). One cycle per second equals 1 Hz.

Pitch is the subjective quality your brain assigns to a frequency. Higher frequencies are generally perceived as higher pitches, and lower frequencies as lower pitches. This correlation is strong, but pitch is a perceptual phenomenon, not a purely physical one. Factors like loudness and timbre can subtly influence how you perceive pitch.

The relationship between pitch and frequency is logarithmic, not linear. That means equal ratios of frequency sound like equal steps in pitch. The clearest example is the octave: every time frequency doubles, you hear the pitch go up by one octave. Going from 220 Hz to 440 Hz sounds like the same "step up" as going from 440 Hz to 880 Hz, even though the second jump is twice as large in absolute terms.

Calculating Frequency from Period

The period ($T$) of a wave is the time it takes to complete one full cycle, measured in seconds. Frequency and period are inversely related:

$f = \frac{1}{T}$

where $f$ is frequency in Hz and $T$ is period in seconds.

Example: If a sound wave has a period of 0.005 seconds:

$f = \frac{1}{0.005} = 200 \text{ Hz}$

This means the wave completes 200 full cycles every second. If the period gets shorter, the frequency goes up. If the period gets longer, the frequency goes down.

How the Human Ear Perceives Frequency

Your ear converts pressure waves in the air into the electrical signals your brain interprets as sound. Here's how that process works:

1. The outer ear (pinna and ear canal) collects sound waves and funnels them toward the eardrum.

2. The middle ear contains three tiny bones (ossicles) that amplify the eardrum's vibrations and transmit them to the inner ear.

3. In the inner ear, the cochlea, a fluid-filled, spiral-shaped structure, performs frequency-to-place coding. Different locations along the cochlea's basilar membrane respond to different frequencies.

   • High frequencies cause vibrations near the base of the cochlea (the wider, stiffer end).
   • Low frequencies cause vibrations near the apex (the narrower, more flexible end).

4. Hair cells sitting on the basilar membrane detect these vibrations and convert them into electrical signals sent along auditory nerve fibers.

5. The auditory cortex in the brain processes and integrates these signals, producing your perception of pitch.

This place-based coding is why damage to specific regions of the cochlea causes hearing loss at particular frequencies.

Frequency Ranges of Instruments and Voice

The human ear can detect frequencies from roughly 20 Hz to 20,000 Hz, though this upper limit decreases with age.

Voices and instruments each occupy characteristic frequency ranges:

Human Voice:

• Adult male: approximately 85–180 Hz (fundamental frequency)
• Adult female: approximately 165–255 Hz
• Child: approximately 250–300 Hz

Common Instruments:

These ranges refer to the fundamental frequencies each instrument produces. Most instruments also generate overtones (harmonics) that extend well above their fundamental range, which is a big part of what gives each instrument its distinctive sound.

Instruments and voices are often classified by their frequency range: bass (low), tenor and alto (mid-range), and soprano (high). Notice how the piano spans nearly the full range of human hearing in its fundamentals, while something like the bass drum sits entirely in the low end.