The Physics of Sound: Decoding the Science Behind What We Hear

At its most fundamental level, the physics of sound concerns the study of mechanical waves. When we discuss audio, we are rarely talking about the movement of matter across a distance (like wind blowing), but rather the movement of energy through matter.

Longitudinal vs. Transverse Waves

It is a common misconception to visualize sound purely as the sine waves we see on an oscilloscope or in a Digital Audio Workstation (DAW). Those visual representations are transverse mappings—showing displacement over time. However, physically, sound travels through air as a longitudinal wave.

Imagine a Slinky stretched out on a table. If you push one end forward, a pulse of compression travels down the spring. The coils themselves move back and forth, but the wave moves forward. This is how sound operates.

1. Compression: A region of high pressure where air molecules are packed tightly together.

2. Rarefaction: A region of low pressure where molecules are spread apart following the compression.

When a loudspeaker cone pushes out, it creates compression; when it pulls back, it creates rarefaction. This alternating pressure cycle is what your microphone diaphragm—and your ear—detects.

Key Wave Parameters

To analyze these waves scientifically, we look at three primary variables:

• Wavelength (λ): The physical distance between two consecutive compressions. Low bass notes have wavelengths spanning several meters (a 20Hz wave is roughly 17 meters long), while high treble notes are mere centimeters. This explains why bass frequencies are so difficult to trap in a small studio room.

• Period (T): The time it takes for one complete cycle to pass a given point.

• Velocity (v): The speed at which the wave propagates through the medium, calculated as v = f × λ (Velocity equals Frequency times Wavelength).

One of the most critical distinctions in acoustic physics is the difference between frequency and pitch. While often used interchangeably in casual conversation, strictly speaking, one is an objective physical quantity, and the other is a subjective perceptual phenomenon.

The Physics: Frequency

Frequency is the number of wave cycles that pass a fixed point in one second. We measure this in Hertz (Hz). If a violin string vibrates back and forth 440 times in a second, the frequency is exactly 440 Hz. This is measurable, quantifiable, and immutable regardless of who (or what) is listening.

The Perception: Pitch

Pitch is the human brain's interpretation of frequency. While pitch generally correlates with frequency (higher frequency equals higher pitch), the relationship is logarithmic, not linear. This is why the musical layout of a piano keyboard repeats in octaves.

The Octave Phenomenon: Mathematically, an octave represents a 2:1 frequency ratio.

• A3: 220 Hz

• A4: 440 Hz

• A5: 880 Hz

To the human ear, the interval between A3 and A4 sounds the "same" in size as the interval between A4 and A5, despite the fact that the second interval spans 440 Hz while the first spans only 220 Hz. We hear in ratios, not absolute numbers.

Frequency Bands in Audio Engineering

Understanding these ranges is vital for mixing and equipment selection. We categorize the frequency spectrum generally as follows:

While frequency determines the "note," amplitude mechanics determine the energy—and consequently, the loudness. Physically, amplitude refers to the maximum displacement of the air molecules from their equilibrium position during the compression phase. Greater displacement equals higher pressure change, which translates to more energy striking the eardrum.

The Decibel (dB) Scale

Just as our ears perceive pitch logarithmically, we also perceive loudness logarithmically. If we used a linear scale to measure sound pressure (Pascals), the numbers would be unmanageably large because the human ear has an immense dynamic range. We can hear a pin drop and a jet engine, representing a pressure difference of a factor of one million.

To manage this, we use the Decibel (dB).

• +3 dB increase: Represents a doubling of signal power (watts).

• +6 dB increase: Represents a doubling of sound pressure (voltage/amplitude).

• +10 dB increase: Roughly represents a doubling of perceived loudness by the human ear.

The Inverse Square Law

For anyone setting up a home theater or a listening room, the Inverse Square Law is a harsh reality of acoustic physics.

The Law: In a free field (no reflections), sound intensity is inversely proportional to the square of the distance from the source.

Mathematically, if you double your distance from a speaker, the sound pressure level drops by 6 dB. This means that moving from 1 meter away to 2 meters away results in a significant loss of energy. This explains why near-field monitors are so effective: they minimize the room's influence and deliver direct energy to the listener before the Inverse Square Law dissipates too much of the signal.

Why does a middle C played on a grand piano sound completely different from a middle C played on a distortion guitar or a flute? They share the same fundamental frequency (approx. 261.6 Hz), yet their character is distinct. This character is called timbre (pronounced tam-ber).

From a physics standpoint, timbre is determined by the Harmonic Series.

Complex Waveforms

In nature, pure sine waves are virtually non-existent. Almost every sound source produces a complex waveform consisting of:

1. The Fundamental Frequency: The lowest and loudest frequency, which determines the perceived pitch.

2. Overtones (Harmonics): Whole-number multiples of the fundamental frequency layered on top.

If the fundamental is 100 Hz, the harmonics will naturally occur at:

• 2nd Harmonic: 200 Hz (Octave)

• 3rd Harmonic: 300 Hz (Perfect Fifth)

• 4th Harmonic: 400 Hz (Two Octaves)

• 5th Harmonic: 500 Hz (Major Third)

The Spectral Signature

The "recipe" of these harmonics—how loud the 3rd harmonic is compared to the 2nd, for example—creates the instrument's unique fingerprint.

• Clarinet: Prominent odd harmonics, giving it a hollow, square-wave-like sound.

• Violin: Rich in all harmonics (sawtooth-like), resulting in a bright, buzzing bowing sound.

• Flute: Very strong fundamental with few weak harmonics, closer to a sine wave.

This is also why tube amplifiers are prized in the audiophile community. When driven hard, tubes tend to generate even-order harmonics (2nd, 4th), which sound musical and warm to the human ear. Solid-state devices, when clipping, often generate odd-order harmonics (3rd, 5th), which can sound harsh and dissonant.

The final piece of the physics of sound puzzle is sound propagation—how the wave interacts with the environment. Unless you are listening in an anechoic chamber, you are never hearing just the speaker; you are hearing the speaker plus the room.

The Speed of Sound

Sound speed is not constant; it depends on the medium's density and elasticity.

• Air (20°C): ~343 meters/second.

• Water: ~1,480 meters/second.

• Steel: ~5,960 meters/second.

Interestingly, in air, temperature is the biggest variable. As temperature rises, air molecules become more energetic and transmit the wave faster. This can cause pitch issues for wind instruments in outdoor concerts.

Reflection, Absorption, and Diffusion

When a sound wave hits a boundary (a wall), three things happen:

1. Reflection: The wave bounces back. In a square room, reflections between parallel walls create standing waves or "room modes," causing massive peaks and dips in bass response at specific frequencies.

2. Absorption: Soft, porous materials (acoustic foam, fiberglass, curtains) convert the sound energy into heat via friction, effectively "killing" the reflection. This is essential for controlling reverberation.

3. Diffusion: Irregular surfaces (bookcases, specialized diffusers) scatter the sound wave in many directions. This keeps the room sounding "live" and natural without the harshness of direct echoes.

The Doppler Effect

A classic example of propagation physics is the Doppler Effect. When a sound source moves relative to the listener, the waves are compressed in front of the source (higher pitch) and stretched behind it (lower pitch). While usually associated with passing ambulances, this physical principle is utilized in the "Leslie Speaker" for Hammond organs to create a swirling, chorus-like effect.