The Physics of Sound Waves — Frequency, Amplitude, and Wavelength

Sound is one of the most fundamental phenomena in the physical world, yet the mechanics behind it are surprisingly elegant. Every conversation you have, every song you enjoy, and every thunderclap that startles you is the result of pressure waves propagating through matter. In this article, we break down the physics of sound waves — what they are, how they behave, and the key properties that define every sound you have ever heard.

What Is a Sound Wave?

A sound wave is a mechanical disturbance that transfers energy through a medium without permanently displacing the medium itself. When a guitar string vibrates, it pushes against the surrounding air molecules, which in turn push against their neighbors. This chain reaction of collisions carries the sound energy outward from the source, much like a wave moving through a crowd at a stadium — the people sway back and forth, but they do not actually travel across the arena.

Unlike electromagnetic waves such as light, which can travel through the vacuum of space, sound requires a physical medium — a gas, liquid, or solid — to propagate. This is why there is no sound in outer space, despite what many science fiction films would have you believe.

Compression and Rarefaction

Sound waves move through air by alternately squeezing and stretching the air molecules along the direction of travel. The region where molecules are pushed closer together is called a compression, and it corresponds to a zone of higher-than-normal air pressure. The region where molecules are spread farther apart is called a rarefaction, and it represents a zone of lower-than-normal pressure.

If you could zoom in and watch individual air molecules during a sound event, you would see them oscillating back and forth around their resting positions. They do not travel from source to listener; rather, they pass energy along through these pressure fluctuations. One complete cycle — from compression to rarefaction and back to compression — constitutes a single wave cycle.

Longitudinal Waves vs. Transverse Waves

Sound waves in air are classified as longitudinal waves because the particle displacement is parallel to the direction in which the wave travels. Picture a Slinky laid on a table: if you push one end forward, a compression pulse travels along its length while the coils themselves move back and forth in the same direction the pulse is traveling. This is exactly how sound behaves in gases and liquids.

By contrast, transverse waves have particle displacement perpendicular to the wave's direction of travel — like the waves you see on a vibrating guitar string or the surface of water. While sound in fluids is purely longitudinal, sound in solids can exhibit both longitudinal and transverse (shear) components, because solids have the rigidity needed to support shear stress. Seismologists use this distinction to study earthquake waves, which include both compressional P-waves (longitudinal) and shear S-waves (transverse).

The Four Key Properties of Sound Waves

1. Frequency

Frequency is the number of complete wave cycles that pass a given point per second, measured in hertz (Hz). A sound wave vibrating at 440 Hz completes 440 full cycles every second. Frequency directly determines pitch: higher frequency means higher pitch, lower frequency means lower pitch. The human ear can typically detect frequencies between 20 Hz and 20,000 Hz, though this range narrows with age and noise exposure.

2. Amplitude

Amplitude is the maximum displacement of particles from their resting position during a wave cycle. In practical terms, amplitude corresponds to the loudness of a sound. A gently plucked guitar string produces a small amplitude wave and a quiet sound; striking the string forcefully produces a large amplitude wave and a loud sound. Amplitude is measured in various units, but for sound pressure it is most commonly expressed in pascals (Pa) or, more usefully, in decibels (dB), a logarithmic scale that better reflects human perception.

3. Wavelength

Wavelength (—) is the physical distance between two consecutive identical points in a wave — for example, from one compression peak to the next. Wavelength is inversely proportional to frequency: high-frequency sounds have short wavelengths, and low-frequency sounds have long wavelengths. In air at room temperature, a 20 Hz sound wave has a wavelength of about 17.15 meters, while a 20,000 Hz sound has a wavelength of only about 1.7 centimeters.

4. Speed

The speed of sound depends on the medium and its conditions. In dry air at 20°C, sound travels at approximately 343 meters per second (about 1,235 km/h or 767 mph). Sound moves significantly faster in water — about 1,480 m/s — and faster still in steel — roughly 5,960 m/s. The speed increases with the density and elasticity of the medium.

The Wave Equation: — = v / f

The three properties of wavelength, speed, and frequency are bound together by one of the most important relationships in wave physics:

— = v / f

Where — is the wavelength in meters, v is the speed of sound in the medium (meters per second), and f is the frequency in hertz. This equation tells us that for a given medium (and therefore a fixed speed), increasing the frequency decreases the wavelength proportionally, and vice versa.

For example, the note A4 at 440 Hz traveling through air at 343 m/s has a wavelength of 343 / 440 — 0.78 meters, or about 78 centimeters. A bass note at 55 Hz in the same air has a wavelength of 343 / 55 — 6.24 meters — large enough to wrap around obstacles and penetrate through walls, which is why bass frequencies are so difficult to soundproof against.

How Amplitude Relates to Loudness

While frequency determines pitch, amplitude determines loudness — but the relationship is not straightforward. Human hearing perceives loudness logarithmically, meaning that a tenfold increase in sound intensity (energy per unit area) corresponds to an increase of only 10 decibels. A normal conversation at about 60 dB is actually a million times more intense than the faintest sound you can hear at 0 dB. This logarithmic compression allows us to perceive an enormous range of sound levels without our auditory system being overwhelmed.

It is also worth noting that our ears are not equally sensitive at all frequencies. We are most sensitive to frequencies between about 2,000 Hz and 5,000 Hz — the range that corresponds to the most important frequencies in human speech. Sounds at the extremes of our hearing range (very low or very high frequencies) need to be much louder for us to perceive them at the same subjective volume.

Waveform Types: Sine, Square, Sawtooth, and Triangle

In the world of audio synthesis and signal processing, waveforms describe the shape of an oscillating signal over time. Each waveform type has a distinct sound character because of its unique harmonic content.

The sine wave is the purest waveform, containing energy at only one frequency. It sounds smooth and featureless — think of a tuning fork or a test tone. The square wave contains the fundamental frequency plus all odd harmonics (3rd, 5th, 7th, and so on), giving it a hollow, buzzy quality often heard in early video game music. The sawtooth wave contains both odd and even harmonics, producing a rich, bright, buzzing tone that is the foundation of many synthesizer patches. The triangle wave, like the square wave, contains only odd harmonics, but their amplitudes drop off much faster, resulting in a softer, more muted sound that sits somewhere between a sine and a square.

Understanding these waveforms is essential for audio engineers, electronic musicians, and anyone who works with synthesized sound, because mixing and filtering these basic shapes is how complex, expressive electronic tones are created.

Sound Waves in the Real World

Real-world sounds are almost never perfect sine waves. A single spoken syllable contains a complex blend of frequencies that change rapidly over time. Musical instruments produce rich spectra of harmonics that evolve as a note is struck, sustained, and released. Environmental sounds — wind, rain, traffic — are broadband noise sources with energy spread across a wide frequency range.

The branch of physics that studies all of these phenomena is called acoustics, and it draws on the wave principles described here to solve problems ranging from concert hall design to noise pollution reduction to ultrasound medical imaging.