17.1 Sound

Sound Waves

Sound waves are vibrations that travel through matter, produced by oscillating objects like vocal cords, tuning forks, or speakers. They require a medium to propagate, which means sound can't travel through a vacuum. Understanding how sound behaves as a wave is the foundation for everything else in this unit.

Creation and Transmission of Sound Waves

Sound begins with a vibrating object. When a tuning fork vibrates, it pushes against the air molecules around it, creating regions of high pressure (compressions) and low pressure (rarefactions) that spread outward through the medium.

These are longitudinal waves, meaning the particle oscillations are parallel to the direction the wave travels. This is different from transverse waves (like waves on a string), where particles move perpendicular to the wave direction.

• Sound can propagate through gases (air), liquids (water), and solids (metal).
• It cannot travel through a vacuum because there are no particles to transfer the energy.

Transmission works through a chain reaction: each particle bumps into its neighbor, passing energy along without any individual particle traveling far from its original position. Think of a long line of billiard balls touching each other. Tap one end, and the energy transfers to the other end, but each ball barely moves.

How efficiently sound transmits depends on the acoustic impedance of the medium. Denser, stiffer materials (like steel) generally transmit sound faster than less dense ones (like air).

Key Characteristics of Sound Waves

Four properties define a sound wave: wavelength, frequency, amplitude, and speed.

Wavelength ($\lambda$) is the distance between two consecutive points in phase on a wave, measured in meters. Shorter wavelengths correspond to higher-pitched sounds (like a piccolo), and longer wavelengths correspond to lower-pitched sounds (like a tuba).

Frequency ($f$) is the number of complete wave cycles passing a fixed point per second, measured in Hertz (Hz). Human hearing typically spans 20 Hz to 20,000 Hz. Frequencies below 20 Hz are called infrasound, and frequencies above 20,000 Hz are called ultrasound.

Amplitude is the maximum displacement of a particle from its equilibrium (rest) position. It determines the energy carried by the wave and directly relates to loudness. A jet engine produces high-amplitude sound waves; a whisper produces low-amplitude ones.

Speed ($v$) is how fast the wave travels through a medium. In air at room temperature (about 20°C), the speed of sound is approximately 343 m/s. Sound travels faster in liquids and faster still in solids (for example, about 1,480 m/s in water and 5,960 m/s in steel).

These three quantities are linked by a fundamental equation:

$v = f \lambda$

If you know any two of these values, you can solve for the third.

Sound Properties and Human Perception

Pitch is how we perceive frequency. Higher-frequency waves sound higher-pitched (soprano voice), and lower-frequency waves sound lower-pitched (bass voice). You can change the pitch of a vibrating object by adjusting its tension (tightening a guitar string raises the pitch), its length (shorter organ pipes produce higher pitches), or its mass per unit length (thinner xylophone bars vibrate faster).

Volume is how we perceive the amplitude of a sound wave.

• Sound intensity is the power a sound wave carries per unit area, measured in watts per square meter ($\text{W/m}^2$).
• Because the range of intensities we can hear is enormous, a logarithmic scale is used. Decibels (dB) express sound intensity levels, where 0 dB is the threshold of human hearing (about $1 \times 10^{-12} \text{ W/m}^2$) and around 120 dB is the threshold of pain.
• Each increase of 10 dB corresponds roughly to a doubling of perceived loudness.

Timbre is the quality that lets you tell different instruments apart even when they play the same note at the same volume. A violin and a piano playing the same pitch sound different because each instrument produces a unique combination of harmonics (multiples of the fundamental frequency). The specific pattern of harmonics present gives each sound source its distinctive character.

Wave Phenomena in Sound

Several important wave behaviors show up in the context of sound:

• Interference occurs when two or more sound waves overlap. If their compressions line up, they add together (constructive interference, producing a louder sound). If a compression lines up with a rarefaction, they cancel (destructive interference, producing a quieter sound or silence).
• Standing waves form when sound reflects back and forth in a confined space (like inside a pipe or on a guitar string), creating fixed points of zero displacement (nodes) and maximum displacement (antinodes).
• Resonance happens when an object is driven at one of its natural frequencies, causing it to oscillate with a much larger amplitude. This is why pushing a swing at just the right timing makes it go higher.
• Beats are periodic rises and falls in loudness that occur when two sound waves with slightly different frequencies overlap. The beat frequency equals the difference between the two frequencies: $f_{\text{beat}} = |f_1 - f_2|$.
• The Doppler effect is the shift in observed frequency when the source and observer are moving relative to each other. An ambulance siren sounds higher-pitched as it approaches you and lower-pitched as it moves away.