Sound as a Mechanical Wave

Sound Requires a Medium

Sound is a mechanical wave, so it must travel through matter.

A vibrating source, such as a speaker cone or tuning fork, pushes on nearby particles in the medium. Those particles then push on neighbouring particles, passing the disturbance from place to place. If there are no particles to pass on the disturbance, the sound cannot propagate. This is fundamentally different from electromagnetic waves such as light and radio, which can travel through vacuum because they do not require a material medium.

The classic bell-jar experiment demonstrates this beautifully. An electric bell is placed inside a sealed glass jar. As air is pumped out, the sound fades even though the bell hammer is still striking the gong. The hammer still vibrates — mechanical energy is still produced — but there are too few air molecules to carry the compressions and rarefactions to the observer's ear.

Sound Is Longitudinal

In a sound wave, particles oscillate parallel to the direction the wave travels.

This means sound in air is not a crest-and-trough pattern like a water-surface drawing. Instead, regions of high particle density and pressure move outward from the source. These crowded regions are compressions, and the spread-out regions are rarefactions. As the wave passes, each particle simply oscillates back and forth about its equilibrium position — it does not travel with the wave.

The longitudinal nature of sound is why it can travel through solids and liquids as well as gases. In solids, the particles are arranged in a lattice and can vibrate along the direction of the wave, transmitting compressions and rarefactions just as air molecules do. In fact, sound often travels faster in solids because the particles are closer together and more tightly bound, allowing the disturbance to be passed on more rapidly.

Sound Speed Depends on the Medium

Sound generally travels fastest in solids, slower in liquids, and slowest in gases.

This is because the medium's particles and interactions determine how efficiently the disturbance is passed along. In tightly linked materials, disturbances are usually transferred more quickly than in widely spaced gases. The speed of sound in air at room temperature is approximately 340 m/s, while in water it is about 1500 m/s and in steel it can exceed 5000 m/s. These differences have real consequences: a swimmer underwater can hear a boat engine long before someone on the surface hears it clearly, because the water transmits the sound much faster.

Temperature also matters in gases. As air warms, its molecules move faster and collide more frequently, increasing the speed of sound. This is why sound travels slightly faster on a hot summer day than on a cold winter morning, and why temperature gradients in the atmosphere can bend sound waves over long distances. The relationship is approximately $v \approx 331 + 0.6T$ m/s, where $T$ is the temperature in degrees Celsius. At 30°C, sound travels at about 349 m/s — nearly 10 m/s faster than at 0°C.

This temperature dependence has surprising consequences. On a still summer evening, the air near the ground can be cooler than the air higher up, creating a temperature inversion. Sound waves bend downward toward the cooler, denser air, which can make distant noises — such as traffic on a highway or music from a festival — audible much farther away than usual. Conversely, on a sunny day the ground heats up and sound bends upward, creating an acoustic shadow where noises from nearby sources seem unexpectedly quiet.

Pitch Is Not Loudness

Frequency affects pitch. Amplitude affects loudness.

A higher-frequency sound is heard as higher pitch. A larger-amplitude sound is heard as louder. These ideas are often confused, especially when a loud sound also feels "stronger," but they measure different aspects of the wave. A whisper can be high-pitched (high frequency, low amplitude), while a bass drum is low-pitched (low frequency, high amplitude). The two properties are independent — you can change one without changing the other.

Physiologically, the human ear detects pitch through the frequency of vibration of the basilar membrane in the cochlea. High frequencies stimulate the base of the cochlea, while low frequencies stimulate the apex. Loudness is detected through the intensity of the vibration — higher amplitude means more energy arriving per second, which the ear interprets as a louder sound.

Relating Speed, Frequency, and Wavelength

The universal wave equation $v = f\lambda$ applies to sound just as it does to any other wave.

For a given medium, the speed $v$ is approximately constant (though it depends on temperature and material properties). This means frequency and wavelength are inversely related: high-pitch sounds have short wavelengths, while low-pitch sounds have long wavelengths. A 20 Hz bass note in air has a wavelength of about 17 metres, while a 20 kHz ultrasound tone has a wavelength of only 1.7 centimetres. This enormous range explains why low-frequency sound bends around obstacles easily, while high-frequency sound is more directional and easily blocked.

In exam questions, students are sometimes given the frequency of a sound and asked to find its wavelength in a different medium. Remember: when sound moves from air to water, its frequency stays the same (determined by the source), but its wavelength increases because the wave speed is higher in water.

Sound and the Human Ear

The ear is a biological transducer: it converts the mechanical vibrations of a sound wave into electrical signals the brain can interpret.

Sound enters the ear canal and causes the eardrum to vibrate. These vibrations are amplified by three tiny bones (the ossicles) and transmitted to the cochlea, a fluid-filled spiral tube. Inside the cochlea, the basilar membrane runs along its length. Different regions of this membrane resonate at different frequencies — high frequencies near the base, low frequencies near the apex. When a particular region vibrates, hair cells there bend and send nerve impulses to the brain. This is how the ear separates pitch.

Loudness is encoded by the intensity of the vibration. A larger-amplitude sound wave delivers more energy to the eardrum, causing stronger vibrations of the ossicles and more vigorous bending of the hair cells. The ear is remarkably sensitive: at its most sensitive frequencies (around 1–4 kHz), it can detect vibrations smaller than the diameter of a hydrogen atom. However, this sensitivity also makes the ear vulnerable to damage from prolonged exposure to high-amplitude sounds, which is why occupational noise limits are strictly enforced in Australian workplaces.

The frequency range of human hearing also shrinks with age. Most adults cannot hear frequencies above 15–17 kHz, while young children may detect tones up to 20 kHz. This gradual high-frequency hearing loss, called presbycusis, is one reason why some electronic mosquito-repellent devices emit high-pitched tones that annoy teenagers but are completely inaudible to many adults.

Ultrasound and Infrasound

The human ear can detect only a narrow band of frequencies — roughly 20 Hz to 20 000 Hz. Below and above this range, sound still exists as a mechanical wave, but we cannot hear it.

Ultrasound refers to sound with frequencies above 20 kHz. Because these high frequencies have short wavelengths, ultrasound can be directed in narrow beams and reflects sharply off boundaries. This makes it invaluable for medical imaging: an ultrasound transducer sends pulses into the body, and the reflected echoes from tissue boundaries are used to build an image of a fetus or internal organ. The same principle is used by bats and dolphins for echolocation — they emit ultrasonic clicks and interpret the returning echoes to navigate and hunt.

Infrasound has frequencies below 20 Hz. Although we cannot hear it, infrasound can be felt as pressure variations. Elephants use infrasound to communicate over distances of several kilometres, and meteorological events such as thunderstorms and volcanic eruptions generate powerful infrasound that can travel around the globe. Because infrasound has such long wavelengths, it diffracts around obstacles easily and experiences very little atmospheric absorption.

The boundary between audible and inaudible sound is not perfectly sharp. Young children can often hear frequencies up to 20 kHz, while most adults lose the ability to hear above 15 kHz due to natural ageing and cumulative exposure to loud sounds. This age-related hearing loss, called presbycusis, explains why teenagers can sometimes hear high-pitched ring tones that older adults cannot. Similarly, some people are more sensitive to infrasound than others, and exposure to very intense infrasound can cause feelings of pressure, anxiety, or nausea even though the sound itself cannot be heard.