Sound as Mechanical Wave
Sound is a mechanical wave — a disturbance that travels through a material medium by causing the particles of that medium to vibrate back and forth. Unlike light, which can cross the vacuum of space, sound cannot exist without matter to carry it. When a guitar string is plucked, it pushes and pulls on neighbouring air molecules, creating alternating regions of higher pressure (compressions) and lower pressure (rarefactions) that propagate outward as a longitudinal wave. Your eardrum detects these pressure fluctuations and your brain interprets them as sound. The key feature of a mechanical wave is that energy travels through the medium, but the medium itself does not travel with it. Think of a stadium 'Mexican wave': each person stands up and sits down (vibrating about a fixed position), yet the visible wave travels all the way around the stadium. Sound behaves in exactly the same way — air molecules oscillate locally while the disturbance propagates forward. This distinction between the motion of the medium and the propagation of energy is fundamental to understanding all wave phenomena. Because sound requires a medium, its speed depends on the properties of that medium — specifically its elasticity (how readily it springs back after being compressed) and its density. Sound travels at roughly 343 m s⁻¹ in air at 20 °C, about 1480 m s⁻¹ in water, and over 5000 m s⁻¹ in steel. The denser but much more elastic solid materials transmit sound far faster than gases.
- Vibrating Sources Create Disturbances
- Longitudinal Propagation Through the Medium
- The Wave Requires a Material Medium
- Frequency, Wavelength and the Wave Equation
- Amplitude and Intensity Determine Loudness
Vibrating Sources Create Disturbances
Every sound begins with a vibrating object — a vocal cord, a loudspeaker cone, a tuning fork, or a drum skin. As the object moves outward it compresses the adjacent layer of air molecules together (compression); as it moves inward it leaves them more spread out (rarefaction). These compressions and rarefactions are regions of slightly above- and below-normal air pressure respectively.
Longitudinal Propagation Through the Medium
Sound waves are longitudinal: the particle displacement is parallel to the direction of wave travel. Each air molecule is pushed by its neighbour, then springs back, passing the disturbance along. This is fundamentally different from transverse waves (like waves on a string), where particles move perpendicular to the direction of propagation. Because gases and liquids cannot support shear (sideways) forces, sound in fluids is always longitudinal.
The Wave Requires a Material Medium
Remove the medium and sound cannot propagate — a famous demonstration places a ringing alarm clock inside a bell jar and pumps out the air: as the vacuum improves, the sound fades to silence even though the clapper is still striking. This proves sound is mechanical, not electromagnetic. The medium can be a gas, liquid, or solid; solids are generally the best conductors because their tightly packed, strongly bonded particles transmit vibrations efficiently.
Frequency, Wavelength and the Wave Equation
The number of compressions passing a fixed point per second is the frequency f (measured in hertz, Hz). The distance from one compression to the next is the wavelength λ. These are linked to the wave speed v by the universal wave equation v = fλ. Human hearing spans roughly 20 Hz to 20 000 Hz; below this range is infrasound, above it is ultrasound.
Amplitude and Intensity Determine Loudness
The amplitude of a sound wave is the maximum displacement of particles from their equilibrium positions (or equivalently, the peak pressure variation). A larger amplitude means more energy is carried per unit time per unit area — this is the intensity I, measured in watts per square metre (W m⁻²). Loudness, as perceived by the human ear, scales logarithmically with intensity, which is why we use the decibel scale.
The Key Equation
- v — Wave speed (m s⁻¹): The speed at which the sound disturbance (compression) travels through the medium. Depends on the medium's elasticity and density, not on the source.
- f — Frequency (Hz (s⁻¹)): The number of complete oscillations (compressions) passing a fixed point per second. Set by the vibrating source; higher frequency means higher pitch.
- \lambda — Wavelength (m): The distance between two successive compressions (or rarefactions). For a given medium, wavelength and frequency are inversely proportional.
Worked Example
Problem. A tuning fork vibrates at 440 Hz (concert A). The speed of sound in air at 20 °C is 343 m s⁻¹. Calculate the wavelength of the sound wave produced.
Answer. The wavelength of the 440 Hz sound wave in air is approximately 0.780 m (78.0 cm).
Origins · 1 minErnst Florens Friedrich Chladni and how this was discovered
Often called the 'father of acoustics', Chladni systematically studied the vibrations of surfaces and the nature of sound as a physical, mechanical phenomenon. His famous 'Chladni figures' — sand patterns on vibrating metal plates — provided the first visual evidence of how vibrating surfaces produce sound, demonstrating the link between mechanical vibration and acoustic wave production. He also measured the speed of sound in various gases by observing the resonant frequencies of closed tubes. When Chladni demonstrated his vibrating sand patterns to Napoleon Bonaparte in 1809, Napoleon was so impressed that he offered a prize of 3000 francs to whoever could provide a satisfactory mathematical explanation — a challenge eventually met by Sophie Germain after six years of effort.
Related Concepts
- Wave Speed, Frequency & Wavelength — The wave equation v = fλ directly governs sound waves; understanding how speed, frequency and wavelength relate is essential for analysing sound in different media.
- Longitudinal and Transverse Waves — Sound is longitudinal; comparing it to transverse waves clarifies why sound cannot travel through a vacuum and behaves differently from light.
- Speed of Sound in Different Media — The speed at which a mechanical wave propagates depends on the medium's properties; this topic explores how temperature, density and elasticity affect the speed of sound.
- Simple Harmonic Motion — Sound sources vibrate in (approximately) simple harmonic motion; the frequency and amplitude of this oscillation directly determine the pitch and loudness of the sound produced.