Longitudinal Nature of Sound
Sound is a mechanical wave — it requires a material medium (solid, liquid, or gas) to travel through. Unlike light, which can cross empty space, sound cannot exist in a vacuum. When an object vibrates, it disturbs the surrounding medium and creates a wave that carries energy outward. The key feature that distinguishes sound from many other waves is its longitudinal nature: the particles of the medium oscillate back and forth parallel to the direction in which the wave is travelling, rather than at right angles to it. This parallel oscillation produces alternating regions of compression and rarefaction. In a compression, air molecules are pushed closer together, raising the local pressure above atmospheric pressure. In a rarefaction, molecules spread apart and the local pressure drops below atmospheric pressure. These pressure fluctuations travel outward from the source as a wave pattern at the speed of sound, roughly 343 m s⁻¹ in air at 20 °C. It is the pressure disturbance that moves through space — the individual air molecules themselves oscillate around fixed equilibrium positions and do not travel with the wave. A useful analogy is a Slinky spring stretched horizontally. If you push one end inward, a region of bunched-up coils (compression) travels along the spring toward the far end, followed by a region of stretched coils (rarefaction). The coils themselves move left and right — parallel to the spring — but the disturbance propagates along the spring's length. Sound in air behaves in exactly the same way, just in three dimensions.
- What 'Longitudinal' Means
- Compressions and Rarefactions
- Particle Displacement vs. Pressure Variation
- Why Sound Needs a Medium
- Frequency, Wavelength, and the Wave Equation
What 'Longitudinal' Means
A wave is classified as longitudinal when the displacement of the medium's particles is parallel to the direction of wave propagation. Contrast this with a transverse wave (like a wave on a string), where particle displacement is perpendicular to propagation. For sound in air, imagine a loudspeaker cone moving outward: it pushes air molecules forward, compressing them. As the cone moves back, it pulls molecules apart, creating a rarefaction. This alternating push-pull action repeats at the source's vibration frequency.
Compressions and Rarefactions
A compression is a region where air molecules are more densely packed than normal, so the local pressure is higher than atmospheric. A rarefaction is the opposite — molecules are more spread out and pressure is lower than atmospheric. These two regions are the longitudinal wave's equivalent of a transverse wave's crests and troughs. The distance from one compression to the next (or one rarefaction to the next) equals one full wavelength λ.
Particle Displacement vs. Pressure Variation
It is important to distinguish two ways of describing the same sound wave. The displacement graph shows how far each molecule moves from its equilibrium position; maximum displacement occurs midway between a compression and a rarefaction. The pressure graph shows excess pressure at each point; maximum positive excess pressure occurs at a compression and maximum negative excess at a rarefaction. These two descriptions are 90° (a quarter wavelength) out of phase with each other, which is a key examination point.
Why Sound Needs a Medium
Because sound propagates through the collision and interaction of neighbouring molecules, it cannot travel where there are no molecules — a vacuum. Increasing the density and elasticity of a medium generally increases the speed of sound. For example, sound travels at about 343 m s⁻¹ in air, roughly 1480 m s⁻¹ in water, and over 5000 m s⁻¹ in steel. The greater the restoring force (elasticity) between particles, the faster compressions and rarefactions travel.
Frequency, Wavelength, and the Wave Equation
Like all waves, longitudinal sound waves obey the universal wave equation v = fλ. The frequency f is set by the source (e.g. a vibrating guitar string) and determines the pitch we perceive. The wavelength λ is determined by both the frequency and the speed of sound in the medium. Higher-frequency sound has a shorter wavelength. The amplitude of the pressure variation determines the loudness — larger pressure swings correspond to louder sounds.
The Key Equation
- v — Speed of sound (m s⁻¹): The speed at which compressions and rarefactions propagate through the medium; approximately 343 m s⁻¹ in air at 20 °C.
- f — Frequency (Hz (s⁻¹)): The number of complete compressions (or rarefactions) passing a fixed point per second; determines the pitch of the sound.
- \lambda — Wavelength (m): The distance between two successive compressions (or rarefactions); equivalently, the distance the wave travels in one period.
Worked Example
Problem. A loudspeaker produces a note of frequency 440 Hz (concert A). If the speed of sound in air is 340 m s⁻¹, calculate the wavelength of the sound wave and state how many compressions pass a stationary observer every second.
Answer. The wavelength is approximately 0.773 m, and 440 compressions pass the observer every second.
Origins · 1 minErnst Chladni and how this was discovered
Ernst Chladni is often called the 'Father of Acoustics'. He conducted pioneering experimental investigations into the vibration of surfaces and the propagation of sound, publishing his landmark work 'Entdeckungen über die Theorie des Klanges' (Discoveries in the Theory of Sound) in 1787. He demonstrated that sound travels as a longitudinal pressure wave, measured the speed of sound in various gases, and invented the famous 'Chladni figures' — patterns formed by sand on vibrating plates — which visually revealed the nodal lines of standing waves and helped establish acoustics as a rigorous science. When Chladni demonstrated his sand-plate experiments before Napoleon Bonaparte in Paris in 1809, Napoleon was so impressed that he offered a prize of 3,000 francs to anyone who could provide a satisfactory mathematical explanation of the patterns — a challenge eventually met by Sophie Germain.
Related Concepts
- Wave Types: Transverse and Longitudinal — Sound's longitudinal nature is best understood by contrasting it with transverse waves, where particle displacement is perpendicular to wave propagation.
- Speed of Sound — The speed at which compressions and rarefactions travel depends on the medium's properties, directly linking to the longitudinal mechanism of sound propagation.
- Simple Harmonic Motion — Air molecules in a sound wave undergo simple harmonic oscillation about their equilibrium positions, making SHM the mathematical foundation of longitudinal wave behaviour.
- Sound Intensity and Loudness — The amplitude of pressure variation in a longitudinal sound wave determines the wave's intensity and the loudness we perceive.