Longitudinal Waves: Definition, Diagram, Examples & vs Transverse

Sound doesn't push air sideways. It squeezes and stretches it — alternating compressions and rarefactions travelling outward from the source. That's a longitudinal wave: the medium moves in the same direction the wave travels, not perpendicular to it. It's a fundamentally different kind of wave motion from light, and that difference explains why sound can't travel through a vacuum, why it bends around corners, and why you can't polarise it.

Longitudinal waves are everywhere: sound in air, seismic P-waves through rock, pressure waves in a doctor's ultrasound machine. Understanding how they work — really understanding, not just memorising the definition — gives you a physical picture that makes sense of all of these at once.

What Is a Longitudinal Wave?

The defining characteristic is the parallel relationship between oscillation direction and propagation direction. Push and pull one end of a horizontal Slinky: the coils compress and expand along the horizontal axis, and the wave pulse also travels horizontally. Both disturbance and propagation are parallel — that is a longitudinal wave.

This contrasts directly with a transverse wave, where oscillation is perpendicular to propagation. Shake the same Slinky up and down: the wave still travels horizontally, but the coils move vertically — transverse. The geometry of oscillation relative to propagation is the fundamental distinction.

Compressions and Rarefactions

Longitudinal waves are characterised by two alternating zones:

Compressions: regions where particles are pushed together — higher density and pressure than equilibrium. These are the "peaks" of the pressure variation.

Rarefactions: regions where particles are pulled apart — lower density and pressure. These are the "troughs" of the pressure variation.

The wavelength of a longitudinal wave is the distance between consecutive compression centres (or consecutive rarefaction centres) — exactly analogous to peak-to-peak distance in a transverse wave.

The Wave Equation

Longitudinal waves obey the universal wave equation:

where v is wave speed (m/s), f is frequency (Hz), and λ is wavelength (m). All wave properties — frequency, amplitude, period, wave speed, wavelength — apply identically to longitudinal and transverse waves. Only the direction of oscillation differs.

Examples of Longitudinal Waves

1. Sound waves

Sound is the most important longitudinal wave in everyday life. A vibrating speaker cone creates alternating compressions and rarefactions in air. These pressure variations travel outward at approximately 343 m/s in air at 20°C, 1,480 m/s in water, and 5,120 m/s in steel. Your ear detects the pressure variations as sound.

2. Seismic P-waves

During earthquakes, the Earth transmits primary waves (P-waves) — longitudinal waves where rock compresses and expands along the propagation direction. P-waves travel at 5–8 km/s through the crust. Crucially, they can pass through solids, liquids, and gases — unlike S-waves (transverse), which cannot pass through liquids. The detection of P-waves but not S-waves on the far side of the Earth from an earthquake epicentre was the evidence that clinched the liquid outer core model in 1936.

3. Ultrasound

Medical ultrasound uses longitudinal waves at frequencies above 20,000 Hz. A transducer sends compressions into the body; tissues reflect them at different strengths. Returning echoes construct images. The same principle works in sonar and industrial non-destructive testing of welds and castings.

4. Spring (Slinky) waves

The classic classroom demo: push and pull one end of a stretched Slinky. Compression zones travel from one end to the other with coils moving parallel to propagation. It is a textbook longitudinal wave — visible and slow enough to observe directly.

5. Infrasound

Frequencies below 20 Hz — inaudible to humans — are infrasound. Elephants, whales, and some birds use infrasound for long-distance communication. Volcanic eruptions and meteor strikes produce infrasound detectable thousands of kilometres away. All sound, including infrasound, is a longitudinal wave.

Speed of Longitudinal Waves Through Different Media

where B is the bulk modulus (resistance to compression) and ρ is density. Stiffer media transmit longitudinal waves faster; denser media transmit them more slowly. Steel transmits sound faster than air despite being denser — its much greater stiffness outweighs the density increase.

Longitudinal vs Transverse Waves: Complete Comparison

What Are Longitudinal Waves?

In a longitudinal wave, particles oscillate parallel to the direction of wave propagation — back and forth along the same axis the wave travels. This creates alternating regions of compression (particles bunched together, higher pressure) and rarefaction (particles spread apart, lower pressure). Sound is the most important example: air molecules oscillate back and forth as the sound wave passes, creating pressure variations that your eardrum detects.

Key Properties

Longitudinal waves require a medium (they cannot travel through a vacuum, unlike electromagnetic waves). Speed depends on the medium's elasticity and density. In air at 20°C: v ≈ 343 m/s. In water: ~1,480 m/s. In steel: ~5,100 m/s — denser and more elastic media transmit longitudinal waves faster. Wavelength is the distance between consecutive compressions (or rarefactions). Frequency is the number of complete compressions passing a point per second. v = fλ applies to longitudinal waves exactly as to transverse waves.

Sound as a Longitudinal Wave

A loudspeaker cone vibrates, alternately compressing and rarefying air. These pressure waves travel outward at 343 m/s. At 440 Hz (concert A): λ = 343/440 = 0.780 m. At 20 Hz (lowest audible): λ = 17.15 m. At 20,000 Hz (highest audible): λ = 0.017 m = 1.7 cm. Infrasound (<20 Hz) propagates further with less absorption — elephants communicate at ~14–35 Hz over kilometres. Ultrasound (>20 kHz) is used in medical imaging because shorter wavelengths resolve finer detail.

Comparing Transverse and Longitudinal Waves

Seismic P-Waves and S-Waves

Earthquakes generate both longitudinal waves (P-waves — primary, travel through solids and liquids) and transverse waves (S-waves — secondary, travel only through solids). P-waves travel at ~6–8 km/s through Earth's crust; S-waves at ~3–4 km/s. The time difference between P and S arrival at a seismometer gives the distance to the earthquake source. That P-waves pass through Earth's liquid outer core while S-waves do not was key evidence that Earth's outer core is liquid — the first seismological proof of Earth's internal structure.

The Speed of Sound in Different Media

The speed of a longitudinal wave depends on the medium's bulk modulus B (resistance to compression) and density ρ: v = √(B/ρ). High bulk modulus (stiff, hard to compress) → faster wave. Higher density → slower wave. For steel: B ≈ 160 GPa, ρ ≈ 7,900 kg/m³ → v = √(160×10⁹/7900) ≈ 4,500 m/s. For air: B ≈ 142 kPa, ρ ≈ 1.2 kg/m³ → v ≈ 343 m/s. Temperature affects speed through changes in B and ρ: in gases, v ∝ √T (speed increases with temperature).

Measuring the Speed of Sound

Historical methods: Marin Mersenne (1636) timed echoes from a wall at a known distance, getting ~450 m/s (too slow due to poor timing). Modern methods: measure the time for a sound pulse to travel a known distance using electronic timing (accurate to microseconds). Interference methods: two microphones at different distances from a speaker; the phase difference at each frequency determines the wavelength, and v = fλ gives the speed. Speed of sound in air is also used to measure temperature in meteorology — weather balloons carry sounders to probe atmospheric temperature profiles.

Frequently Asked Questions