If you have ever heard a thunderclap, felt a bass beat through a wall, or watched a Slinky spring ripple back and forth, you have experienced longitudinal waves. Unlike transverse waves — where the medium oscillates perpendicular to propagation — in a longitudinal wave the medium moves parallel to the direction the wave travels. Sound is the most important example, making longitudinal waves fundamental to acoustics, seismology, ultrasound medicine, and musical instrument design.
A longitudinal wave is a wave in which the displacement of the medium is parallel to the direction of wave propagation. The medium oscillates back and forth along the same axis the wave travels, producing alternating regions of compression (particles crowded together, high pressure) and rarefaction (particles spread apart, low pressure).
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.
Diagram — Longitudinal wave: compressions and rarefactions
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.
| Medium | Speed of sound (m/s) |
|---|---|
| Air (20°C) | 343 m/s |
| Water (20°C) | 1,480 m/s |
| Steel | 5,120 m/s |
| Granite (crust) | ~6,000 m/s |
Longitudinal vs Transverse Waves: Complete Comparison
| Feature | Longitudinal | Transverse |
|---|---|---|
| Oscillation direction | Parallel to propagation | Perpendicular to propagation |
| Wave features | Compressions and rarefactions | Crests and troughs |
| Travel in vacuum? | No — requires medium | Yes (EM waves can) |
| Can be polarized? | No | Yes |
| Examples | Sound, P-waves, ultrasound | Light, radio, S-waves, water surface |
Only transverse waves can be polarized. Polarization restricts oscillation to a single plane. Because longitudinal waves already oscillate in only one dimension (parallel to propagation), there is no additional direction to restrict. If a wave can be polarized by a filter, it must be transverse.
Frequently Asked Questions
What is a longitudinal wave?
A longitudinal wave is a wave where particles of the medium oscillate parallel to the direction of wave propagation, creating alternating compressions (high pressure) and rarefactions (low pressure). Sound is the most common example.
What is an example of a longitudinal wave?
Sound waves are the most important example. Other examples include seismic P-waves (which travel through the Earth during earthquakes), medical ultrasound, sonar, and waves along a compressed Slinky spring.
Is sound a longitudinal or transverse wave?
Sound is a longitudinal wave. Air molecules oscillate back and forth (compress and expand) along the same direction the sound wave travels. Sound cannot be a transverse wave because air cannot support the shear forces that transverse mechanical waves require.
Can longitudinal waves travel through a vacuum?
No. Longitudinal waves are mechanical — they require a medium (matter) to propagate. They transfer energy by vibrating particles; compressions and rarefactions cannot exist without matter. This is why there is no sound in space.
What are compressions and rarefactions?
Compressions are regions where particles are packed together (high pressure). Rarefactions are regions where particles are spread apart (low pressure). These alternating zones travel through the medium at the wave's speed. They are the longitudinal equivalents of crests and troughs in a transverse wave.
Can longitudinal waves be polarized?
No. Longitudinal waves cannot be polarized. Oscillation is restricted to one dimension (parallel to propagation) by definition — there is no additional direction to restrict. Only transverse waves can be polarized.
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Written by
Dr. Elena VasquezOptics researcher and physics educator specializing in wave phenomena and electromagnetic theory. PhD in Applied Physics from Stanford University.
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