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 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
| Property | Longitudinal | Transverse |
|---|---|---|
| Oscillation direction | Parallel to propagation | Perpendicular to propagation |
| Examples | Sound, seismic P-waves | Light, water surface, seismic S-waves |
| Travels in vacuum? | No | EM waves: yes. Mechanical: no |
| Can be polarised? | No | Yes |
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.
Frequently Asked Questions
What is a longitudinal wave?
A longitudinal wave is a wave in which particles of the medium oscillate parallel to the direction of wave propagation. This creates alternating regions of compression (higher density/pressure) and rarefaction (lower density/pressure) along the wave's path. Sound is the most common example: air molecules move back and forth along the direction the sound travels, creating pressure variations. Longitudinal waves require a medium and cannot travel through a vacuum, unlike electromagnetic (transverse) waves.
What is the difference between compression and rarefaction?
In a longitudinal wave, compression is a region where particles are pushed closer together — local density and pressure are higher than normal. Rarefaction (or dilation) is a region where particles are spread further apart — local density and pressure are lower than normal. Compressions and rarefactions alternate along the wave, with a full compression-rarefaction cycle comprising one wavelength. In sound waves, compressions correspond to pressure peaks and rarefactions to pressure troughs; your eardrum detects these pressure variations.
Why can't longitudinal waves travel through a vacuum?
Longitudinal waves propagate by molecules pushing their neighbours — compression in one region pushes adjacent molecules together, which push the next region, and so on. This requires a physical medium of particles to do the pushing. In a vacuum, there are no molecules, so there is nothing to be compressed or rarefied. Sound cannot travel in space — the vacuum between planets is completely silent. This is different from electromagnetic (transverse) waves like light and radio, which are oscillating electric and magnetic fields that require no medium.
What is the speed of sound in air?
The speed of sound in dry air at 20°C is approximately 343 m/s (≈ 1,235 km/h or 767 mph). It depends on temperature: v ≈ 331 + 0.6T m/s, where T is in Celsius. At 0°C: 331 m/s. At 100°C: 391 m/s. Sound travels much faster in denser and more elastic materials: ~1,480 m/s in water and ~5,100 m/s in steel. The speed depends on the medium's bulk modulus (resistance to compression) and density, not on frequency or amplitude of the sound.
Can longitudinal waves be polarised?
No — polarisation is a property of transverse waves only. Polarisation refers to restricting the direction of oscillation to one plane; since transverse waves oscillate perpendicular to propagation, there are multiple possible oscillation planes to select from. In longitudinal waves, oscillation is always parallel to propagation — there is only one possible direction, so there is nothing to polarise. This is why polaroids and polarising filters work for light (transverse) but have no effect on sound (longitudinal).
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.
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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