What Is a Wave? Transverse vs Longitudinal
A wave is a disturbance that transfers energy from one place to another without transferring matter; in a transverse wave the particles of the medium vibrate perpendicular to the direction of travel, while in a longitudinal wave they vibrate parallel to it. In brief: light and other electromagnetic waves, and waves on a rope, are transverse; sound waves in air are longitudinal. Mechanical waves need a medium, while electromagnetic waves can travel through a vacuum. The wave speed is v = fλ.
Ripples on a pond, sound from a guitar and light from the Sun are all waves. This guide defines waves and explains how they move energy, describes transverse and longitudinal waves with examples, compares them in a table, works through wave speed calculations and corrects common mistakes.
What is a wave?
A wave is a repeating disturbance that travels through space or a medium. The source oscillates, and the disturbance is passed from one particle (or field) to the next. The particles of the medium move only a small distance about their equilibrium positions, but the energy travels long distances. A floating cork on water bobs up and down as a wave passes, but does not travel along with it. There are two main groups: mechanical waves (water waves, sound, waves on strings, seismic waves), which need a material medium, and electromagnetic waves (radio, light, X-rays), which are oscillations of electric and magnetic fields and travel through a vacuum at 3.00 × 108 m/s.
What are transverse waves?
In a transverse wave, the oscillation is at right angles to the direction in which the wave travels. A rope shaken up and down produces a wave moving along the rope, with crests (highest points) and troughs (lowest points). Examples: waves on strings, electromagnetic waves (the electric and magnetic fields oscillate perpendicular to the direction of travel), S-waves in earthquakes, and ripples on water (which actually combine transverse and longitudinal motion). Transverse waves can be polarized: restricted to oscillate in one plane. Mechanical transverse waves can travel only in solids or on the surface of liquids, because fluids do not resist shear.
What are longitudinal waves?
In a longitudinal wave, particles oscillate parallel to the direction of travel. This produces regions where the particles are close together, compressions (high pressure), and regions where they are spread apart, rarefactions (low pressure). Examples: sound in air, water and solids, P-waves in earthquakes, and a compression pulse in a slinky spring. They can travel in solids, liquids and gases, and cannot be polarized.
Transverse and longitudinal waves compared
| Feature | Transverse | Longitudinal |
|---|---|---|
| Direction of vibration | Perpendicular to the wave direction | Parallel to the wave direction |
| Features | Crests and troughs | Compressions and rarefactions |
| Medium | Solids, surfaces; EM waves need none | Solids, liquids, gases |
| Can be polarized? | Yes | No |
| Examples | Light, waves on a rope, S-waves | Sound, P-waves |
Worked example: wave speed and type
- Wave on a rope. A student shakes the end of a long rope up and down 2.0 times per second (f = 2.0 Hz), producing crests that are 1.5 m apart (λ = 1.5 m). Speed v = fλ = 2.0 × 1.5 = 3.0 m/s. The motion of the rope is vertical while the wave moves horizontally: transverse.
- Sound. A speaker emits a tone of frequency 440 Hz. In air at 20 °C, v = 343 m/s, so λ = v ÷ f = 343 ÷ 440 = 0.78 m. The air molecules vibrate along the direction of the wave: longitudinal.
- Earthquake waves. P-waves (longitudinal) travel at about 6 km/s and S-waves (transverse) at about 3.5 km/s in the crust. At 100 km, the P-wave arrives after 100 ÷ 6 = 16.7 s, the S-wave after 100 ÷ 3.5 = 28.6 s, a delay of about 12 s. The delay is used to find the distance to the earthquake.
- Light. A radio wave of frequency 100 MHz has λ = c ÷ f = 3.00 × 108 ÷ 1.00 × 108 = 3.0 m.
How were waves studied?
Christiaan Huygens proposed a wave theory of light in 1678, and Thomas Young’s double-slit experiment (1801) supported it. Augustin-Jean Fresnel explained polarization in the 1820s, which showed that light waves are transverse. Heinrich Hertz produced radio waves in 1887, confirming Maxwell’s prediction of electromagnetic waves. The study of earthquake waves led to the discovery of the Earth’s liquid outer core in 1906, since S-waves cannot pass through liquids.
Which mistakes are common?
Mistake 1: Thinking that a wave carries matter along
The medium’s particles oscillate. Energy is transferred.
Mistake 2: Thinking that sound is a transverse wave
Sound in fluids is longitudinal. Diagrams show it as a sine wave for the pressure variation, but that is only a graph.
Mistake 3: Saying that all waves need a medium
Electromagnetic waves travel through a vacuum.
Mistake 4: Confusing the speed of the wave with the speed of the particles
The wave speed is determined by the medium. The particles oscillate with a different speed that varies with time.