Transverse and longitudinal waves

Direction of disturbance

Waves are often classified by the direction of the disturbance compared with the direction the wave travels. The two main types are transverse waves and longitudinal waves.

In a transverse wave, the disturbance is perpendicular to the direction of propagation. In a longitudinal wave, the disturbance is parallel to the direction of propagation.

This distinction describes how the medium moves, not necessarily how the wave energy moves. Wave energy travels in the direction of propagation.

Transverse waves

A wave on a stretched string is a standard transverse wave. If the wave travels horizontally along the string, the string elements move up and down. The displacement is perpendicular to the wave's direction of travel.

A transverse sinusoidal wave on a string may be written

$y(x,t)=Acos(kx-omega t)$

where $y$ is the transverse displacement and $x$ is the direction along the string.

Electromagnetic waves are also transverse. In light, electric and magnetic fields oscillate perpendicular to the direction of propagation and perpendicular to each other.

Longitudinal waves

Sound in air is a longitudinal wave. As sound travels, air molecules oscillate back and forth along the same direction the wave moves. The wave consists of compressions and rarefactions.

A compression is a region where particles are closer together than normal. A rarefaction is a region where particles are farther apart than normal. These pressure and density variations travel through the medium.

A longitudinal displacement wave can be represented by a function such as

$s(x,t)=s_0cos(kx-omega t)$

where $s$ is the displacement of medium elements along the x-direction.

Pressure waves

For sound, it is often more useful to describe pressure variation rather than particle displacement. The pressure variation may be written

$Delta P(x,t)=Delta P_{max}sin(kx-omega t)$

In a sinusoidal sound wave, pressure variation and particle displacement are out of phase by $pi/2$ in many simple descriptions. Pressure is greatest where particles are crowded together.

Waves in solids

Solids can support both transverse and longitudinal mechanical waves because solids resist both compression and shear deformation. Fluids such as air and water generally do not support shear waves in the same way, so sound in fluids is primarily longitudinal.

Earthquakes produce both P-waves and S-waves. P-waves are longitudinal pressure waves and travel through solids and liquids. S-waves are transverse shear waves and do not travel through liquids effectively. This difference helps scientists study Earth's interior.

Polarization

Only transverse waves can be polarized. Polarization describes the direction of oscillation. Light can be polarized because its electric field oscillates transverse to the direction of travel. Sound in air cannot be polarized in the same way because it is longitudinal.

Polarized sunglasses reduce glare by blocking light with certain electric field orientations.

Energy transport

In both transverse and longitudinal waves, the medium does not travel with the wave over long distances. Individual particles oscillate around equilibrium positions while energy moves through the medium.

For example, air molecules in a sound wave vibrate back and forth, but they do not travel from a speaker to your ear. The disturbance travels.

The big idea

Transverse and longitudinal waves differ by the direction of disturbance relative to propagation. String waves and electromagnetic waves are transverse; sound in air is longitudinal. This classification helps explain polarization, acoustics, seismic waves, and the physical mechanisms by which waves carry energy through matter or fields.