KAHIBARO
Table of Contents
Compression and rarefaction
A longitudinal wave is a wave in which the particles of the medium oscillate back and forth parallel to the direction in which the wave travels. This is the key feature that makes it different from a transverse wave. The disturbance moves through the material, but the material itself does not travel along with the wave.
In a longitudinal wave, some regions of the medium become crowded together. These regions are called compressions. Other regions become more spread out. These regions are called rarefactions. As the wave passes, each particle moves around its equilibrium position, first one way and then the other, causing these alternating dense and less dense regions to travel through the medium.
In a longitudinal wave, particle motion is parallel to wave propagation.
Compressions are high-density, high-pressure regions.
Rarefactions are low-density, low-pressure regions.
How the medium moves
To picture this, imagine a row of particles connected loosely, like air molecules in a tube or coils in a slinky. If one end is pushed and pulled repeatedly, the particles do not move with the wave from one end to the other. Instead, each particle oscillates back and forth along the same line. This repeated motion transfers energy and creates a traveling pattern of compression and rarefaction.
This means that in longitudinal waves, displacement is measured along the direction of travel. If the wave moves to the right, the particles also vibrate left and right.
Everyday examples
The most familiar example of a longitudinal wave is sound in air. When a speaker vibrates, it pushes nearby air molecules closer together and then allows them to spread apart. These pressure changes move outward through the air as a sound wave.
Longitudinal waves can also travel in liquids and solids. In general, they are especially easy to form in fluids because the particles can be compressed and expanded along the direction of motion.
| Medium | Example of longitudinal wave |
|---|---|
| Air | Sound wave |
| Water | Pressure wave |
| Solid rod or spring | Compression wave |
| Earth | Some seismic waves, such as P waves |
Wavelength in a longitudinal wave
For longitudinal waves, wavelength is measured as the distance between two successive compressions, or the distance between two successive rarefactions. These points represent repeating parts of the wave.
Although the wave is often drawn as crowded and spread-out particles, it can also be represented by a graph of pressure or density versus position. In that graph, compressions correspond to maxima and rarefactions correspond to minima.
For a longitudinal wave, one wavelength $\lambda$ is the distance between adjacent compressions or adjacent rarefactions.
What changes in the medium
A longitudinal wave often involves changes in pressure, density, and particle displacement. In sound waves, for example, the air pressure rises in a compression and falls in a rarefaction. So the wave is not only about motion of particles, but also about a pattern of changing physical conditions in the medium.
This gives two useful ways to describe the same wave.
| Description | What is shown |
|---|---|
| Particle picture | Crowded and spread-out regions |
| Pressure or density graph | High and low values |
| Displacement picture | Back-and-forth motion of particles |
Longitudinal waves and sound
Sound is one of the most important longitudinal waves in physics. When a source vibrates, it creates alternating pressure disturbances in the surrounding medium. These disturbances travel outward, carrying energy to a listener. The particles of the medium simply oscillate around their equilibrium positions.
In a vacuum, sound cannot travel because there is no medium to compress and rarefy. This is why longitudinal sound waves need matter, such as air, water, or a solid.
Mechanical longitudinal waves require a material medium.
Sound cannot travel through a vacuum.
A simple model
A slinky is a very useful model for longitudinal waves. If several coils are pushed together and released, a compression pulse travels along the slinky. Each coil moves forward and backward, but the pulse itself moves down the length of the spring.
Key idea to remember
A longitudinal wave is defined by the direction of particle vibration relative to the direction of wave travel. If both are along the same line, the wave is longitudinal. Its most visible features are compressions and rarefactions, and sound is its most common example.
A longitudinal wave has particle oscillation parallel to the direction of propagation, and it travels through alternating compressions and rarefactions.