13.1 Types of Waves

Types of Waves

Waves transfer energy from one place to another without permanently displacing the matter they travel through. Understanding the different types of waves and how they behave is foundational to everything else in wave physics, from sound and light to seismic activity.

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Types of Waves

Mechanical Waves and Medium Relationship

A mechanical wave is a disturbance that transfers energy through a medium. The medium can be a solid (seismic waves through rock), a liquid (ripples across water), or a gas (sound waves through air). The key idea: energy moves through the medium, but the matter itself doesn't travel with the wave. Each particle just oscillates around its equilibrium position and passes energy to its neighbor.

The speed of a mechanical wave depends on properties of the medium, particularly its density and elasticity. A stiffer, more elastic medium generally allows faster propagation. For example, sound travels at about 343 m/s in air but roughly 1,480 m/s in water and about 5,960 m/s in steel.

The medium also determines which types of waves can travel through it:

• Transverse waves require a medium with shear elasticity, which is why they travel through solids but not through liquids or gases (the particles in fluids can't sustain the side-to-side restoring force).
• Longitudinal waves can propagate through solids, liquids, and gases because they rely on compressions and expansions, which all three states of matter can support.

Wave speed can be calculated using the wave equation:

$v = f\lambda$

where $v$ is wave speed, $f$ is frequency, and $\lambda$ is wavelength.

Pulse Waves vs. Periodic Waves

• A pulse wave is a single, non-repeating disturbance. Think of snapping a rope once or dropping a single pebble into a still pond. It carries energy, but there's no repeating pattern.
• A periodic wave is a continuous, repeating disturbance. Ocean swells, sound from a tuning fork, and light waves are all periodic. These waves have well-defined properties:
  • Wavelength ($\lambda$): the distance between two consecutive identical points on the wave (crest to crest, for example)
  • Frequency ($f$): the number of complete cycles per second, measured in hertz (Hz)
  • Period ($T$): the time for one complete cycle, where $T = \frac{1}{f}$
  • Amplitude: the maximum displacement from equilibrium, which determines how much energy the wave carries. Greater amplitude means more energy.

Both pulse and periodic waves transfer energy through a medium, and both can be either transverse or longitudinal.

Longitudinal vs. Transverse Waves

The distinction here comes down to the direction particles move relative to the direction the wave travels.

Transverse waves have particle motion perpendicular to the direction of wave propagation. Picture shaking a rope up and down: the wave moves horizontally along the rope, but each point on the rope moves vertically. Other examples include electromagnetic waves (light) and ripples on a water surface.

Longitudinal waves have particle motion parallel to the direction of wave propagation. The wave consists of alternating compressions (regions where particles are pushed close together) and rarefactions (regions where particles are spread apart). Sound waves are the most common example. Seismic P-waves and pressure waves in hydraulic systems are also longitudinal.

Both types share the same core properties: wavelength, frequency, speed, and amplitude. The difference is purely in the direction of particle oscillation.

Wave Interactions

When two or more waves occupy the same space at the same time, they interfere with each other. The superposition principle governs this: the resultant displacement at any point equals the algebraic sum of the individual wave displacements at that point.

• Constructive interference occurs when waves combine to produce a larger displacement. This happens when crests align with crests (or troughs with troughs).
• Destructive interference occurs when waves combine to produce a smaller displacement (or cancel entirely). This happens when a crest aligns with a trough of equal magnitude.

After the waves pass through each other, they continue on unchanged. Superposition doesn't permanently alter the individual waves.

A wave front is a surface connecting all points of the same phase in a wave. Wave fronts are always perpendicular to the direction of propagation. For a point source, wave fronts spread out as expanding circles (in 2D) or spheres (in 3D). Far from the source, wave fronts appear nearly flat and are called plane waves.