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C.2.1 Classification of waves

Classification of Waves

Definition

Waves

Waves are disturbances that transfer energy from one place to another without transferring matter.

They can be classified based on how the particles of the medium move relative to the direction of wave propagation.

Transverse Waves: Particle Motion Perpendicular to Wave Propagation

In transverse waves, the particles of the medium oscillate perpendicularly to the direction of wave propagation.

Example

  • Water Waves:
    • In water waves, the water molecules move up and down while the wave travels horizontally across the surface.
  • Electromagnetic Waves:
    • Light waves, radio waves, and X-rays are all transverse waves.
    • In these waves, oscillating electric and magnetic fields are perpendicular to the direction of wave travel.

Note

  • Transverse waves can travel through solids and on the surface of liquids, but not through gases or within liquids.
  • This is because gases and liquids do not have the structural rigidity needed to support perpendicular oscillations.

Longitudinal Waves: Particle Motion Parallel to Wave Propagation

In longitudinal waves, the particles of the medium oscillate parallel to the direction of wave propagation.

Example

  • Sound Waves:
    • In sound waves, air molecules compress and rarefy as the wave travels through the air.
  • Compression Waves in a Slinky:
    • When you push and pull a slinky, coils move back and forth in the same direction as the wave.

Note

Longitudinal waves can travel through solids, liquids, and gases because they rely on compressions and rarefactions, which all states of matter can support.

Illustrating transverse and longitudinal waves.
Illustrating transverse and longitudinal waves.
Definition

Compression

A compression is a region in a longitudinal wave where the particles of the medium are close together, resulting in a high-pressure area. In sound waves, compressions correspond to regions of increased air density and pressure.

Definition

Rarefaction

A rarefaction is a region in a longitudinal wave where the particles of the medium are spread apart, resulting in a low-pressure area. In sound waves, rarefactions correspond to regions of decreased air density and pressure.

Key Wave Parameters: Wavelength, Frequency, Time Period, and Wave Speed

To fully describe a wave, we need to understand several key parameters:

Wavelength (λ)

  • The wavelength (λ) is the distance between two consecutive points in phase on a wave, such as crest to crest or trough to trough.
  • It is measured in meters (m).

Example

If the distance between two crests of a water wave is 2 meters, the wavelength of the wave is 2 m.

Definition

Crest

A crest is the highest point of a wave, where the displacement of the medium is at its maximum positive value relative to the equilibrium position. In a transverse wave, crests correspond to peaks in the wave motion.

Definition

Trough

A trough is the lowest point of a wave, where the displacement of the medium is at its maximum negative value relative to the equilibrium position. In a transverse wave, troughs correspond to the lowest points in the wave motion.

Frequency (f)

  • The frequency (f) is the number of complete waves that pass a given point in one second.
  • It is measured in hertz(Hz), where 1 Hz = 1 wave per second.

Example

If 5 waves pass a point in 1 second, the frequency of the wave is 5 Hz.

Time Period (T)

  • The time period (T) is the time taken for one complete wave to pass a given point.
  • It is measured in seconds (s).

Note

Frequency and time period are reciprocally related: T=1f

Wave Speed (v)

  • The wave speed (v) is the speed at which the wave propagates through the medium.
  • It is measured in meters per second (m/s).
Key parameters of a wave.
Key parameters of a wave.

Wave Speed Equations

  1. The speed of a wave is determined by its wavelength and frequency.
  2. The relationship between these parameters is given by the wave speed equation:

v=fλ

This equation can also be expressed in terms of the time period:

v=λT

Tip

The wave speed depends only on the properties of the medium, not on the frequency or wavelength of the wave. For example, the speed of sound in air is approximately 340 m/s, regardless of the frequency of the sound wave.

Example question

Calculating Wave Speed

A sound wave has a frequency of 440 Hz and a wavelength of 0.78 m. What is its speed?

Solution

  1. Use the wave speed equation: v=fλ
  2. Substitute the values: v=440Hz×0.78m
  3. Calculate the result: v=343.2m/s

The speed of the sound wave is 343.2 m/s.

Comparing Transverse and Longitudinal Waves

FeatureTransverse WavesLongitudinal Waves
Particle MotionPerpendicular to wave directionParallel to wave direction
ExamplesLight waves, water wavesSound waves, compression waves
MediumSolids, surfaces of liquidsSolids, liquids, gases

Common Mistake

Don’t confuse the direction of particle motion with the direction of wave propagation.

In both transverse and longitudinal waves, energy is transferred in the direction of wave propagation, not in the direction of particle motion.

Self-Assessment

Theory of Knowledge

How does the classification of waves influence the technologies we develop? For example, why are electromagnetic waves used for communication instead of sound waves?

Self review

  1. What is the main difference between transverse and longitudinal waves?
  2. How are wavelength and frequency related to wave speed?
  3. If the frequency of a wave doubles, what happens to its wavelength (assuming the wave speed remains constant)?

Understanding the classification of waves and their key parameters provides a foundation for exploring more complex wave phenomena, such as interference, diffraction, and polarization.

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Questions

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Question 1

How do the properties of transverse waves, such as light waves, differ from those of longitudinal waves, such as sound waves?

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Note

Definition of Waves

A wave is a disturbance that transfers energy from one place to another without transferring matter. This fundamental concept underlies all types of waves.

  • Think of a wave as a "disturbance" that moves through a medium, like a ripple on a pond.
  • The medium (e.g., water, air) doesn't travel with the wave; only the energy does.

Analogy

Imagine a crowd doing a "wave" at a stadium. The people (particles) stay in their seats, but the wave (energy) moves around the stadium.

Example

When you drop a pebble into a pond, the ripples that spread out are waves transferring energy from the point of impact.

Definition

Wave

A disturbance that transfers energy without transferring matter.

Note

Waves can travel through different media, including solids, liquids, and gases.