Wave Model

Introduction: Why waves are a powerful model

students, imagine dropping a pebble into a still pond 🌊. Ripples spread outward, carrying energy across the surface without the water itself traveling all the way across the pond. That is the big idea behind the wave model in physics: a wave is a way energy is transferred from one place to another through an oscillation or disturbance.

In IB Physics SL, the wave model helps explain sound, light, water waves, and many other situations. It is part of the broader topic of Wave Behaviour, which looks at how waves move, interact, reflect, refract, diffract, and resonate. In this lesson, you will learn the main ideas and vocabulary of the wave model, how to use key wave relationships, and how the model connects to real-world evidence.

By the end of this lesson, you should be able to:

explain the main ideas and terminology behind the wave model,
use the wave model to describe wave motion and calculate wave quantities,
connect the wave model to the wider topic of wave behaviour,
summarize why the wave model is useful in physics,
interpret examples and evidence that support the wave model.

What the wave model says

The wave model describes a wave as a repeating disturbance that transfers energy while the medium’s particles usually oscillate about fixed positions. In many cases, the particles do not move along with the wave over long distances. Instead, they vibrate locally, while the disturbance travels through the medium.

This distinction is important. For example, in a sound wave moving through air, air molecules move back and forth around their equilibrium positions. The sound itself travels outward, but the air does not flow from the speaker to your ear as a whole. Similarly, in ocean surface waves, water particles mostly move in circular or up-and-down paths while the wave pattern moves forward.

The wave model is especially useful because it allows physicists to predict what waves do when they encounter boundaries, openings, or other waves. It is one of the main tools used throughout wave behaviour.

Waves are often classified as either transverse or longitudinal:

In a transverse wave, the oscillations are perpendicular to the direction of travel.
In a longitudinal wave, the oscillations are parallel to the direction of travel.

A water wave on the surface is often treated as a transverse-type wave in school physics, while sound in air is a longitudinal wave. Light is also modeled as a transverse electromagnetic wave.

Key wave terms and quantities

To use the wave model well, students, you need the basic vocabulary.

Displacement is the distance and direction of a particle from its equilibrium position. Displacement can be positive or negative depending on the chosen reference point.

Amplitude is the maximum displacement from equilibrium. Larger amplitude usually means more energy carried by the wave.

Wavelength, written as $\lambda$, is the distance between two points in phase, such as crest to crest or compression to compression.

Period, written as $T$, is the time for one complete oscillation.

Frequency, written as $f$, is the number of oscillations per second. Its unit is hertz, $\text{Hz}$.

These quantities are linked by the relationship

$$f=\frac{1}{T}$$

Wave speed, written as $v$, is the speed at which the wave pattern travels. The basic wave equation is

$$v=f\lambda$$

This equation is one of the most important tools in the topic. It shows that wave speed depends on frequency and wavelength. If wave speed stays constant in a medium, then increasing frequency means wavelength must decrease.

Example 1: calculating wave speed

A water wave has frequency $f=4.0\,\text{Hz}$ and wavelength $\lambda=1.5\,\text{m}$. The speed is

$$v=f\lambda=(4.0)(1.5)=6.0\,\text{m s}^{-1}$$

So the wave travels at $6.0\,\text{m s}^{-1}$.

Example 2: finding wavelength

A sound wave travels at $v=340\,\text{m s}^{-1}$ and has frequency $f=170\,\text{Hz}$. Then

$$\lambda=\frac{v}{f}=\frac{340}{170}=2.0\,\text{m}$$

This means one full cycle of the sound wave extends over $2.0\,\text{m}$.

How waves transfer energy

The wave model emphasizes that waves transfer energy, not matter in bulk. This is one of the clearest reasons the model is useful.

Think of stadium spectators doing “the wave” ⚽. Each person stands up and sits down, but the wave moves around the stadium. The people stay near their seats while the pattern travels. In physics, a similar idea applies: the medium’s particles oscillate, but the energy propagates.

The energy carried by a wave is related to its amplitude. A wave with larger amplitude generally carries more energy. This is why louder sound waves can transfer more energy to your ear and why larger ocean waves can do more damage.

The exact energy relationship depends on the type of wave and the situation, but the general idea is that stronger oscillations mean greater energy transfer.

Phase and wave shape

Another important idea is phase. Two points are in phase if they are at the same point in their oscillation cycle. For example, two crests on a wave are in phase, and two compressions in a longitudinal wave are also in phase.

Points that are half a wavelength apart are out of phase by $180^\circ$ or $\pi\,\text{rad}$.

Understanding phase is essential for explaining interference and resonance later in the topic. It also helps when comparing oscillations at different positions along a wave.

A wave can be represented in a displacement-time graph or a displacement-distance graph:

A displacement-time graph shows how one particle of the medium moves over time.
A displacement-distance graph shows the shape of the wave at one moment in time.

These graphs are related but not the same. Students often confuse them, so students, it helps to ask: am I looking at motion at one point, or the wave pattern across space?

Using the wave model in real situations

The wave model explains many everyday and experimental situations.

Sound

Sound is a longitudinal wave that needs a medium such as air, water, or solids. It cannot travel through a vacuum because there are no particles to oscillate. This is why astronauts in space need radios rather than shouting through the vacuum.

In air, sound waves are made of compressions and rarefactions. Compresssions are regions of higher pressure and density, and rarefactions are regions of lower pressure and density.

Water waves

Water waves show how energy can move across a surface. They are often used in labs to study reflection, refraction, diffraction, and interference because they are easy to observe.

Light

Light is modeled as a wave too. In the wave model, light is an electromagnetic wave that can travel through a vacuum. This helps explain reflection, refraction, interference, and diffraction patterns.

The wave model does not mean light is only a wave in every context. But within IB Physics SL, the wave description is crucial for understanding many optical phenomena.

Evidence for the wave model

Physics models are supported by evidence, and the wave model has strong experimental support.

One major piece of evidence is interference. When two waves overlap, their displacements add together. This can produce larger or smaller resulting waves depending on phase.

Constructive interference happens when waves meet in phase, producing a larger amplitude.
Destructive interference happens when waves meet out of phase, reducing or canceling the amplitude.

The fact that light can produce interference patterns, such as in a double-slit experiment, is strong evidence for its wave nature. Sound can also interfere, creating regions where sound is louder or quieter.

Another piece of evidence is diffraction, the spreading of waves as they pass through gaps or around obstacles. Diffraction is most noticeable when the gap size is similar to the wavelength. This is why water waves spread through an opening in a barrier, and why sound can be heard around corners more easily than light can.

The wave model also helps explain reflection and refraction. Reflection is the bouncing of a wave off a boundary. Refraction is the change in direction of a wave when its speed changes as it enters a new medium.

Connecting wave model to broader wave behaviour

Wave model is not a separate island inside physics; it is the foundation for many parts of Wave Behaviour.

In reflection, the wave model explains how waves bounce from surfaces.
In refraction, it explains how waves change speed and direction.
In diffraction, it explains how waves spread out after passing through gaps.
In interference, it explains how overlapping waves combine.
In resonance, it helps explain why systems vibrate strongly at certain frequencies.

For IB Physics SL, the wave model acts like the language of the entire topic. If you can describe waves using amplitude, frequency, wavelength, period, phase, and speed, then you can build on that knowledge to explain almost every later wave idea.

Conclusion

The wave model is a core idea in physics because it explains how energy travels through disturbances and oscillations. students, the key points are that waves carry energy, not matter in bulk, and that their behaviour can be described using quantities such as $\lambda$, $f$, $T$, $v$, and amplitude. The relationships $f=\frac{1}{T}$ and $v=f\lambda$ are essential tools for solving wave problems.

This model also provides the evidence-based foundation for understanding the wider topic of Wave Behaviour. Reflection, refraction, diffraction, interference, and resonance all make sense when viewed through the wave model. By mastering these ideas, you build a strong base for sound, light, and other wave phenomena in IB Physics SL 📘

Study Notes

A wave is a repeating disturbance that transfers energy.
Particles of the medium usually oscillate about equilibrium positions.
Waves can be transverse or longitudinal.
Amplitude is maximum displacement from equilibrium.
Wavelength $\lambda$ is the distance between points in phase.
Period $T$ is the time for one complete oscillation.
Frequency $f$ is the number of oscillations per second.
Use $f=\frac{1}{T}$ to convert between frequency and period.
Use $v=f\lambda$ to connect wave speed, frequency, and wavelength.
Larger amplitude usually means more energy transfer.
In phase means same point in the oscillation cycle.
Half a wavelength corresponds to a phase difference of $180^\circ$ or $\pi\,\text{rad}$.
Sound is a longitudinal wave and needs a medium.
Light is an electromagnetic wave and can travel through vacuum.
Interference, diffraction, reflection, refraction, and resonance all build on the wave model.
The wave model is central to understanding Wave Behaviour in IB Physics SL.