Nature and Properties of Waves: Your Friendly Study Guide!
Hey there! Welcome to the amazing world of waves. It might sound complicated, but waves are everywhere – from the sound of your favourite music and the light from your phone screen to the ripples in a pond. In this chapter, we're going to break down what waves are, how they behave, and how we can describe them. Understanding waves is fundamental to so much of physics, so let's get started. Don't worry if it seems tricky at first, we'll take it one step at a time!
Section 1: What is a Wave? The Basics
So, what exactly is a wave?
At its core, a wave is a disturbance that transfers energy from one place to another. The most important thing to remember is this:
Waves transfer energy, but they DO NOT transfer matter.
Think about a "Mexican Wave" in a stadium. The wave travels all the way around the stadium, but each person just stands up and sits down in their own seat. They don't run around with the wave! The energy (the 'wave') moves, but the people (the 'matter' or 'medium') just oscillate.
Waves are all about Oscillations
An oscillation is just a fancy word for a vibration, or a repeating back-and-forth movement around a central position (the equilibrium position). Wave motion is caused by particles of a medium oscillating. The wave itself is the pattern of these oscillations travelling through the medium.
Key Takeaway
A wave is a travelling oscillation that carries energy without carrying matter. Simple as that!
Section 2: Two Flavours of Waves - Transverse & Longitudinal
Waves come in two main types, based on the direction of oscillation compared to the direction of energy transfer.
1. Transverse Waves
In a transverse wave, the particles of the medium oscillate perpendicular (at 90°) to the direction of energy transfer.
- How to remember: The word "Transverse" has a "T" which looks like perpendicular lines.
- Examples: Light waves, all electromagnetic waves, ripples on water, a wave on a guitar string or a rope shaken up and down.
- Features: They have high points called crests and low points called troughs.
2. Longitudinal Waves
In a longitudinal wave, the particles of the medium oscillate parallel to the direction of energy transfer.
- How to remember: Think "longitudinal" is a "long" wave that pushes along the same direction it travels.
- Examples: Sound waves, a slinky spring being pushed and pulled.
- Features: They have areas where particles are bunched together, called compressions, and areas where they are spread apart, called rarefactions.
Did you know?
Earthquakes produce both transverse (S-waves) and longitudinal (P-waves) waves. P-waves travel faster and can go through liquids, while S-waves are slower and can only travel through solids. This is how scientists learned that the Earth's outer core is liquid!
Key Takeaway
Transverse = oscillation perpendicular to energy direction (like a rope wave).
Longitudinal = oscillation parallel to energy direction (like a sound wave).
Section 3: Describing Waves - The Wave Lingo
To talk about waves like a pro, we need some key terms. Let's imagine a snapshot of a transverse wave to help us.
Displacement (s or y): The distance of a particle from its equilibrium (rest) position at any instant.
Amplitude (A): The maximum displacement of a particle from its equilibrium position. For sound, a larger amplitude means a louder sound. For light, it means a brighter light.
Wavelength (λ, pronounced 'lambda'): The shortest distance between two consecutive points that are in phase. For example, the distance from one crest to the next crest. It's the length of one complete wave. Its unit is metres (m).
Period (T): The time taken for one complete oscillation of a particle, or the time for one complete wave to pass a point. Its unit is seconds (s).
Frequency (f): The number of complete oscillations per second. Its unit is Hertz (Hz).
Phase: This describes the position and direction of motion of a particle in its oscillation. Two points are in phase if they are moving in the same way at the same time (e.g., two crests). They are in antiphase (or completely out of phase) if they are moving in exactly opposite ways (e.g., a crest and a trough).
Wavefront: An imaginary line or surface connecting all adjacent points that are in phase. For ripples in a pond, the wavefronts are the circular crests spreading out.
Wave Speed (v): The speed at which energy is transferred by the wave. Its unit is m s⁻¹.
Wave Graphs - Super Important!
This is a common spot for confusion, so let's make it clear. There are two types of graphs for waves.
1. Displacement-Time Graph
- What it shows: The oscillation of ONE SINGLE PARTICLE over a period of time.
- What you can read from it: Amplitude (A) (the peak of the graph) and Period (T) (the time for one full cycle on the x-axis).
2. Displacement-Distance Graph (a 'snapshot')
- What it shows: The position of ALL PARTICLES at ONE SINGLE MOMENT in time.
- What you can read from it: Amplitude (A) (the peak of the graph) and Wavelength (λ) (the length of one full cycle on the x-axis).
Quick Review: Don't Mix Them Up!
If the x-axis is time (t), you can find the Period (T).
If the x-axis is distance (x), you can find the Wavelength (λ).
Both graphs can give you the Amplitude (A).
Section 4: The Wave Equation - The Magic Formula
These wave properties are all connected by two simple but powerful equations.
Frequency and Period
Frequency is the number of waves per second, and Period is the time for one wave. They are inverses of each other.
$$ f = \frac{1}{T} $$
If a wave has a period of 0.5 s, it means it takes 0.5 seconds for one wave to pass. So in one second, two waves must pass. The frequency is f = 1 / 0.5 = 2 Hz. It makes sense!
The Wave Equation
This is one of the most important equations in this topic. It connects wave speed, frequency, and wavelength.
Wave Speed = Frequency × Wavelength
$$ v = f\lambda $$
Step-by-step thinking:
1. Frequency (f) is how many waves pass a point every second.
2. Wavelength (λ) is the length of each of those waves.
3. So, if you multiply the number of waves per second by the length of each wave, you get the total distance the wave travels per second... which is its speed!
Example: A wave has a frequency of 50 Hz and a wavelength of 2 m. What is its speed?
v = fλ
v = 50 Hz × 2 m
v = 100 m s⁻¹
Section 5: Wave Properties Part 1 - Bouncing and Bending
Reflection
Reflection is when a wave bounces off a barrier. Think of an echo (reflection of sound) or your image in a mirror (reflection of light).
Key facts for reflection:
- The wave bounces off the surface.
- The frequency, wavelength, and speed of the wave DO NOT change.
- Only the direction of travel changes.
We can show this using wavefronts. The wavefronts hit the barrier and bounce off, maintaining their spacing (wavelength).
Refraction
Refraction is when a wave changes direction as it passes from one medium into another, due to a change in speed.
Analogy: Imagine you're pushing a lawnmower from smooth concrete onto thick grass at an angle. The first wheel that hits the grass slows down, while the other wheel on the concrete keeps going fast. This difference in speed causes the lawnmower to turn. Waves do the same thing!
Key facts for refraction:
- The frequency of the wave STAYS THE SAME. (The source is still producing the same number of waves per second).
- The wave speed changes. (It travels slower in a 'denser' medium).
- Since v = fλ and f is constant, the wavelength (λ) must also change. If the wave slows down, the wavelength gets shorter.
Refractive Index (n)
We can describe how much a medium slows down a wave using its refractive index. The syllabus defines it in terms of speeds:
$$ n = \frac{\text{speed of wave in medium 1}}{\text{speed of wave in medium 2}} $$
If a wave goes from air into water, it slows down. So the speed in medium 2 (water) is less than in medium 1 (air), making the refractive index of water greater than 1.
Section 6: Wave Properties Part 2 - Spreading and Meeting
Diffraction
Diffraction is the spreading out of waves as they pass through a narrow gap or around an obstacle.
The key rule of diffraction:
Diffraction is most significant (the wave spreads out the most) when the size of the gap is similar to the wavelength (λ) of the wave.
- If the gap is much larger than the wavelength, the wave passes through almost unchanged, with only a little spreading at the edges.
- If the gap is much smaller than the wavelength, most of the wave is blocked.
This is why you can hear someone talking around a corner (sound waves have a long wavelength and diffract easily) but you can't see them (light waves have a tiny wavelength and barely diffract around large objects like walls).
Superposition and Interference
What happens when two waves meet? They combine!
The Principle of Superposition states that when two or more waves overlap, the resultant displacement at any point is the vector sum of the individual displacements of the waves.
This combining of waves is called interference. To see a clear interference pattern, we need coherent sources. This is a very important term! Coherent sources are sources that produce waves with:
- The same frequency.
- A constant phase difference.
1. Constructive Interference
- What happens: A crest meets a crest, or a trough meets a trough. The waves are in phase.
- Result: The amplitudes add up to create a 'super-crest' or 'super-trough' with a larger amplitude.
- Condition: The path difference from the two sources is a whole number of wavelengths.
Path Difference = nλ (where n = 0, 1, 2, ...)
2. Destructive Interference
- What happens: A crest meets a trough. The waves are in antiphase.
- Result: The amplitudes cancel each other out, resulting in a smaller or even zero amplitude.
- Condition: The path difference from the two sources is a half-number of wavelengths.
Path Difference = (n + ½)λ (where n = 0, 1, 2, ...)
Section 7: When Waves Stand Still - Stationary Waves
So far we've talked about progressive waves, which travel and transfer energy. But what if a wave meets a reflection of itself coming back the other way?
A stationary wave (or standing wave) is formed from the superposition of two progressive waves with the same frequency, amplitude, and speed, travelling in opposite directions.
Characteristics of Stationary Waves
They look very different from travelling waves:
- Nodes (N): Points that do not move at all. They have zero amplitude. This is where permanent destructive interference occurs.
- Antinodes (A): Points where the oscillation has the maximum amplitude. This is where permanent constructive interference occurs.
- Energy: Energy is not transferred along the wave. It is 'trapped' and stored between the nodes.
- Phase: All particles between two adjacent nodes oscillate in phase with each other. Particles in the next segment are in antiphase.
A great example is a guitar string. When you pluck it, you create a stationary wave. The points where the string is fixed are nodes, and the middle part that vibrates the most is an antinode.
Quick Comparison: Progressive vs. Stationary Wave
Progressive Wave:
- Wave profile moves forward.
- Transfers energy.
- All particles have the same amplitude.
- Phase changes continuously along the wave.
Stationary Wave:
- Wave profile stays in the same place.
- Does not transfer energy.
- Amplitude varies from zero (nodes) to maximum (antinodes).
- All particles in one segment are in phase.
Key Takeaway
Stationary waves are formed when a wave interferes with its own reflection. They have nodes (no movement) and antinodes (max movement) and do not transfer energy.