General Properties of WavesCambridge IGCSE Physics: Revision notes
Section 1
How do waves transfer energy?
Waves transfer energy from one place to another without transferring matter. This is a fundamental property that distinguishes wave motion from particle motion.
When a wave passes through a medium:
- The medium particles vibrate about their equilibrium position
- These particles do not move with the wave; they oscillate back and forth
- Energy is passed from particle to particle, allowing the wave to propagate
Examples of energy transfer without matter transfer:
- Water waves transfer energy across the ocean surface; the water molecules rise and fall but do not travel with the wave
- Sound waves transfer energy through air; air molecules vibrate but do not move in the direction of sound propagation
- Electromagnetic waves (light, radio) transfer energy through space without requiring a medium
A wave is like a Mexican wave at a stadium: the energy passes around the crowd, but each person only moves up and down momentarily before returning to their seat.
Section 2
What are the key features of a wave?
All waves have measurable properties that describe their characteristics and behaviour:
| Feature | Definition | Symbol |
|---|---|---|
| Amplitude | Maximum displacement of a particle from its equilibrium position | A |
| Wavelength | Distance between consecutive crests (or troughs) or any two identical points on adjacent waves | λ |
| Frequency | Number of complete oscillations (or waves) passing a point per second; measured in hertz (Hz) | f |
| Period | Time taken for one complete oscillation or for one complete wave to pass a point | T |
| Wave speed | Distance travelled by a wave per unit time | v |
| Crest | The highest point of a wave (maximum positive displacement) | — |
| Trough | The lowest point of a wave (maximum negative displacement) | — |
| Wavefront | A line or surface joining all points of the wave that are in phase (oscillating together) | — |
Important relationship: Frequency and period are inversely related: f = 1/T or T = 1/f
Examiners expect you to identify amplitude as the distance from equilibrium to crest (not crest to trough). State values with correct units and show which feature you are measuring on a diagram.
If a wave has a wavelength of 0.5 m and passes a point 10 times per second, then frequency f = 10 Hz and period T = 0.1 s. The wavelength is the distance between two consecutive crests or troughs.
Section 3
How does the wave equation relate wave properties?
The wave equation connects wave speed, frequency and wavelength:
v = fλ
Where:
- v = wave speed (m/s)
- f = frequency (Hz)
- λ = wavelength (m)
Using the equation:
- Calculating wave speed: If you know frequency and wavelength, multiply them together
- Calculating frequency: Divide wave speed by wavelength (f = v/λ)
- Calculating wavelength: Divide wave speed by frequency (λ = v/f)
Key principle: For a given medium, wave speed is constant (determined by the medium's properties). Therefore, if frequency increases, wavelength must decrease proportionally, and vice versa.
Example calculation: A sound wave travels at 330 m/s with a frequency of 440 Hz. Using v = fλ: λ = v/f = 330/440 = 0.75 m
Always check your units before calculating: frequency should be in Hz, wavelength in metres, and speed in m/s. Show all working and include units in your final answer.
Students often confuse which property changes when a wave enters a new medium. Frequency never changes, but speed and wavelength both decrease if the medium is denser.
A water wave has a speed of 2 m/s and frequency of 4 Hz. Wavelength λ = v/f = 2/4 = 0.5 m. If the wave speed decreased to 1.5 m/s (in shallower water), the new wavelength would be 1.5/4 = 0.375 m, but frequency remains 4 Hz.
Section 4
What is the difference between transverse and longitudinal waves?
Waves are classified by the direction of particle vibration relative to the direction of wave propagation:
| Property | Transverse Waves | Longitudinal Waves |
|---|---|---|
| Direction of vibration | Perpendicular (at right angles) to direction of propagation | Parallel to direction of propagation |
| Particle motion | Up and down (or side to side) while wave moves horizontally | Back and forth (compression and rarefaction) in direction of wave travel |
| Crests and troughs | Clearly visible and identifiable | Not present; instead have compressions and rarefactions |
| Examples | Electromagnetic radiation, water waves, seismic S-waves | Sound waves, seismic P-waves |
| Medium required | Can travel through solids, liquids and gases (or no medium for EM waves) | Require a medium to propagate |
Transverse wave features:
- Direction of vibration is perpendicular to direction of propagation
- Display clear crests (highest points) and troughs (lowest points)
- Amplitude measured from equilibrium to crest or trough
Longitudinal wave features:
- Direction of vibration is parallel to direction of propagation
- Display compressions (regions of high density/pressure) and rarefactions (regions of low density/pressure)
- Cannot exist in a vacuum (except electromagnetic waves, which are transverse)
When describing wave type, always state the direction of vibration relative to propagation. Say 'particles vibrate perpendicular to propagation' for transverse and 'parallel to propagation' for longitudinal.
A transverse wave is like a skipping rope being flicked up and down—the rope vibrates vertically while the wave travels horizontally. A longitudinal wave is like a slinky being pushed along its length—compressions and rarefactions travel in the same direction as the particle motion.
Section 5
How do waves behave when they meet boundaries or obstacles?
Waves interact with their environment in three main ways:
1. Reflection
- Occurs when a wave meets a plane (flat) surface and bounces back
- The angle of incidence equals the angle of reflection (measured from the normal)
- The reflected wave travels back into the original medium
- Energy is not lost (or minimal loss in ideal cases)
- Examples: Light reflecting off a mirror, sound echoes off walls, water waves bouncing off barriers
2. Refraction
- Occurs when a wave changes speed due to entering a different medium
- The wavelength changes (frequency remains constant)
- If the wave slows down, it bends towards the normal
- If the wave speeds up, it bends away from the normal
- The direction of propagation changes, but the wave continues to travel
- Examples: Light bending through glass, water waves changing speed in shallower water, seismic waves bending through different rock layers
3. Diffraction
- Occurs when a wave passes through a narrow gap or past an edge/obstacle
- The wave spreads out and bends into the region behind the gap or obstacle
- Creates a pattern where the wave no longer travels in straight lines
- More noticeable when the wavelength is large compared to gap size
- Examples: Sound waves bending around buildings, light passing through a doorway, water waves spreading through a harbour entrance
Factors affecting diffraction:
- Larger wavelength → more diffraction (greater spreading)
- Smaller gap or obstacle → more diffraction
- Smaller wavelength → less diffraction (straighter propagation)
For refraction, remember: frequency is always constant, but speed and wavelength change. Use v = fλ to predict how wavelength changes when speed changes.
Students often confuse diffraction with refraction. Diffraction requires a gap or edge and produces spreading; refraction requires a change of medium and produces bending with a specific direction.
Sound with frequency 1000 Hz and wavelength 0.34 m travels at 340 m/s in air. When it enters water where sound speed is 1500 m/s, the frequency stays 1000 Hz but the new wavelength becomes λ = 1500/1000 = 1.5 m. The sound refracts (bends) because of the speed change.
Section 6
How is a ripple tank used to demonstrate wave properties?
A ripple tank is a shallow tank of water with a light source above and a screen below, used to observe water wave behaviour in a controlled way.
Demonstrating Reflection:
- A plane barrier (flat wall) is placed in the tank
- Water waves from the dipper hit the barrier and bounce back
- The reflected wavefront is observed on the screen
- Angle of incidence = angle of reflection is clearly visible
- Shows that wave direction changes but speed remains constant
Demonstrating Refraction due to Change in Depth:
- A shallow region is created in part of the tank (using a glass sheet slightly submerged)
- Waves travel from deep water into shallow water and slow down
- The wavelength decreases (frequency constant)
- Waves bend towards the normal as they enter shallower water
- Demonstrates that wave speed is reduced in shallower water
Demonstrating Diffraction through a Gap:
- A gap (narrow opening) is created using two barriers with space between them
- Waves pass through the gap and spread out (diffract) beyond it
- A wider gap produces less diffraction
- A narrower gap produces more diffraction
- Shows relationship: smaller gap → more spreading
Demonstrating Diffraction at an Edge:
- Waves encounter a single straight barrier edge
- The waves bend around the edge into the shadow region
- Shows that waves do not travel in perfectly straight lines
- Demonstrates how waves spread into regions that would be blocked if light was used instead
Key Observation about Wavelength:
- Short wavelength waves: show less diffraction (more concentrated propagation)
- Long wavelength waves: show more diffraction (wider spreading)
- This is controlled by adjusting the frequency of the dipper in the ripple tank
When describing ripple tank observations, reference what is seen on the screen (the shadow pattern of wavefronts). State clearly whether wavelength, frequency or direction changes for each phenomenon.
In a ripple tank, a wave with wavelength 4 cm travels into shallower water where it slows to half its original speed. The frequency remains constant, but the new wavelength is λ = (v/2)/f = 2 cm. On the screen, the wavefronts appear closer together in the shallow region.
Must Know
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Waves transfer energy without transferring matter. Particles vibrate about equilibrium; the wave propagates through the medium, not the matter itself.
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Key wave features: amplitude (maximum displacement), wavelength (distance between crests/troughs), frequency (oscillations per second), period (time per oscillation), and wave speed (v = fλ). Always measure amplitude from equilibrium, not peak-to-peak.
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The wave equation v = fλ connects speed, frequency and wavelength. Frequency never changes when a wave changes media; speed and wavelength change together to maintain the equation.
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Transverse waves have vibration perpendicular to propagation (water waves, light, S-waves); longitudinal waves have vibration parallel to propagation (sound, P-waves). Only longitudinal waves have compressions and rarefactions.
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Reflection (bounces from surfaces, angle in = angle out), refraction (bends due to speed change entering new medium, frequency constant), and diffraction (spreads through gaps or past edges) are three distinct phenomena. More wavelength = more diffraction; more diffraction with smaller gap size.
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Ripple tank demonstrates all three: reflection off barriers (equal angles), refraction in shallow water (wavelength decreases, direction bends towards normal), and diffraction through gaps (narrower gaps show more spreading) and at edges. Short wavelengths diffract less; long wavelengths diffract more.
That's the notes covered.
Carry on to the next subtopic.