General Wave Properties
Section: Physics | Syllabus: Cambridge IGCSE Combined Science (0653)
Waves and Energy Transfer
A wave is a disturbance that transfers energy from one place to another without transferring matter.
- As a wave travels through a medium, the particles of the medium vibrate about a fixed position - they do not travel along with the wave
- Only energy moves from the source to other points; the matter of the medium stays, on average, in the same place
- Example: a cork floating on water bobs up and down as ripples pass beneath it, but it does not travel outward with the ripples
Demonstrating Wave Motion
Wave motion can be shown using vibrations in ropes and springs, and using water waves.
Vibrations in a Rope or Spring
- Fix one end of a rope or spring and give the free end a single sharp flick, or shake it continuously from side to side
- A pulse (or a continuous wave) travels along the rope, carrying energy from the hand to the fixed end
- Each point on the rope moves briefly away from its rest position and then returns to it - the rope itself does not move along its length
A single pulse travelling along a rope
Water Wave Experiments
- Dip a finger, ruler or dipper repeatedly into a tray or tank of still water at one point
- Circular ripples spread outward from the point of disturbance, carrying energy away from the source
- A small floating object, such as a cork, bobs up and down as the ripples pass but does not travel outward with them - showing that the wave transfers energy, not water
Ripples spreading from a point source on water
Features of a Wave
Wavefront
- A wavefront is a line (or surface) joining points on a wave that are vibrating in phase with each other - for example, a line joining all the points that are at a crest at the same instant
- A wavefront represents the shape of the wave at one instant in time, and the wave travels in the direction perpendicular to its wavefronts
- Waves spreading from a point source have circular wavefronts; waves far from their source, or generated by a straight source, have straight, parallel wavefronts (plane waves)
Crest, Trough and Amplitude
- Crest (peak): the highest point of a wave, above the undisturbed (rest) position
- Trough: the lowest point of a wave, below the undisturbed (rest) position
- Amplitude: the maximum displacement of a point on the wave from its rest position
Wavelength, Frequency and Wave Speed
- Wavelength (λ): the distance between two adjacent points on a wave that are vibrating in phase, such as from one crest to the next, or between corresponding points on two adjacent wavefronts
- Frequency (f): the number of complete waves passing a fixed point per second
- Wave speed (v): the distance travelled by the wave per unit time
Features of a transverse wave
| Feature | Symbol | Unit | Description |
|---|---|---|---|
| Wavefront | - | - | Line joining points on a wave that are in phase |
| Amplitude | A | metre (m) | Maximum displacement from the rest position |
| Wavelength | λ | metre (m) | Distance between two adjacent points in phase |
| Frequency | f | hertz (Hz) | Number of complete waves passing a point per second |
| Wave speed | v | metre/second (m/s) | Distance travelled by the wave per second |
Transverse Waves
In a transverse wave, the direction of vibration of the particles is at right angles (perpendicular) to the direction in which the wave travels (the direction of propagation).
- Direction of vibration: perpendicular to the direction of wave travel
- Key features: crests (peaks) and troughs
- Electromagnetic radiation, water waves and seismic S-waves (secondary) can be modelled as transverse waves
A transverse wave: vibration is perpendicular to the direction of travel
Longitudinal Waves
In a longitudinal wave, the direction of vibration of the particles is parallel to the direction in which the wave travels.
- Direction of vibration: parallel to the direction of wave travel
- Key features: compressions (particles pushed close together) and rarefactions (particles spread apart)
- Sound waves and seismic P-waves (primary) can be modelled as longitudinal waves
A longitudinal wave: vibration is parallel to the direction of travel, producing compressions and rarefactions
| Property | Transverse Waves | Longitudinal Waves |
|---|---|---|
| Direction of vibration | Perpendicular to direction of travel | Parallel to direction of travel |
| Key features | Crests (peaks) and troughs | Compressions and rarefactions |
| Modelled examples | Electromagnetic radiation, water waves, seismic S-waves | Sound waves, seismic P-waves |
Reflection and Refraction of Waves
When a wave meets a barrier, or crosses a boundary into a different medium, it can change direction.
Reflection
- Reflection occurs when a wave bounces back after meeting a plane (flat) surface
- Wavelength, frequency and speed are unchanged by reflection
- Formula:
- angle i = angle r
- Where:
- angle i = angle of incidence
- angle r = angle of reflection
- both measured from the normal - a line drawn at right angles to the surface at the point where the wave strikes it
Reflection at a plane surface: angle of incidence equals angle of reflection
Refraction
- Refraction is the change in direction of a wave caused by a change in its speed as it crosses a boundary into a different medium
- When a wave slows down, it bends toward the normal; when it speeds up, it bends away from the normal
- Wavelength changes in proportion to the change in speed; frequency stays the same
- A wave crossing the boundary along the normal changes speed and wavelength but does not change direction
Refraction: a wave bends toward the normal as it slows down
The Wave Equation
- Formula:
- v = flambda
- Where:
- v = wave speed (m/s)
- f = frequency (Hz)
- λ = wavelength (m)
Question: Museli generates waves in a ripple tank with a frequency of 50 Hz and a wavelength of 2 m. Find the speed of the waves.
Given: f = 50 Hz, λ = 2 m v = flambda Answerv = 50 × 2 = 100 m/s
Worked Example: Finding WavelengthQuestion: Muchindu measures a sound wave travelling at 330 m/s with a frequency of 440 Hz. Calculate its wavelength.
Given: v = 330 m/s, f = 440 Hz Rearrange: λ = (v/f) Answerλ = (330/440) = 0.75 m
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