What you'll learn
Waves transfer energy from one place to another without transferring matter. Understanding the general properties of waves is fundamental to CIE IGCSE Physics and forms the basis for topics including sound, light, and the electromagnetic spectrum. This topic appears across multiple exam papers, with questions testing your ability to describe wave motion, perform calculations using the wave equation, and distinguish between transverse and longitudinal waves.
Key terms and definitions
Wavelength (λ) — the distance between two consecutive points on a wave that are in phase, measured in metres (m)
Frequency (f) — the number of complete waves passing a point per second, measured in hertz (Hz)
Amplitude — the maximum displacement of a point on the wave from its rest position, measured in metres (m)
Period (T) — the time taken for one complete wave to pass a point, measured in seconds (s)
Wavefront — a line or surface joining points on a wave that are in phase, typically represented as lines perpendicular to the direction of energy transfer
Transverse wave — a wave in which the direction of vibration is perpendicular to the direction of energy transfer
Longitudinal wave — a wave in which the direction of vibration is parallel to the direction of energy transfer
Wave speed (v) — the distance travelled by a wave per unit time, measured in metres per second (m/s)
Core concepts
Transverse and longitudinal waves
Waves fall into two fundamental categories based on the direction of particle oscillation relative to energy transfer.
Transverse waves have vibrations perpendicular to the direction of energy transfer. Key characteristics:
- Consist of peaks (crests) and troughs
- Can be polarised (though this is beyond IGCSE scope)
- Examples include electromagnetic waves (light, radio waves, X-rays), water waves, and waves on strings
- When drawn, amplitude is measured from the rest position to the peak or trough
- Wavelength is measured from peak to peak or trough to trough
Longitudinal waves have vibrations parallel to the direction of energy transfer. Key characteristics:
- Consist of compressions (where particles are closer together) and rarefactions (where particles are further apart)
- Cannot be polarised
- The primary example is sound waves in air, liquids, and solids
- When drawn, compressions appear as regions where the wave representation is denser
- Wavelength is measured from the centre of one compression to the centre of the next compression
In CIE IGCSE exam questions, you must be able to draw diagrams showing the direction of vibration and energy transfer for both wave types. Use arrows clearly: one for particle oscillation direction and one for wave direction.
Wave properties and measurements
Amplitude determines the energy carried by a wave. A larger amplitude means more energy is transferred. For transverse waves, measure amplitude vertically from the equilibrium position to a peak. For sound waves (longitudinal), greater amplitude corresponds to louder sounds, while for light waves it corresponds to brighter light.
Wavelength (λ) is always measured between corresponding points on consecutive waves:
- Peak to peak
- Trough to trough
- Any point to the equivalent point on the next wave, provided both points are in the same stage of oscillation
Common wavelength ranges in CIE IGCSE contexts:
- Sound waves: approximately 17 mm to 17 m (audible range)
- Visible light: approximately 400 nm (violet) to 700 nm (red)
- Radio waves: 1 mm to over 100 km
Frequency (f) and period (T) are reciprocals of each other:
f = 1/T or T = 1/f
If a wave has a frequency of 50 Hz, it means 50 complete waves pass a point every second. The period would be T = 1/50 = 0.02 s, meaning each wave takes 0.02 seconds to pass.
The wave equation
The fundamental relationship connecting wave speed, frequency, and wavelength is:
v = f × λ
where:
- v = wave speed (m/s)
- f = frequency (Hz)
- λ = wavelength (m)
This equation appears in every CIE IGCSE Physics specification and is tested repeatedly. You must be able to:
- Rearrange the equation to find any variable
- Use appropriate units
- Apply it to different wave types (sound, light, water waves)
Rearranged forms:
- f = v/λ
- λ = v/f
The wave equation demonstrates an inverse relationship between frequency and wavelength when wave speed is constant. For electromagnetic waves in a vacuum, speed is constant at 3.0 × 10⁸ m/s, so higher frequency waves have shorter wavelengths.
Wave behaviour and energy transfer
Waves transfer energy and information without transferring matter. The particles of the medium oscillate about fixed positions but do not travel with the wave.
Demonstrations of this principle:
- A cork floating on water bobs up and down as waves pass but does not move horizontally with the wave
- Sound carries energy from a source to your ear, but the air molecules do not travel from the source to you
The energy transferred by a wave depends on:
- Amplitude: larger amplitude = more energy (proportional to amplitude squared)
- Frequency: higher frequency = more energy per wave
Wavefronts provide a useful way to represent waves in diagrams, particularly for ripple tank experiments. Each wavefront represents a line of constant phase (such as all the peaks). The distance between successive wavefronts equals one wavelength. Wavefronts are always perpendicular to the direction of energy transfer.
Practical wave demonstrations
The ripple tank is standard apparatus in CIE IGCSE practical work:
- Produces water waves visible from above
- A vibrating bar creates straight wavefronts (plane waves)
- A vibrating dipper creates circular wavefronts
- Stroboscopic light can 'freeze' wave motion when frequency matches wave frequency
- Used to demonstrate reflection, refraction, and diffraction
Slinky spring demonstrations:
- Moving one end side-to-side creates transverse waves
- Pushing and pulling one end creates longitudinal waves (like sound)
- Clearly shows compressions and rarefactions in longitudinal waves
- Demonstrates that the spring itself does not travel, only the wave pattern
Stretched string or rope:
- Creates transverse waves when flicked
- Can demonstrate standing waves (though this is typically covered separately)
- Shows clear amplitude, wavelength, and frequency relationships
Measuring wave properties experimentally
For frequency measurement:
- Use a signal generator for electromagnetic waves or sound
- Count oscillations and divide by time: f = number of waves / time taken
- For sound, use a calibrated frequency meter or oscilloscope
For wavelength measurement:
- Water waves: measure distance across multiple wavelengths, then divide by the number
- Sound waves: use interference patterns or resonance tubes
- Light: use diffraction gratings or Young's double-slit (typically A-level)
For wave speed measurement:
- Directly: measure distance travelled and time taken (v = distance/time)
- Using the wave equation: measure f and λ, then calculate v = f × λ
- Sound in air: approximately 330 m/s (varies with temperature)
- Light in vacuum/air: 3.0 × 10⁸ m/s
Worked examples
Example 1: Wave equation calculation
Question: A sound wave has a frequency of 256 Hz and travels at 336 m/s through air. Calculate the wavelength of the sound wave.
Solution:
Given information:
- Frequency, f = 256 Hz
- Wave speed, v = 336 m/s
- Wavelength, λ = ?
Using the wave equation: v = f × λ
Rearranging: λ = v/f
Substituting: λ = 336/256
λ = 1.3125 m
Answer: 1.3 m (or 1.31 m to 3 significant figures) [3 marks]
Mark scheme: 1 mark for correct rearrangement, 1 mark for substitution with units, 1 mark for correct answer with unit
Example 2: Frequency and period
Question: A water wave in a ripple tank has a period of 0.40 s.
(a) Calculate the frequency of the wave. [2]
(b) 8 complete waves occupy a length of 2.4 m. Calculate the wavelength. [2]
(c) Calculate the speed of the wave. [2]
Solution:
(a) Using T = 1/f
Rearranging: f = 1/T = 1/0.40
f = 2.5 Hz [2 marks]
(b) Wavelength = total distance / number of waves
λ = 2.4 / 8
λ = 0.30 m [2 marks]
(c) Using v = f × λ
v = 2.5 × 0.30
v = 0.75 m/s [2 marks]
Example 3: Wave types and properties
Question:
(a) State one difference between transverse and longitudinal waves. [1]
(b) Give one example of each type of wave. [2]
(c) Explain why sound cannot travel through a vacuum but light can. [2]
Solution:
(a) In transverse waves, vibrations are perpendicular to the direction of energy transfer, whereas in longitudinal waves, vibrations are parallel to the direction of energy transfer. [1 mark]
Alternative acceptable answer: Transverse waves have peaks and troughs; longitudinal waves have compressions and rarefactions.
(b) Transverse: light / electromagnetic waves / water waves / waves on strings [1 mark]
Longitudinal: sound waves [1 mark]
(c) Sound requires a medium (particles) to travel because it consists of vibrating particles passing energy through compressions and rarefactions [1 mark]. Light is an electromagnetic wave and does not require a medium / can travel through empty space [1 mark].
Common mistakes and how to avoid them
Mistake: Confusing amplitude with wavelength or measuring amplitude as the distance from peak to trough. Correction: Amplitude is always measured from the rest/equilibrium position to the maximum displacement (peak or trough), not peak to trough. The peak-to-trough distance is actually 2× amplitude.
Mistake: Using incorrect units in wave equation calculations, particularly using cm instead of m or kHz without converting to Hz. Correction: Always convert to standard SI units before calculating: wavelength in metres (m), frequency in hertz (Hz), speed in metres per second (m/s). Show unit conversions explicitly in your working.
Mistake: Stating that waves transfer matter or that particles move along with the wave. Correction: Waves transfer energy and information only. Particles oscillate about fixed positions but do not travel with the wave. Use the cork-on-water analogy to remember this.
Mistake: Drawing longitudinal waves with perpendicular oscillations or failing to show compressions and rarefactions clearly. Correction: For longitudinal waves, show particle displacement parallel to wave direction using arrows, and clearly label regions of compression (particles close together) and rarefaction (particles spread apart).
Mistake: Mixing up frequency and period in calculations, or forgetting they are reciprocals. Correction: Remember f = 1/T and T = 1/f. Check reasonableness: high frequency means short period, low frequency means long period. A frequency of 100 Hz means 100 waves per second, so each wave takes 1/100 = 0.01 s.
Mistake: Incorrectly rearranging v = f × λ, particularly when finding frequency. Correction: Practice triangle method or algebraic rearrangement. To find f: f = v/λ (divide speed by wavelength). To find λ: λ = v/f (divide speed by frequency). Check by substituting back into the original equation.
Exam technique for Waves - General Properties
Command word 'State' or 'Give': Brief answers required, usually one line. For example, "State one property of transverse waves" needs only "vibrations perpendicular to direction of energy transfer" — no extended explanation needed. Worth typically 1 mark.
Calculation questions: Always show working clearly in three steps: (1) write the formula, (2) substitute values with units, (3) calculate answer with unit. Marks are often allocated as 1 mark for method/formula, 1 mark for correct answer. You can score the method mark even if your final answer is wrong due to arithmetic errors.
'Explain' questions: Require reasoning, not just description. Link cause and effect. For example, "Explain why increasing amplitude increases energy transferred" needs: "Larger amplitude means particles move through greater distance [1], so more work is done / more energy is transferred [1]." Typically 2-3 marks for explanation questions.
Diagram questions: Use a ruler for straight lines representing wavefronts, rays, or axes. Label key features (wavelength, amplitude, compression, rarefaction) with clear annotation lines. When asked to draw wave diagrams to scale, measure carefully and show at least two complete wavelengths for clarity.
Quick revision summary
Waves transfer energy without transferring matter. Transverse waves vibrate perpendicular to energy transfer direction (light, water); longitudinal waves vibrate parallel (sound). Key measurements: wavelength (λ) between consecutive corresponding points; frequency (f) as waves per second; amplitude from rest position to maximum displacement. The wave equation v = f × λ connects speed, frequency, and wavelength — memorise this and practise rearrangements. Period T = 1/f. Wave energy increases with amplitude and frequency. Particles oscillate about fixed positions as waves pass through.