CIE AS/A Level Physics 7.2 Transverse and longitudinal waves Study Notes- 2025-2027 Syllabus
CIE AS/A Level Physics 7.2 Transverse and longitudinal waves Study Notes – New Syllabus
CIE AS/A Level Physics 7.2 Transverse and longitudinal waves Study Notes at IITian Academy focus on specific topic and type of questions asked in actual exam. Study Notes focus on AS/A Level Physics latest syllabus with Candidates should be able to:
- compare transverse and longitudinal waves
- analyse and interpret graphical representations of transverse and longitudinal waves
Comparison of Transverse and Longitudinal Waves
Waves can be classified into transverse or longitudinal types, depending on the direction in which the particles of the medium vibrate relative to the direction of energy propagation.
Transverse Waves
- Particles of the medium vibrate perpendicular to the direction in which the wave travels.
- Wave motion consists of crests and troughs.
- Can travel through solids and on surfaces, but not through fluids (since fluids cannot support shear stress).
- Examples: waves on a string, electromagnetic waves, light waves, surface water ripples.
Longitudinal Waves
- Particles of the medium vibrate parallel to the direction of wave travel.
- Wave motion consists of compressions (regions of high pressure) and rarefactions (regions of low pressure).
- Can travel through solids, liquids, and gases.
- Examples: sound waves in air, seismic P-waves, compressions in a spring.
Comparison Table — Transverse vs Longitudinal Waves
| Property | Transverse Waves | Longitudinal Waves |
|---|---|---|
| Particle vibration | Perpendicular to wave direction | Parallel to wave direction |
| Wave features | Crests and troughs | Compressions and rarefactions |
| Medium | Solids and surfaces (not in fluids) | All states: solids, liquids, gases |
| Energy transfer | Perpendicular to vibration | Parallel to vibration |
| Examples | Light, EM waves, waves on a rope | Sound, P-waves, slinky compressions |
Example
State two differences between transverse and longitudinal waves, and give one example of each.
▶️ Answer / Explanation
- In transverse waves, particle motion is perpendicular to wave travel; in longitudinal waves, it is parallel.
- Transverse waves form crests and troughs; longitudinal waves form compressions and rarefactions.
- Example: Light wave (transverse), Sound wave (longitudinal).
Graphical Representation of Transverse and Longitudinal Waves
Graphs are used to visualise how the displacement of particles varies with time or position for different types of waves.
(a) Transverse Waves — Displacement–Distance Graph
- Shows the position of each particle along the medium at a given instant.
- The graph is sinusoidal, representing crests and troughs.
- Horizontal axis → position along the medium.
- Vertical axis → displacement of particles (up and down motion).
Key feature: Distance between two crests = one wavelength \( \mathrm{(\lambda)} \).
(b) Longitudinal Waves — Displacement–Distance Graph
- Shows how air particles (or medium particles) are displaced along the wave direction.
- Graph shows compressions (where particles are close together) and rarefactions (where they are far apart).
- Displacement of particles is along the same axis as wave travel.
Key feature: Distance between two successive compressions = \( \mathrm{\lambda.} \)
(c) Displacement–Time Graphs
- Show how the displacement of one particle changes with time.
- Both transverse and longitudinal waves give sinusoidal time graphs.
- Time for one complete cycle = period \( \mathrm{(T)} \).
Example
A displacement–distance graph for a sound wave shows five compressions over a distance of \( \mathrm{1.7\,m.} \) Determine the wavelength of the wave.
▶️ Answer / Explanation
Distance between five compressions = \( \mathrm{5\lambda.} \)
\( \mathrm{\lambda = \dfrac{1.7}{5} = 0.34\,m.} \)
The wavelength of the sound wave = \( \mathrm{0.34\,m.} \)
Example
At a fixed point, a transverse wave passes such that the particle completes 20 vibrations in 10 seconds. What is the frequency and period of the wave?
▶️ Answer / Explanation
Step 1: Frequency \( \mathrm{f = \dfrac{20}{10} = 2.0\,Hz.} \)
Step 2: Period \( \mathrm{T = \dfrac{1}{f} = 0.5\,s.} \)
The wave has frequency \( \mathrm{2.0\,Hz} \) and period \( \mathrm{0.5\,s.} \)