5.1 Fundamentals of Waves
Waves are produced when an oscillating or vibrating system transfers energy from one point to another without transferring matter. By exploring progressive and stationary waves, mechanical and electromagnetic waves, as well as transverse and longitudinal waves, students can analyze wave characteristics, sketch displacement graphs, and apply the wave formula \(v = f\lambda\).
Learning Objectives
- Describe how waves are produced by oscillating and vibrating systems.
- Explain that waves transfer energy from one place to another without transferring matter.
- Differentiate between progressive waves and stationary waves.
- Differentiate between mechanical waves and electromagnetic waves.
- Compare and contrast transverse waves and longitudinal waves.
- Define amplitude (\(A\)), period (\(T\)), frequency (\(f\)), wavelength (\(\lambda\)), and wave speed (\(v\)).
- Sketch and interpret graphs of displacement against time and displacement against distance.
- Apply the wave formula \(v = f\lambda\) to solve problems.
- Describe the use of a ripple tank to determine wavelength, frequency, and wave speed of water waves.
Comparison of Wave Types and Wave Profile Anatomy
Distinguish transverse waves from longitudinal waves, and learn how to read amplitude, period and wavelength from displacement graphs.
Transverse Wave
Longitudinal Wave
Short Explanation
What is a Wave?
A wave is a disturbance that travels through a medium or vacuum, carrying energy from one point to another without carrying the matter itself.
Wave Production
Waves are generated by an oscillating or vibrating system. An oscillating iron bob at the end of a spring produces water waves, while a vibrating tuning fork produces sound waves.
Energy Transfer without Matter Transfer
When a medium vibrates at a fixed position, wave propagation transfers energy from one place to another without transferring the matter of the medium. A ribbon tied to a slinky spring only vibrates about a fixed position; it does not move along the direction of propagation.
Progressive vs Stationary Waves
A progressive wave has a wave profile that propagates with time. A stationary wave has a wave profile that does not propagate with time, formed when two identical progressive waves moving in opposite directions collide.
| Classification | Type | Key Feature | Examples |
|---|---|---|---|
| By wave profile movement | Progressive wave | Wave profile propagates with time | Water waves on a pond, waves along a slinky spring |
| By wave profile movement | Stationary wave | Wave profile does not propagate with time | Plucked guitar string, ukulele, flute, drum |
| By medium requirement | Mechanical wave | Requires a medium to transfer energy | Water waves, sound waves, seismic waves |
| By medium requirement | Electromagnetic wave | Does not require a medium; oscillating electric and magnetic fields | Radio waves, light waves, gamma rays |
| By particle motion | Transverse wave | Particles vibrate perpendicular to wave direction; crests and troughs | Radio waves, light waves, water waves, seismic S-waves |
| By particle motion | Longitudinal wave | Particles vibrate parallel to wave direction; compressions and rarefactions | Sound waves, seismic P-waves |
Wave Characteristics and Wave Formula
\(f = \dfrac{1}{T}\)Frequency is the reciprocal of period.
\(v = f\lambda\)Wave speed equals frequency multiplied by wavelength.
Wave Quantities
Amplitude (\(A\)): Maximum displacement of a particle from its equilibrium position.
Period (\(T\)): Time taken by a particle to make one complete oscillation. SI unit: s.
Frequency (\(f\)): Number of complete oscillations made by a particle in one second. SI unit: Hz or s⁻¹.
Wavelength (\(\lambda\)): Distance between two consecutive points in phase. SI unit: m.
Wave speed (\(v\)): Distance travelled per second by a wave profile.
Wave Graphs
Displacement against time graph: Gives amplitude (\(A\)) and period (\(T\)). Frequency is found using \(f = \frac{1}{T}\).
Displacement against distance graph: Gives amplitude (\(A\)) and wavelength (\(\lambda\)).
Combine frequency from the displacement-time graph with wavelength from the displacement-distance graph to calculate wave speed using \(v = f\lambda\).
Ripple Tank Experiment
A ripple tank consists of a perspex/glass water tank, ripple generator, digital xenon stroboscope, mirror, glass screen and dippers. A plane dipper produces plane waves, while a spherical dipper produces circular waves.
Switch on the plane dipper and adjust the stroboscope frequency until the wave pattern appears stationary. Read the frequency, \(f\), from the stroboscope. Measure the distance between consecutive bright fringes to obtain the wavelength, \(\lambda\). Calculate wave speed using \(v = f\lambda\).
Wave Graphs: Reading A, T and \(\lambda\)
The same wave read two ways: against time it gives amplitude and period, against distance it gives amplitude and wavelength.
Graph of Displacement against Time
The time axis gives the period directly. Here one complete oscillation takes \(T = 0.50\text{ s}\), so the frequency is \(f = \dfrac{1}{T} = 2\text{ Hz}\). The amplitude is the maximum displacement from the equilibrium position, \(A = 3\text{ cm}\).
Graph of Displacement against Distance
The distance axis gives the wavelength directly, \(\lambda = 16\text{ cm}\), measured between two consecutive points in phase. The amplitude read from this graph is the same, \(A = 3\text{ cm}\).
Combining the two graphs gives the wave speed: \(v = f\lambda = 2\text{ Hz} \times 16\text{ cm} = 32\text{ cm s}^{-1} = 0.32\text{ m s}^{-1}\). Note that the two graphs have the same shape but different horizontal axes, so a period must never be read off a displacement-distance graph, nor a wavelength off a displacement-time graph.
Try to Answer First
Answer in your mind, then press “Check Answer”.
Based on a displacement-time graph, a crest is at \(3\text{ cm}\) and one complete wave cycle takes \(0.4\text{ s}\). Find the amplitude, period, and frequency of the wave.
Check Answer
State the primary difference between a progressive wave and a stationary wave in terms of wave profile propagation.
Check Answer
In a ripple tank experiment, a plane dipper produces water waves with a frequency of \(5\text{ Hz}\). If the distance between two consecutive bright fringes is \(1.5\text{ cm}\), calculate the wave speed.
Check Answer
Common Mistakes
- Reading wavelength (\(\lambda\)) from a displacement-time graph instead of reading period (\(T\)). A displacement-time graph only gives time-related information, not wavelength.
- Confusing the direction of particle vibration: thinking particles move forward along with the wave, rather than oscillating around fixed equilibrium positions.
- Measuring wavelength from a crest to an adjacent trough instead of between two consecutive crests, troughs, or consecutive points in phase.
- Forgetting to convert units, for example using centimetres for wavelength without matching the wave speed unit, leading to confusion between cm s⁻¹ and m s⁻¹.
Concept Misunderstandings
Matter travels together with the wave from source to destination.
Only energy is transferred. Medium particles merely vibrate about their fixed equilibrium positions, as proven by the vibrating ribbon on a slinky spring.
All waves require a physical medium to propagate.
Only mechanical waves require a medium. Electromagnetic waves consist of oscillating electric and magnetic fields and can travel through a vacuum.
Longitudinal waves have crests and troughs just like transverse waves.
Longitudinal waves consist of alternating compressions and rarefactions, with vibrations parallel to wave travel.
Summary
- Wave Production: Created by oscillating or vibrating systems; transfers energy without transferring matter.
- Classification by profile movement: Progressive waves (wave profile propagates) vs stationary waves (wave profile does not propagate).
- Classification by medium requirement: Mechanical waves (need medium) vs electromagnetic waves (do not need medium).
- Classification by particle motion: Transverse waves (perpendicular vibration; crests and troughs) vs longitudinal waves (parallel vibration; compressions and rarefactions).
- Key Quantities: Amplitude (\(A\)), Period (\(T\)), Frequency (\(f = \frac{1}{T}\)), Wavelength (\(\lambda\)), Speed (\(v = f\lambda\)).
- Wave Graphs: Displacement-time gives \(A\) and \(T\); displacement-distance gives \(A\) and \(\lambda\).
- Ripple Tank: Used to observe plane and circular waves and determine \(f\), \(\lambda\), and \(v\).
Short Activity
Objective: Test your understanding of wave types, wave characteristics and the wave formula.
A. Objective Quiz
1 Which of the following statements correctly differentiates a transverse wave from a longitudinal wave?
2 A wave has a frequency of \(20\text{ Hz}\) and a wavelength of \(0.3\text{ m}\). What is the speed of the wave?
B. Fill in the Blanks
3 The formula relating wave speed \(v\), frequency \(f\), and wavelength \(\lambda\) is \(v =\) .
4 A wave where the profile of the wave does not propagate with time is called a wave.
C. Matching / Drag and Drop
Match each wave term to its correct textbook definition. If using a phone, tap the answer first, then tap the matching box.
