Understanding the behavior of waves is fundamental in physics, particularly at the AS & A Level under the Physics - 9702 curriculum. Transverse and longitudinal waves are two primary types of mechanical waves that transport energy through different mediums. Analyzing and interpreting their graphical representations is essential for comprehending their characteristics and applications in various scientific and technological fields.

Key Concepts

1. Definition of Waves

Waves are disturbances that transfer energy from one location to another without the physical movement of the medium itself. They are characterized by parameters such as wavelength ($\lambda$), frequency ($f$), amplitude ($A$), and wave speed ($v$). Understanding these parameters is crucial for analyzing wave behavior and their graphical representations.

2. Transverse Waves

Transverse waves are characterized by oscillations perpendicular to the direction of wave propagation. Common examples include electromagnetic waves, such as light, and surface waves on water.

Displacement: In transverse waves, particles of the medium move up and down or side to side relative to the direction of wave travel.
Graphical Representation: Typically depicted as sine or cosine curves, with the x-axis representing the position and the y-axis representing displacement.
Equation: The general equation for a transverse wave is: $$ y(x,t) = A \sin(kx - \omega t + \phi) $$ where $A$ is amplitude, $k$ is the wave number, $\omega$ is angular frequency, and $\phi$ is the phase constant.

3. Longitudinal Waves

Longitudinal waves involve oscillations parallel to the direction of wave propagation. Sound waves in air are classic examples.

Displacement: Particles of the medium move back and forth along the direction of wave travel, creating compressions and rarefactions.
Graphical Representation: Often shown as compressions and rarefactions on a longitudinal wave diagram, or using sinusoidal graphs to represent pressure variations.
Equation: The standard equation for a longitudinal wave is similar to transverse waves: $$ s(x,t) = A \cos(kx - \omega t) $$ where $s$ is the displacement in the direction of propagation.

4. Wave Parameters and Their Graphical Interpretation

Understanding the key parameters of waves is essential for interpreting their graphical representations.

Wavelength ($\lambda$): The distance between successive crests (for transverse waves) or compressions (for longitudinal waves). On a graph, it is the horizontal distance between repeating points.
Frequency ($f$): The number of wave cycles passing a point per unit time. On a displacement-time graph, it is related to the number of oscillations per second.
Amplitude ($A$): The maximum displacement from the rest position. Graphically, it is the height of the wave's peaks and the depth of its troughs.
Wave Speed ($v$): The rate at which the wave propagates through the medium. It can be calculated using the equation: $$ v = f \lambda $$ Graphically, it relates to the slope of the wave on a displacement-time graph.

5. Superposition Principle

The superposition principle states that when two or more waves overlap, the resultant displacement is the sum of the individual displacements.

Constructive Interference: Occurs when waves meet in phase, resulting in increased amplitude.
Destructive Interference: Happens when waves meet out of phase, leading to decreased amplitude or cancellation.
Graphical Representation: Demonstrated by adding wave graphs point by point to show the resultant wave.

6. Standing Waves

Standing waves result from the interference of two waves traveling in opposite directions with the same frequency and amplitude.

Nodes: Points of zero amplitude where destructive interference occurs.
Antinodes: Points of maximum amplitude where constructive interference takes place.
Graphical Representation: Shown as a stationary pattern with fixed nodes and antinodes, unlike traveling waves.
Equation: The equation for a standing wave can be written as: $$ y(x,t) = 2A \sin(kx) \cos(\omega t) $$ illustrating the product of a spatial sine function and a temporal cosine function.

7. Wave Transformations

Waves undergo various transformations when interacting with boundaries or different media.

Reflection: The bouncing back of a wave when it hits a boundary.
Refraction: The bending of a wave as it passes from one medium to another due to a change in speed.
Diffraction: The spreading out of waves when they encounter obstacles or openings.
Graphical Representation: Each transformation can be depicted through changes in wave patterns on graphs, such as angle changes in refraction.

8. Energy Transfer in Waves

Waves transfer energy through the medium without transferring matter.

Kinetic and Potential Energy: In transverse waves, particles oscillate vertically, converting kinetic energy to potential energy and vice versa.
Energy Density: The energy per unit area, which depends on the amplitude and frequency of the wave.
Graphical Interpretation: Energy transmission can be inferred from wave amplitude and frequency on graphs.

9. Mathematical Analysis of Waves

Mathematical descriptions are essential for analyzing wave behavior and interpreting their graphical representations.

Wave Equations: Describe the motion of waves mathematically, allowing for predictions of wave behavior.
Fourier Analysis: Decomposes complex waveforms into simpler sinusoidal components, aiding in the interpretation of graphical data.
Graphical Solutions: Solving wave equations graphically to understand intersections, phase shifts, and other wave properties.

10. Practical Applications

Understanding transverse and longitudinal waves is critical in various practical applications.

Medical Imaging: Ultrasound (longitudinal) and MRI (transverse) technologies rely on wave principles.
Communication Systems: Radio waves (transverse) are fundamental to wireless communication.
Engineering: Stress waves (longitudinal) are analyzed in material testing.
Graphical Interpretation: Application-specific wave graphs are used to design and optimize these technologies.

11. Doppler Effect

The Doppler Effect describes the change in frequency or wavelength of a wave relative to an observer moving relative to the wave source.

Formula: The observed frequency ($f'$) is given by: $$ f' = \left( \frac{v + v_o}{v + v_s} \right) f $$ where $v$ is the wave speed, $v_o$ is the observer's speed, and $v_s$ is the source's speed.
Graphical Representation: Shifts in wave crests and compressions on graphs illustrate the Doppler Effect.
Applications: Used in radar, astronomy, and medical diagnostics.

Advanced Concepts

1. Mathematical Derivation of Wave Speed

The wave speed ($v$) is derived from the relationship between frequency and wavelength.

Basic Equation: $$ v = f \lambda $$ This equation establishes that wave speed is the product of its frequency and wavelength.
Derivation: Starting from the definition of frequency ($f$), the number of oscillations per second, and wavelength ($\lambda$), the distance between successive crests: $$ v = \lambda \times f $$ This fundamental relationship applies to all types of waves, whether transverse or longitudinal.
Example Calculation: If a transverse wave has a frequency of 5 Hz and a wavelength of 2 meters, its speed is: $$ v = 5 \times 2 = 10 \text{ m/s} $$

2. Energy Transport and Power in Waves

The energy transported by waves and the power associated with them involves more complex calculations.

Energy Density: For a transverse wave on a string, energy density ($u$) is given by: $$ u = \frac{1}{2} \mu \omega^2 A^2 $$ where $\mu$ is the linear mass density, $\omega$ is the angular frequency, and $A$ is the amplitude.
Power: The power ($P$) transported by the wave is: $$ P = u \times v $$ Combining the two: $$ P = \frac{1}{2} \mu \omega^2 A^2 v $$
Graphical Interpretation: Analyzing graphs to determine energy and power by assessing amplitude and frequency changes.

3. Polarization of Transverse Waves

Polarization is a property unique to transverse waves, describing the orientation of their oscillations.

Linear Polarization: Oscillations occur in a single plane.
Circular and Elliptical Polarization: Oscillations occur in multiple planes, creating circular or elliptical patterns.
Graphical Representation: Polarization can be visualized using vector diagrams showing the direction of oscillations.
Applications: Used in optics, telecommunications, and electromagnetic theory.

4. Reflection and Refraction of Waves

Advanced understanding of wave behavior involves detailed analysis of reflection and refraction.

Snell's Law: Describes the relationship between the angles of incidence and refraction: $$ n_1 \sin(\theta_1) = n_2 \sin(\theta_2) $$ where $n_1$ and $n_2$ are the refractive indices of the two media.
Graphical Solutions: Graphs illustrating incident and refracted angles help in visualizing Snell's Law.
Total Internal Reflection: Occurs when the angle of incidence exceeds the critical angle, leading to all waves being reflected back into the medium.
Applications: Fiber optics, lenses, and waveguides rely on these principles.

5. Wave Interference and Beats

Interference patterns and beat frequencies are sophisticated phenomena arising from wave superposition.

Constructive and Destructive Interference: Detailed mathematical analysis of wave interactions leading to varying amplitudes.
Beat Frequency: Occurs when two waves of slightly different frequencies interfere, producing a new wave with a frequency equal to the difference: $$ f_{\text{beat}} = |f_1 - f_2| $$
Graphical Representation: Beats appear as periodic variations in amplitude on a displacement-time graph.
Applications: Used in tuning musical instruments and in various signal processing techniques.

6. Doppler Effect in Detail

An advanced exploration of the Doppler Effect encompasses both theoretical derivations and practical applications.

Relative Motion: Analysis of scenarios where either the source, the observer, or both are in motion.
Graphical Representation: Shift in wavefronts depicted in diagrams illustrating approaching and receding sources.
Applications: Radar guns, astronomical measurements of star velocities, and medical ultrasound rely on Doppler principles.

7. Wave Polarization and Its Applications

Polarization has profound implications in various technological applications, especially in electromagnetism.

Optical Polarization: Techniques to control light polarization are essential in photography, LCD screens, and sunglasses.
Polarization Filters: Used to manipulate and analyze waves in scientific experiments and consumer electronics.
Graphical Analysis: Polarization states can be represented using Poincaré spheres and Stokes parameters.

8. Quantum Mechanical Perspective on Waves

Delving into the quantum realm, wave-particle duality introduces a deeper understanding of wave behavior.

Wavefunctions: Describe the probability amplitudes of particles, akin to classical wave descriptions.
Interference in Quantum Mechanics: Similar to classical waves, but with implications for probability distributions.
Graphical Representation: Probability density graphs illustrate the likelihood of particle positions and momenta.

9. Sound Wave Analysis

Sound waves, as longitudinal waves, offer complex scenarios for analysis and interpretation.

Waveform Analysis: Detailed examination of sound waveforms for applications in acoustics and audio engineering.
Frequency Spectrum: Breaking down sound into constituent frequencies using Fourier transforms aids in understanding timbre and pitch.
Graphical Representation: Spectrograms visually represent frequency variations over time, crucial in fields like linguistics and music.

10. Nonlinear Wave Phenomena

Nonlinear waves exhibit behaviors that differ significantly from linear wave assumptions, leading to complex interactions.

Wave Steepening: Occurs when different parts of the wave travel at different speeds, leading to distortion.
Shock Waves: Formed when wavefronts become infinitely steep, important in astrophysics and aerodynamics.
Graphical Representation: Nonlinear effects are depicted through asymmetric waveforms and abrupt changes in graphs.
Applications: Used in supersonic flight, earthquake analysis, and plasma physics.

11. Energy Considerations in Wave Mechanics

Advanced energy analysis involves understanding how waves transport and dissipate energy.

Energy Conservation: Ensuring that energy calculations account for all forms of energy transfer in wave interactions.
Dissipative Forces: Analyzing how friction and other forces lead to energy loss in wave propagation.
Graphical Interpretation: Energy graphs show the distribution and flow of energy in wave systems.
Applications: Critical in designing efficient transmission systems and understanding natural phenomena.

12. Interdisciplinary Connections

Wave analysis transcends traditional physics, integrating with various scientific and engineering disciplines.

Engineering: Wave principles are fundamental in structural engineering, acoustics, and telecommunications.
Medicine: Ultrasound imaging and other wave-based diagnostic tools rely on wave mechanics.
Environmental Science: Understanding ocean waves and atmospheric waves is vital for climate studies.
Graphical Representation: Cross-disciplinary graphs and models enhance the application-specific understanding of waves.

13. Advanced Problem-Solving Techniques

Complex wave problems require multi-step reasoning and the integration of various concepts.

Boundary Condition Problems: Solving for wave behavior at interfaces between different media.
Resonance: Analyzing systems that exhibit maximum amplitude at specific frequencies.
Graphical Solutions: Using graphical methods to solve simultaneous wave equations and interpret their intersections.
Applications: Critical in designing musical instruments, buildings, and electronic circuits.

14. Fourier Series and Wave Decomposition

Fourier series allow the decomposition of complex waveforms into simpler sinusoidal components.

Mathematical Foundations: Understanding how periodic functions can be expressed as sums of sine and cosine terms.
Graphical Representation: Visualizing the addition of multiple sine and cosine waves to form complex patterns.
Applications: Used in signal processing, image analysis, and solving differential equations related to waves.

15. Wave Propagation in Different Media

The behavior of waves varies significantly across different media, affecting their speed, attenuation, and mode of propagation.

Solid, Liquid, and Gas Media: Each medium offers distinct properties affecting wave transmission.
Graphical Analysis: Comparing wave graphs in different media highlights variations in speed, amplitude, and wavelength.
Applications: Essential in fields like seismology, acoustics, and material science.

Comparison Table

Aspect	Transverse Waves	Longitudinal Waves
Oscillation Direction	Perpendicular to wave propagation	Parallel to wave propagation
Examples	Light waves, electromagnetic waves, water waves	Sound waves, seismic P-waves
Wave Speed Equation	$v = f \lambda$	$v = f \lambda$
Energy Transport	Energy oscillates perpendicular to direction of travel	Energy oscillates along direction of travel
Polarization	Possible	Not possible
Graphical Representation	Sine/Cosine displacement curves	Compression and rarefaction diagrams
Applications	Optics, radio communications	Acoustics, medical ultrasound

Summary and Key Takeaways

Transverse and longitudinal waves differ in oscillation direction relative to propagation.
Graphical representations aid in visualizing wave properties like amplitude, wavelength, and frequency.
Advanced concepts include wave interactions, energy transport, and interdisciplinary applications.
Understanding wave behavior is essential for practical applications across various scientific and engineering fields.

Examiner Tip

Tips

Mnemonics for Wave Types: Remember "T for Transverse" where "T" stands for "Tilted" oscillations, and "L for Longitudinal" where "L" stands for "Line" of oscillation.

Visual Learning: Sketch both transverse and longitudinal waves to reinforce their differences and enhance memory retention.

Practice with Graphs: Regularly interpret and draw wave graphs to become proficient in identifying key features like amplitude, wavelength, and frequency.

Did You Know

Polarization and Real-World Applications: Only transverse waves can be polarized. This property is utilized in polarized sunglasses to reduce glare by filtering out horizontally polarized light.

Seismic Waves: Earthquakes generate both transverse (S-waves) and longitudinal (P-waves), which travel through different layers of the Earth, providing valuable information about the planet's internal structure.

Advancements in Communication: Modern technologies like fiber optics rely on the principles of transverse waves to transmit data over long distances with minimal loss.

Common Mistakes

Confusing Wave Types: Students often mix up transverse and longitudinal waves. Remember, transverse waves oscillate perpendicular to the direction of travel, while longitudinal waves oscillate parallel.

Incorrect Wave Speed Calculation: Using the wrong formula for wave speed can lead to errors. Always apply $v = f \lambda$ correctly, ensuring frequency and wavelength units match.

Misinterpreting Graphs: Misreading displacement-time graphs by confusing amplitude with wavelength. Carefully identify each axis to accurately interpret wave properties.

FAQ

What is the primary difference between transverse and longitudinal waves?

Transverse waves oscillate perpendicular to the direction of wave propagation, whereas longitudinal waves oscillate parallel to the direction of propagation.

How is wave speed calculated?

Wave speed ($v$) is calculated using the formula $v = f \lambda$, where $f$ is the frequency and $\lambda$ is the wavelength.

Can longitudinal waves be polarized?

No, only transverse waves can be polarized because polarization involves the orientation of oscillations perpendicular to the wave's direction.

What are some real-life applications of transverse waves?

Transverse waves are used in technologies like fiber optic communications, radio transmissions, and various forms of imaging such as MRI.

How does the Doppler Effect apply to longitudinal waves?

In longitudinal waves like sound, the Doppler Effect causes a perceived change in frequency when the source or observer is moving relative to the medium, resulting in higher frequencies as they approach and lower as they recede.

1. Capacitance

1.1 Energy Stored in a Capacitor

1.1.1 Determine electric potential energy stored in a capacitor from the area under the potential–charge g

1.1.2 Recall and use W = ½QV = ½CV²

1.2 Discharging a Capacitor

1.2.1 Analyze graphs of potential difference, charge, and current during capacitor discharge

1.2.2 Recall and use τ = RC for the time constant during discharge

1.2.3 Use equations of the form x = x₀e^(-t / RC) for current, charge, or potential during discharge

1.3 Capacitors and Capacitance

1.3.1 Define capacitance for isolated spherical conductors and parallel plate capacitors

1.3.2 Recall and use C = Q / V

1.3.3 Derive formulae for combined capacitance of capacitors in series and parallel

1.3.4 Use capacitance formulae for capacitors in series and parallel

2. Nuclear Physics

2.1 Mass Defect and Nuclear Binding Energy

2.1.1 Sketch the variation of binding energy per nucleon with nucleon number

2.1.2 Explain nuclear fusion and nuclear fission

2.1.3 Calculate the energy released in nuclear reactions using E = c²∆m

2.1.4 Understand the equivalence between energy and mass (E = mc²)

2.1.5 Define and use the terms mass defect and binding energy

2.2 Radioactive Decay

2.2.1 Understand that fluctuations in count rate provide evidence for random decay

2.2.2 Understand that radioactive decay is spontaneous and random

2.2.3 Define activity and decay constant, and recall A = λN

2.2.4 Define half-life

2.2.5 Use λ = 0.693 / t₁/₂ for the half-life relationship

2.2.6 Understand exponential decay and use the relationship x = x₀e^(-λt)

3. Kinematics

3.1 Equations of Motion

3.1.1 Define and use distance, displacement, speed, velocity, acceleration

3.1.2 Use graphical methods to represent motion

3.1.3 Determine displacement from velocity–time graph

3.1.4 Determine velocity using gradient of displacement–time graph

3.1.5 Determine acceleration using gradient of velocity–time graph

3.1.6 Derive equations for uniformly accelerated motion

3.1.7 Solve problems of uniformly accelerated motion

3.1.8 Describe experiment to determine acceleration due to gravity

3.1.9 Explain motion with uniform velocity and perpendicular acceleration

4. Deformation of Solids

4.1 Stress and Strain

4.1.1 Understand and use the terms load, extension, compression, and limit of proportionality

4.1.2 Recall and use Hooke’s law

4.1.3 Recall and use the formula for spring constant k = F / x

4.1.4 Define and use terms stress, strain, and Young's modulus

4.1.5 Describe an experiment to determine Young’s modulus

4.1.6 Understand deformation caused by tensile or compressive forces

4.2 Elastic and Plastic Behaviour

4.2.1 Understand elastic and plastic deformation and elastic limit

4.2.2 Understand area under the force–extension graph as work done

4.2.3 Calculate elastic potential energy using EP = ½kx²

5. Gravitational Fields

5.1 Gravitational Field of a Point Mass

5.1.1 Understand that g is approximately constant for small height changes near Earth's surface

5.1.2 Recall and use g = GM / r²

5.1.3 Derive and use g = GM / r² for gravitational field strength

5.2 Gravitational Potential

5.2.1 Define gravitational potential as work done per unit mass in bringing a test mass from infinity

5.2.2 Use ϕ = -GM / r for gravitational potential due to a point mass

5.2.3 Use EP = -GMm / r for gravitational potential energy between two point masses

5.3 Gravitational Field

5.3.1 Define gravitational field as force per unit mass

5.3.2 Represent a gravitational field using field lines

5.4 Gravitational Force Between Point Masses

5.4.1 For point outside uniform sphere, treat mass as a point mass at its center

5.4.2 Analyze circular orbits in gravitational fields

5.4.3 Recall and use Newton's law of gravitation F = Gm₁m₂ / r²

6. Electricity

6.1 Resistance and Resistivity

6.1.1 Understand that the resistance of a thermistor decreases as temperature increases

6.1.2 Define resistance and recall and use V = IR

6.1.3 Sketch I–V characteristics for metallic conductor, semiconductor diode, and filament lamp

6.1.4 Explain that the resistance of a filament lamp increases as current increases

6.1.5 State Ohm’s law and recall and use R = ρL / A

6.1.6 Understand that the resistance of an LDR decreases as light intensity increases

6.2 Electric Current

6.2.1 Understand that an electric current is a flow of charge carriers

6.2.2 Understand that the charge on charge carriers is quantised

6.2.3 Recall and use Q = It

6.2.4 Use I = Anvq for current-carrying conductors

6.3 Potential Difference and Power

6.3.1 Define potential difference as energy transferred per unit charge

6.3.2 Recall and use V = W / Q

6.3.3 Recall and use P = VI, P = I²R, P = V² / R

7. D.C. Circuits

7.1 Practical Circuits

7.1.1 Recall and use the circuit symbols in the syllabus

7.1.2 Draw and interpret circuit diagrams using circuit symbols

7.1.3 Define electromotive force (e.m.f.) of a source as energy transferred per unit charge

7.1.4 Distinguish between e.m.f. and potential difference (p.d.)

7.1.5 Understand the effects of internal resistance on terminal potential difference

7.2 Kirchhoff’s Laws

7.2.1 Recall Kirchhoff’s first law: conservation of charge

7.2.2 Recall Kirchhoff’s second law: conservation of energy

7.2.3 Derive the formula for combined resistance of resistors in series using Kirchhoff’s laws

7.2.4 Use the formula for combined resistance of resistors in series

7.2.5 Derive the formula for combined resistance of resistors in parallel using Kirchhoff’s laws

7.2.6 Use the formula for combined resistance of resistors in parallel

7.2.7 Use Kirchhoff’s laws to solve simple circuit problems

7.3 Potential Dividers

7.3.1 Understand the principle of a potential divider circuit

7.3.2 Recall and use the principle of the potentiometer for comparing potential differences

7.3.3 Understand the use of a galvanometer in null methods

7.3.4 Explain the use of thermistors and LDRs in potential dividers to provide a potential dependent on te

8. Thermal Equilibrium

8.1 Thermal Energy Transfer

8.1.1 Understand that thermal energy transfers from higher to lower temperature

8.1.2 Understand that regions of equal temperature are in thermal equilibrium

9. Temperature Scales

9.1 Temperature Measurement

9.1.1 Understand physical properties that vary with temperature (e.g., density, gas volume, resistance)

9.1.2 Convert temperatures between Kelvin and Celsius, and recall T(K) = θ(°C) + 273.15

10. Magnetic Fields

10.1 Concept of a Magnetic Field

10.1.1 Understand that a magnetic field is a field of force produced by moving charges or permanent magnets

10.1.2 Represent a magnetic field using field lines

10.2 Force on a Current-Carrying Conductor

10.2.1 Understand that a force acts on a current-carrying conductor in a magnetic field

10.2.2 Recall and use F = BIL sin θ for the force on a current-carrying conductor in a magnetic field

10.2.3 Define magnetic flux density as the force per unit current per unit length on a wire at right angles

10.3 Force on a Moving Charge

10.3.1 Determine the direction of the force on a charge moving in a magnetic field

10.3.2 Recall and use F = BQv sin θ for the force on a moving charge in a magnetic field

10.3.3 Understand the origin of the Hall voltage and use the expression VH = BI / (ntq) for the Hall voltag

10.3.4 Understand the use of a Hall probe to measure magnetic flux density

10.4 Magnetic Fields Due to Currents

10.4.1 Sketch magnetic field patterns due to currents in a straight wire, flat coil, and solenoid

10.4.2 Understand that magnetic field in a solenoid is increased by a ferrous core

10.4.3 Explain the origin of forces between current-carrying conductors and determine the direction of the

10.5 Electromagnetic Induction

10.5.1 Define magnetic flux as the product of magnetic flux density and area perpendicular to flux directio

10.5.2 Recall and use Φ = BA for magnetic flux

10.5.3 Understand and use the concept of magnetic flux linkage

10.5.4 Explain experiments that show changing magnetic flux induces an e.m.f.

10.5.5 Recall and use Faraday’s and Lenz’s laws of electromagnetic induction

11. Specific Heat Capacity and Latent Heat

11.1 Specific Heat Capacity

11.1.1 Define and use specific heat capacity

11.2 Latent Heat

11.2.1 Define and use specific latent heat; distinguish between fusion and vaporisation

12. Dynamics

12.1 Momentum and Newton’s Laws of Motion

12.1.1 Mass resists change in motion

12.1.2 Recall F = ma and solve related problems

12.1.3 Define and use linear momentum

12.1.4 Force as rate of change of momentum

12.1.5 State and apply Newton’s laws

12.1.6 Describe weight as effect of gravitational field

12.1.7 Weight of an object is mass × gravitational acceleration

12.2 Non-uniform Motion

12.2.1 Understand frictional and drag forces

12.2.2 Describe motion in uniform gravitational field with air resistance

12.2.3 Objects moving against resistive force may reach terminal velocity

12.3 Linear Momentum and its Conservation

12.3.1 State conservation of momentum

12.3.2 Apply conservation of momentum to solve problems

12.3.3 For elastic collision, kinetic energy and relative speed are conserved

12.3.4 Momentum is conserved, but some kinetic energy may change

13. Medical Physics

13.1 Production and Use of Ultrasound

13.1.1 Understand that a piezo-electric crystal changes shape when a p.d. is applied and generates an e.m.f

13.1.2 Understand how ultrasound waves are generated and detected by a piezoelectric transducer

13.1.3 Understand how ultrasound reflection at boundaries provides diagnostic information about internal st

13.1.4 Define specific acoustic impedance as Z = ρc

13.1.5 Use the equation IR / I₀ = (Z₁ – Z₂)² / (Z₁ + Z₂)² for the intensity reflection coefficient

13.2 Production and Use of X-rays

13.2.1 Explain that X-rays are produced by electron bombardment of a metal target and calculate the minimum

13.2.2 Understand the use of X-rays in imaging internal body structures and the term 'contrast' in X-ray im

13.2.3 Recall and use I = I₀e^(-μx) for the attenuation of X-rays in matter

13.2.4 Understand how computed tomography (CT) produces 3D images by combining multiple 2D X-ray images

13.3 PET Scanning

13.3.1 Understand that a tracer contains radioactive nuclei and is introduced into the body for imaging

13.3.2 Understand that β+ decay is used in positron emission tomography (PET)

13.3.3 Understand that annihilation occurs when a particle interacts with its antiparticle, conserving mass

13.3.4 Explain how gamma-ray photons from annihilation are detected to create an image of tracer concentrat

14. Waves

14.1 Progressive Waves

14.1.1 Describe wave motion in ropes, springs, and ripple tanks

14.1.2 Understand and use the terms displacement, amplitude, phase difference, period, frequency, wavelengt

14.1.3 Use time-base and y-gain on a cathode-ray oscilloscope (CRO) to determine frequency and amplitude

14.1.4 Derive and use v = f λ for the wave equation

14.1.5 Recall and use v = f λ

14.1.6 Understand energy transfer by a progressive wave

14.1.7 Recall and use intensity = power / area, intensity ∝ (amplitude)²

14.2 Transverse and Longitudinal Waves

14.2.1 Compare transverse and longitudinal waves

14.2.2 Analyze and interpret graphical representations of transverse and longitudinal waves

14.3 Doppler Effect for Sound Waves

14.3.1 Understand the change in frequency when a sound source moves relative to a stationary observer

14.3.2 Use the expression f₀ = fₛ(v / (v ± vₛ)) for the observed frequency

14.4 Electromagnetic Spectrum

14.4.1 State all electromagnetic waves are transverse waves traveling at the same speed in free space

14.4.2 Recall the range of wavelengths from radio waves to γ-rays

14.4.3 Recall that wavelengths 400–700 nm are visible to the human eye

14.5 Polarisation

14.5.1 Understand that polarisation is a phenomenon associated with transverse waves

14.5.2 Recall and use Malus's law (I = I₀ cos²θ) to calculate intensity of a plane-polarised wave after pas

15. The Mole

15.1 The Mole

15.1.1 Understand that amount of substance is an SI base quantity with the unit mol

15.1.2 Use molar quantities where one mole contains Avogadro's constant of particles

16. Equation of State

16.1 Ideal Gas Law

16.1.1 Understand that a gas obeying pV ∝ T is an ideal gas

16.1.2 Recall and use the equation pV = nRT for an ideal gas

16.1.3 Recall pV = NkT, where N = number of molecules and k is Boltzmann constant

16.1.4 Use the relationship k = R / NA

17. Kinetic Theory of Gases

17.1 Kinetic Theory

17.1.1 State the basic assumptions of the kinetic theory of gases

17.1.2 Explain pressure exerted by a gas due to molecular movement

17.1.3 Derive and use pV = (3/2)NmkT for pressure of a gas

17.1.4 Compare pV = (3/2)NmkT with pV = NkT to deduce average kinetic energy of a molecule

18. Particle Physics

18.1 Atoms, Nuclei and Radiation

18.1.1 Infer the existence and small size of the nucleus from α-particle scattering

18.1.2 Describe the nuclear atom model: protons, neutrons, and electrons

18.1.3 Distinguish between nucleon number and proton number

18.1.4 Understand isotopes as forms of the same element with different neutrons

18.1.5 Use the notation AZX for nuclides representation

18.1.6 Understand conservation of nucleon number and charge in nuclear processes

18.1.7 Describe the composition, mass, and charge of α-, β-, and γ-radiations

18.1.8 Understand antiparticles and positrons as antiparticles of electrons

18.1.9 State that (electron) antineutrinos are produced during β- decay and neutrinos during β+ decay

18.1.10 Represent α- and β-decay using radioactive decay equations

18.1.11 Use unified atomic mass unit (u) for mass

18.2 Fundamental Particles

18.2.1 Understand quarks as fundamental particles with six flavours

18.2.2 Understand hadrons as baryons (three quarks) or mesons (one quark and one antiquark)

18.2.3 Describe changes in quark composition during β- and β+ decay

18.2.4 Describe protons and neutrons as composed of quarks

18.2.5 Recall and use the charge of each quark and its respective antiquark

18.2.6 Recall electrons and neutrinos as fundamental particles (leptons)

19. Internal Energy

19.1 Internal Energy

19.1.1 Understand that internal energy is the sum of kinetic and potential energies of molecules in a syste

19.1.2 Relate rise in temperature to an increase in internal energy

20. Forces, Density and Pressure

20.1 Turning Effects of Forces

20.1.1 Weight acts at a single point: centre of gravity

20.1.2 Define and apply the moment of a force

20.1.3 Understand the concept of a couple

20.1.4 Define and apply torque of a couple

20.2 Equilibrium of Forces

20.2.1 State and apply the principle of moments

20.2.2 System in equilibrium has no resultant force or torque

20.2.3 Use a vector triangle to represent coplanar forces in equilibrium

20.3 Density and Pressure

20.3.1 Define and use density

20.3.2 Define and use pressure

20.3.3 Derive equation for hydrostatic pressure ∆p = ρg∆h

20.3.4 Use the equation ∆p = ρg∆h

20.3.5 Understand upthrust as the effect of hydrostatic pressure

20.3.6 Calculate upthrust using F = ρgV (Archimedes' principle)

21. Astronomy and Cosmology

21.1 Standard Candles

21.1.1 Understand luminosity as the total power radiated by a star

21.1.2 Recall and use the inverse square law F = L / (4πd²) for radiant flux intensity

21.1.3 Understand that an object with known luminosity is a standard candle

21.1.4 Use standard candles to determine distances to galaxies

21.2 Stellar Radii

21.2.1 Recall and use Wien’s displacement law λmax ∝ 1 / T to estimate the surface temperature of a star

21.2.2 Use Stefan–Boltzmann law L = 4πσr²T⁴

21.2.3 Use Wien’s law and Stefan–Boltzmann law to estimate the radius of a star

21.3 Hubble’s Law and Big Bang Theory

21.3.1 Understand redshift and the increase in wavelength of light from distant objects

21.3.2 Use ∆λ / λ = ∆f / f = v / c for redshift

21.3.3 Explain why redshift suggests the Universe is expanding

21.3.4 Recall and use Hubble’s law v = H₀d to explain the Big Bang theory

22. First Law of Thermodynamics

22.1 First Law

22.1.1 Recall and use W = p∆V for work done when the volume of a gas changes at constant pressure

22.1.2 Understand the difference between work done by a gas and work done on a gas

22.1.3 Recall and use the first law of thermodynamics: ∆U = q + W

23. Alternating Currents

23.1 Characteristics of Alternating Currents

23.1.1 Understand and use terms period, frequency, and peak value for alternating current or voltage

23.1.2 Use x = x₀ sin(ωt) for sinusoidal alternating current or voltage

23.1.3 Recall that the mean power in a resistive load is half the maximum power for sinusoidal current

23.1.4 Distinguish between root-mean-square (r.m.s.) and peak values and recall I₀r.m.s = I₀ / √2 and V₀r.m

23.2 Rectification and Smoothing

23.2.1 Distinguish graphically between half-wave and full-wave rectification

23.2.2 Explain the use of a single diode for half-wave rectification

23.2.3 Explain the use of four diodes (bridge rectifier) for full-wave rectification

23.2.4 Analyze the effect of a capacitor in smoothing, including the effect of capacitance and load resista

24. Superposition

24.1 Stationary Waves

24.1.1 Explain and use the principle of superposition

24.1.2 Understand experiments demonstrating stationary waves using microwaves, stretched strings, and air c

24.1.3 Explain the formation of stationary waves using graphical methods and identify nodes and antinodes

24.1.4 Determine wavelength from the positions of nodes or antinodes

24.2 Diffraction

24.2.1 Explain diffraction and show understanding of related experiments

24.2.2 Understand the effect of gap width relative to wavelength in diffraction experiments

24.3 Interference

24.3.1 Understand the terms interference and coherence

24.3.2 Demonstrate two-source interference using water waves, sound, light, and microwaves

24.3.3 Understand the conditions required for two-source interference fringes

24.3.4 Recall and use λ = ax / D for double-slit interference with light

24.4 Diffraction Grating

24.4.1 Recall and use d sin θ = nλ for diffraction grating calculations

24.4.2 Describe the use of a diffraction grating to determine the wavelength of light

25. Simple Harmonic Oscillations

25.1 Simple Harmonic Motion

25.1.1 Understand and use terms displacement, amplitude, period, frequency, angular frequency, and phase di

25.1.2 Understand that simple harmonic motion occurs when acceleration is proportional to displacement from

25.1.3 Use a = -ω²x and recall x = x₀ sin(ωt) as the solution

25.1.4 Use v = v₀ cos(ωt) and v = ±ω√(x₀² - x²) for velocity

26. Energy in Simple Harmonic Motion

26.1 Energy in SHM

26.1.1 Describe the interchange between kinetic and potential energy during SHM

26.1.2 Recall and use E = ½mω²x₀² for the total energy of a system undergoing SHM

27. Quantum Physics

27.1 Energy and Momentum of a Photon

27.1.1 Understand that electromagnetic radiation has a particulate nature

27.1.2 Recall and use E = hf for the energy of a photon

27.1.3 Use the electronvolt (eV) as a unit of energy

27.1.4 Understand that a photon has momentum and use p = E / c for photon momentum

27.2 Photoelectric Effect

27.2.1 Understand that photoelectrons are emitted from a metal surface when illuminated by electromagnetic

27.2.2 Understand and use the terms threshold frequency and threshold wavelength

27.2.3 Explain photoelectric emission in terms of photon energy and work function

27.2.4 Recall and use hf = Φ + ½mv² for the maximum kinetic energy of photoelectrons

27.2.5 Explain why the maximum kinetic energy of photoelectrons is independent of intensity, while current

27.3 Wave-Particle Duality

27.3.1 Understand that the photoelectric effect shows the particulate nature of light, while diffraction sh

27.3.2 Describe and interpret electron diffraction as evidence for the wave nature of particles

27.3.3 Understand the de Broglie wavelength as the wavelength associated with a moving particle

27.3.4 Recall and use λ = h / p for de Broglie wavelength

27.4 Energy Levels in Atoms and Line Spectra

27.4.1 Understand discrete electron energy levels in atoms (e.g., atomic hydrogen)

27.4.2 Understand the appearance and formation of emission and absorption line spectra

27.4.3 Recall and use hf = E₁ – E₂ for the energy difference between electron energy levels

28. Damped and Forced Oscillations, Resonance

28.1 Damped Oscillations

28.1.1 Understand that damping occurs due to resistive forces

28.1.2 Understand the types of damping: light, critical, and heavy damping

28.2 Resonance

28.2.1 Understand that resonance occurs when an oscillating system is forced to oscillate at its natural fr

29. Work, Energy and Power

29.1 Energy Conservation

29.1.1 Understand the concept of work, and recall W = F × s

29.1.2 Apply the principle of conservation of energy

29.1.3 Understand efficiency as useful energy output / total energy input

29.1.4 Use efficiency concept to solve problems

29.1.5 Define power as work done per unit time

29.1.6 Solve problems using P = W / t

29.1.7 Derive P = Fv and solve problems

29.2 Gravitational Potential Energy and Kinetic Energy

29.2.1 Derive ∆EP = mg∆h for gravitational potential energy changes

29.2.2 Recall and use ∆EP = mg∆h for gravitational potential energy changes

29.2.3 Derive EK = ½mv² for kinetic energy

29.2.4 Recall and use EK = ½mv² for kinetic energy

30. Electric Fields

30.1 Electric Fields and Field Lines

30.1.1 Understand that an electric field is a field of force and define it as force per unit positive charg

30.1.2 Represent an electric field using field lines

30.2 Uniform Electric Fields

30.2.1 Recall and use E = ∆V / ∆d to calculate electric field strength between charged parallel plates

30.2.2 Describe the effect of a uniform electric field on the motion of charged particles

30.3 Electric Force Between Point Charges

30.3.1 Understand that, for a point outside a spherical conductor, the charge may be considered a point mas

30.3.2 Recall and use Coulomb’s law F = Q₁Q₂ / (4πε₀r²) for the force between two point charges

30.4 Electric Field of a Point Charge

30.4.1 Recall and use E = Q / (4πε₀r²) for the electric field strength due to a point charge

30.5 Electric Potential

30.5.1 Define electric potential as work done per unit positive charge in bringing a test charge from infin

30.5.2 Recall and use V = Q / (4πε₀r) for electric potential due to a point charge

30.5.3 Understand how electric potential leads to electric potential energy of two point charges and use EP

31. Physical Quantities and Units

31.1 Physical Quantities

31.1.1 Physical quantities consist of magnitude and unit

31.1.2 Estimate physical quantities from the syllabus

31.2 SI Units

31.2.1 SI base units: mass, length, time, current, temperature

31.2.2 Express derived units from SI base units

31.2.3 Check homogeneity of physical equations

31.2.4 Use prefixes (pico, nano, micro, kilo, etc.)

31.3 Errors and Uncertainties

31.3.1 Understand systematic and random errors

31.3.2 Assess uncertainty in derived quantities

31.4 uniform Electric Fields

31.4.1 Distinguish between precision and accuracy

31.5 Scalars and Vectors

31.5.1 Difference between scalar and vector quantities

31.5.2 Add and subtract coplanar vectors

31.5.3 Represent a vector as components

32. Motion in a Circle

32.1 Centripetal Acceleration

32.1.1 Understand centripetal acceleration and its role in circular motion

32.1.2 Recall and use a = rω² and a = v² / r

32.1.3 Recall and use F = mrω² and F = mv² / r

32.1.4 Understand force causing centripetal acceleration is always perpendicular to motion

32.2 Kinematics of Uniform Circular Motion

32.2.1 Recall and use ω = 2π / T and v = rω

32.2.2 Understand and use angular speed

32.2.3 Define and express angular displacement in radians

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Analyze and Interpret Graphical Representations of Transverse and Longitudinal Waves

Introduction