Topic 4 & 9

Topic 4: Oscillations and Waves

4.1 Oscillations
4.1 Essential idea: A study of oscillations underpins many areas of physics with simple harmonic motion (shm), a fundamental oscillation that appears in various natural phenomena.

4.1 Nature of science:
Models: Oscillations play a great part in our lives, from the tides to the motion of the swinging pendulum that once governed our perception of time. General principles govern this area of physics, from water waves in the deep ocean or the oscillations of a car suspension system. This introduction to the topic reminds us that not all oscillations are isochronous. However, the simple harmonic oscillator is of great importance to physicists because all periodic oscillations can be described through the mathematics of simple harmonic motion. (1.10)

4.1 Understandings:
• Simple harmonic oscillations
• Time period, frequency, amplitude, displacement and phase difference
• Conditions for simple harmonic motion

4.1 Applications and skills:
• Qualitatively describing the energy changes taking place during one cycle of an oscillation
• Sketching and interpreting graphs of simple harmonic motion examples

4.1 International-mindedness:
• Oscillations are used to define the time systems on which nations agree so that the world can be kept in synchronization. This impacts most areas of our lives including the provision of electricity, travel and location-determining devices and all microelectronics.

4.1 Theory of knowledge:
• The harmonic oscillator is a paradigm for modelling where a simple equation is used to describe a complex phenomenon. How do scientists know when a simple model is not detailed enough for their requirements?

4.1 Guidance:
• Graphs describing simple harmonic motion should include displacement–time, velocity–time, acceleration–time and acceleration–displacement
• Students are expected to understand the significance of the negative sign in the relationship: a~-x

4.1 Utilization:
• Isochronous oscillations can be used to measure time
• Many systems can approximate simple harmonic motion: mass on a spring, fluid in U-tube, models of icebergs oscillating vertically in the ocean, and motion of a sphere rolling in a concave mirror
• Simple harmonic motion is frequently found in the context of mechanics (see Physics topic 2)

4.1 Aims:
• Aim 6: experiments could include (but are not limited to): mass on a spring; simple pendulum; motion on a curved air track
• Aim 7: IT skills can be used to model the simple harmonic motion defining equation; this gives valuable insight into the meaning of the equation itself

4.1 Data booklet reference

4.2 Travelling waves
4.2 Essential idea: There are many forms of waves available to be studied. A common characteristic of all travelling waves is that they carry energy, but generally the medium through which they travel will not be permanently disturbed.

4.2 Nature of science:
Patterns, trends and discrepancies: Scientists have discovered common features of wave motion through careful observations of the natural world, looking for patterns, trends and discrepancies and asking further questions based on these findings. (3.1)

4.2 Understandings:
• Travelling waves
• Wavelength, frequency, period and wave speed
• Transverse and longitudinal waves
• The nature of electromagnetic waves
• The nature of sound waves

4.2 Applications and skills:
• Explaining the motion of particles of a medium when a wave passes through it for both transverse and longitudinal cases
• Sketching and interpreting displacement–distance graphs and displacement–time graphs for transverse and longitudinal waves
• Solving problems involving wave speed, frequency and wavelength
• Investigating the speed of sound experimentally

4.2 Guidance:
• Students will be expected to derive c = f/L
• Students should be aware of the order of magnitude of the wavelengths of radio, microwave, infra-red, visible, ultraviolet, X-ray and gamma rays

4.2 International-mindedness:
• Electromagnetic waves are used extensively for national and international communication

4.2 Theory of knowledge:
• Scientists often transfer their perception of tangible and visible concepts to explain similar non-visible concepts, such as in wave theory. How do scientists explain concepts that have no tangible or visible quality?

4.2 Utilization:
• Communication using both sound (locally) and electromagnetic waves (near and far) involve wave theory
• Emission spectra are analysed by comparison to the electromagnetic wave spectrum (see Chemistry topic 2 and Physics sub-topic 12.1)
• Sight (see Biology sub-topic A.2)

4.2 Aims:
• Aim 2: there is a common body of knowledge and techniques involved in wave theory that is applicable across many areas of physics
• Aim 4: there are opportunities for the analysis of data to arrive at some of the models in this section from first principles
• Aim 6: experiments could include (but are not limited to): speed of waves in different media; detection of electromagnetic waves from various sources; use of echo methods (or similar) for determining wave speed, wavelength, distance, or medium elasticity and/or density

4.2 Data booklet reference

4.3 Wave characteristics
4.3 Essential idea: All waves can be described by the same sets of mathematical ideas. Detailed knowledge of one area leads to the possibility of prediction in another.

4.3 Nature of science:
Imagination: It is speculated that polarization had been utilized by the Vikings through their use of Iceland Spar over 1300 years ago for navigation (prior to the introduction of the magnetic compass). Scientists across Europe in the 17th–19th centuries continued to contribute to wave theory by building on the theories and models proposed as our understanding developed. (1.4)

4.3 Understandings:
• Wavefronts and rays
• Amplitude and intensity
• Superposition
• Polarization

4.3 Applications and skills:
• Sketching and interpreting diagrams involving wavefronts and rays
• Solving problems involving amplitude, intensity and the inverse square law
• Sketching and interpreting the superposition of pulses and waves
• Describing methods of polarization
• Sketching and interpreting diagrams illustrating polarized, reflected and transmitted beams
• Solving problems involving Malus’s law

4.3 Guidance:
• Students will be expected to calculate the resultant of two waves or pulses both graphically and algebraically
• Methods of polarization will be restricted to the use of polarizing filters and reflection from a non-metallic plane surface

4.3 Theory of knowledge:
• Wavefronts and rays are visualizations that help our understanding of reality, characteristic of modelling in the physical sciences. How does the methodology used in the natural sciences differ from the methodology used in the human sciences?
• How much detail does a model need to contain to accurately represent

4.3 Utilization:
• A number of modern technologies, such as LCD displays, rely on polarization for their operation

4.3 Aims:
• Aim 3: these universal behaviours of waves are applied in later sections of the course in more advanced topics, allowing students to generalize the various types of waves
• Aim 6: experiments could include (but are not limited to): observation of polarization under different conditions, including the use of microwaves; superposition of waves; representation of wave types using physical models (eg slinky demonstrations)
• Aim 7: use of computer modelling enables students to observe wave motion in three dimensions as well as being able to more accurately adjust wave characteristics in superposition demonstrations

4.3 Data booklet reference:

4.4 Wave behaviour
4.4 Essential idea: Waves interact with media and each other in a number of ways that can be unexpected and useful.

4.4 Nature of science:
Competing theories: The conflicting work of Huygens and Newton on their theories of light and the related debate between Fresnel, Arago and Poisson are demonstrations of two theories that were valid yet flawed and incomplete. This is an historical example of the progress of science that led to the acceptance of the duality of the nature of light. (1.9)

4.4 Understandings:
• Reflection and refraction
• Snell’s law, critical angle and total internal reflection
• Diffraction through a single-slit and around objects
• Interference patterns
• Double-slit interference
• Path difference

4.4 Applications and skills:
• Sketching and interpreting incident, reflected and transmitted waves at boundaries between media
• Solving problems involving reflection at a plane interface
• Solving problems involving Snell’s law, critical angle and total internal reflection
• Determining refractive index experimentally
• Qualitatively describing the diffraction pattern formed when plane waves are incident normally on a single-slit
• Quantitatively describing double-slit interference intensity patterns

4.4 Guidance:
• Quantitative descriptions of refractive index are limited to light rays passing between two or more transparent media. If more than two media, only parallel interfaces will be considered
• Students will not be expected to derive the double-slit equation
• Students should have the opportunity to observe diffraction and interference patterns arising from more than one type of wave

4.4 International-mindedness:
• Characteristic wave behaviour has been used in many cultures throughout human history, often tying closely to myths and legends that formed the basis for early scientific studies

4.4 Theory of knowledge:
• Huygens and Newton proposed two competing theories of the behaviour of light. How does the scientific community decide between competing theories?

4.4 Utilization:
• A satellite footprint on Earth is governed by the diffraction at the dish on the satellite
• Applications of the refraction and reflection of light range from the simple plane mirror through the medical endoscope and beyond. Many of these applications have enabled us to improve and extend our sense of vision
• The simple idea of the cancellation of two coherent light rays reflecting from two surfaces leads to data storage in compact discs and their successors
• The physical explanation of the rainbow involves refraction and total internal reflection. The bright and dark bands inside the rainbow, supernumeraries, can be explained only by the wave nature of light and diffraction

4.4 Aims:
• Aim 1: the historical aspects of this topic are still relevant science and provide valuable insight into the work of earlier scientists
• Aim 6: experiments could include (but are not limited to): determination of refractive index and application of Snell’s law; determining conditions under which total internal reflection may occur; examination of diffraction patterns through apertures and around obstacles; investigation of the double-slit experiment
• Aim 8: the increasing use of digital data and its storage density has implications on individual privacy through the permanence of a digital footprint

4.4 Data booklet reference:

4.5 Standing waves
4.5 Essential idea: When travelling waves meet they can superpose to form standing waves in which energy may not be transferred.

4.5 Nature of science:
Common reasoning process: From the time of Pythagoras onwards the connections between the formation of standing waves on strings and in pipes have been modelled mathematically and linked to the observations of the oscillating systems. In the case of sound in air and light, the system can be visualized in order to recognize the underlying processes occurring in the standing waves. (1.6)

4.5 Understandings:
• The nature of standing waves
• Boundary conditions
• Nodes and antinodes

4.5 Applications and skills:
• Describing the nature and formation of standing waves in terms of superposition
• Distinguishing between standing and travelling waves
• Observing, sketching and interpreting standing wave patterns in strings and pipes
• Solving problems involving the frequency of a harmonic, length of the standing wave and the speed of the wave

4.5 Guidance:
• Students will be expected to consider the formation of standing waves from the superposition of no more than two waves
• Boundary conditions for strings are: two fixed boundaries; fixed and free boundary; two free boundaries
• Boundary conditions for pipes are: two closed boundaries; closed and open boundary; two open boundaries
• For standing waves in air, explanations will not be required in terms of pressure nodes and pressure antinodes
• The lowest frequency mode of a standing wave is known as the first harmonic
• The terms fundamental and overtone will not be used in examination

4.5 Aims:
• Aim 3: students are able to both physically observe and qualitatively measure the locations of nodes and antinodes, following the investigative techniques of early scientists and musicians
• Aim 6: experiments could include (but are not limited to): observation of standing wave patterns in physical objects (eg slinky springs); prediction of harmonic locations in an air tube in water; determining the frequency of tuning forks; observing or measuring vibrating violin/guitar strings
• Aim 8: the international dimension of the application of standing waves is important in music

Topic 9: Wave Phenomena (HL)
9.1 Essential idea: The solution of the harmonic oscillator can be framed around the variation of kinetic and potential energy in the system.

9.1 – Simple harmonic motion

9.1 Nature of science:
Insights: The equation for simple harmonic motion (SHM) can be solved analytically and numerically. Physicists use such solutions to help them to visualize the behaviour of the oscillator. The use of the equations is very powerful as any oscillation can be described in terms of a combination of harmonic oscillators. Numerical modelling of oscillators is important in the design of electrical circuits. (1.11)

9.1 Understandings:
• The defining equation of SHM
• Energy changes

9.1 Applications and skills:
• Solving problems involving acceleration, velocity and displacement during simple harmonic motion, both graphically and algebraically
• Describing the interchange of kinetic and potential energy during simple harmonic motion
• Solving problems involving energy transfer during simple harmonic motion, both graphically and algebraically

9.1 Guidance
• Contexts for this sub-topic include the simple pendulum and a mass-spring system

9.1 Utilization:
• Fourier analysis allows us to describe all periodic oscillations in terms of simple harmonic oscillators. The mathematics of simple harmonic motion is crucial to any areas of science and technology where oscillations occur
• The interchange of energies in oscillation is important in electrical phenomena
• Quadratic functions (see Mathematics HL sub-topic 2.6; Mathematics SL subtopic 2.4; Mathematical studies SL sub-topic 6.3)
• Trigonometric functions (see Mathematics SL sub-topic 3.4)

9.1 Aims:
• Aim 4: students can use this topic to develop their ability to synthesize complex and diverse scientific information
• Aim 6: experiments could include (but are not limited to): investigation of simple or torsional pendulums; measuring the vibrations of a tuning fork; further extensions of the experiments conducted in sub-topic 4.1. By using the force law, a student can, with iteration, determine the behaviour of an object
under simple harmonic motion. The iterative approach (numerical solution), with given initial conditions, applies basic uniform acceleration equations in successive small time increments. At each increment, final values become the following initial conditions.
• Aim 7: the observation of simple harmonic motion and the variables affected can be easily followed in computer simulations

9.1 Data booklet reference

9.2 Single-slit diffraction

9.2 Essential idea: Single-slit diffraction occurs when a wave is incident upon a slit of approximately the same size as the wavelength.

9.2 Nature of science:
Development of theories: When light passes through an aperture the summation of all parts of the wave leads to an intensity pattern that is far removed from the geometrical shadow that simple theory predicts. (1.9)

9.2 Understandings:
• The nature of single-slit diffraction

9.2 Applications and skills:
• Describing the effect of slit width on the diffraction pattern
• Determining the position of first interference minimum
• Qualitatively describing single-slit diffraction patterns produced from white light and from a range of monochromatic light frequencies

9.2 Guidance:
• Only rectangular slits need to be considered
• Diffraction around an object (rather than through a slit) does not need to be considered in this sub-topic (see Physics sub-topic 4.4)
• Students will be expected to be aware of the approximate ratios of successive intensity maxima for single-slit interference patterns
• Calculations will be limited to a determination of the position of the first minimum for single-slit interference patterns using the approximation equation

9.2 Theory of knowledge:
• Are explanations in science different from explanations in other areas of knowledge such as history?

9.2 Utilization:
• X-ray diffraction is an important tool of the crystallographer and the material scientist

9.2 Aims:
• Aim 2: this topic provides a body of knowledge that characterizes the way that science is subject to modification with time
• Aim 6: experiments can be combined with those from sub-topics 4.4 and 9.3

9.2 Data booklet reference:

9.3 – Interference
9.3 Essential idea: Interference patterns from multiple slits and thin films produce accurately repeatable patterns.

9.3 Nature of science:
Curiosity: Observed patterns of iridescence in animals, such as the shimmer of peacock feathers, led scientists to develop the theory of thin film interference. (1.5)
Serendipity: The first laboratory production of thin films was accidental. (1.5)

9.3 Understandings:
• Young’s double-slit experiment
• Modulation of two-slit interference pattern by one-slit diffraction effect
• Multiple slit and diffraction grating interference patterns
• Thin film interference

9.3 Applications and skills:
• Qualitatively describing two-slit interference patterns, including modulation by one-slit diffraction effect
• Investigating Young’s double-slit experimentally
• Sketching and interpreting intensity graphs of double-slit interference patterns
• Solving problems involving the diffraction grating equation
• Describing conditions necessary for constructive and destructive interference from thin films, including phase change at interface and effect of refractive index
• Solving problems involving interference from thin films

9.3 Theory of knowledge:
• Most two-slit interference descriptions can be made without reference to the
one-slit modulation effect. To what level can scientists ignore parts of a model
for simplicity and clarity?

9.3 Utilization:
• Compact discs are a commercial example of the use of diffraction gratings
• Thin films are used to produce anti-reflection coatings

9.3 Guidance:
• Students should be introduced to interference patterns from a variety of coherent sources such as (but not limited to) electromagnetic waves, sound and simulated demonstrations
• Diffraction grating patterns are restricted to those formed at normal incidence
• The treatment of thin film interference is confined to parallel-sided films at normal incidence
• The constructive interference and destructive interference formulae listed below and in the data booklet apply to specific cases of phase changes at interfaces and are not generally true

9.3 Aims:
• Aim 4: two scientific concepts (diffraction and interference) come together in this sub-topic, allowing students to analyse and synthesize a wider range of scientific information
• Aim 6: experiments could include (but are not limited to): observing the use of diffraction gratings in spectroscopes; analysis of thin soap films; sound wave and microwave interference pattern analysis
• Aim 9: the ray approach to the description of thin film interference is only an approximation. Students should recognize the limitations of such a visualization

9.3 Data booklet reference:

9.4 – Resolution
9.4 Essential idea: Resolution places an absolute limit on the extent to which an optical or other system can separate images of objects.

9.4 Nature of science:
Improved technology: The Rayleigh criterion is the limit of resolution. Continuing advancement in technology such as large diameter dishes or lenses or the use of smaller wavelength lasers pushes the limits of what we can resolve. (1.8)

9.4 Understandings:
• The size of a diffracting aperture
• The resolution of simple monochromatic two-source systems

9.4 Applications and skills:
• Solving problems involving the Rayleigh criterion for light emitted by two sources diffracted at a single slit
• Resolvance of diffraction gratings

9.4 Guidance:
• Proof of the diffraction grating resolvance equation is not required

9.4 International-mindedness:
• Satellite use for commercial and political purposes is dictated by the resolution capabilities of the satellite

9.4 Theory of knowledge:
• The resolution limits set by Dawes and Rayleigh are capable of being surpassed by the construction of high quality telescopes. Are we capable of breaking other limits of scientific knowledge with our advancing technology?

9.4 Utilization:
• An optical or other reception system must be able to resolve the intended images. This has implications for satellite transmissions, radio astronomy and many other applications in physics and technology (see Physics option C)
• Storage media such as compact discs (and their variants) and CCD sensors rely on resolution limits to store and reproduce media accurately

9.4 Aims:
• Aim 3: this sub-topic helps bridge the gap between wave theory and real-life applications
• Aim 8: the need for communication between national communities via satellites raises the awareness of the social and economic implications of technology

9.4 Data booklet reference

9.5 – Doppler effect
9.5 Essential idea: The Doppler effect describes the phenomenon of wavelength/frequency shift when relative motion occurs.

9.5 Nature of science:
Technology: Although originally based on physical observations of the pitch of fast moving sources of sound, the Doppler effect has an important role in many different areas such as evidence for the expansion of the universe and generating images used in weather reports and in medicine. (5.5)

9.5 Understandings:
• The Doppler effect for sound waves and light waves

9.5 Applications and skills:
• Sketching and interpreting the Doppler effect when there is relative motion between source and observer
• Describing situations where the Doppler effect can be utilized
• Solving problems involving the change in frequency or wavelength observed due to the Doppler effect to determine the velocity of the source/observer

9.5 Guidance:
• For electromagnetic waves, the approximate equation should be used for all calculations
• Situations to be discussed should include the use of Doppler effect in radars and in medical physics, and its significance for the red-shift in the light spectra of receding galaxies

9.5 International-mindedness:
• Radar usage is affected by the Doppler effect and must be considered for applications using this technology

9.5 Theory of knowledge:
• How important is sense perception in explaining scientific ideas such as the Doppler effect?

9.5 Utilization:
• Astronomy relies on the analysis of the Doppler effect when dealing with fast moving objects (see Physics option D)

9.5 Aims:
• Aim 2: the Doppler effect needs to be considered in various applications of technology that utilize wave theory
• Aim 6: spectral data and images of receding galaxies are available from professional astronomical observatories for analysis
• Aim 7: computer simulations of the Doppler effect allow students to visualize complex and mostly unobservable situations

9.5 Data booklet reference