Topic 4 (Core)

Waves

15 hours


4.1 – Oscillations


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.
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.
Understandings:
• Simple harmonic oscillations Concept Pendulum waves Pendulum wave machine formulasTuning fork
• Time period, frequency, amplitude, displacement and phase difference Concept, test
• Conditions for simple harmonic motion Simple pendulum lab
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
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: F = -kx
Data Booklet reference:
T = 1 / f
• The T represents the period of the oscillation, and the f represents the frequency of the oscillation.
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.
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?
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)
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


4.2 – Traveling waves


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.
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.
Understandings:
• Travelling waves Traveling waves, advanced!
• Wavelength, frequency, period and wave speed Wavelength Frequency and period Wave speed
• Transverse and longitudinal waves Waves on a string Wave animations
• The nature of electromagnetic waves Microwave your frickin' brain with your frickin' cellphones!
• The nature of sound waves Russel's wave animations
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
Guidance:
• Students will be expected to derive
• Students should be aware of the order of magnitude of the wavelengths of radio, microwave, infrared, visible, ultraviolet, X-ray and gamma rays
Data Booklet reference:
c = lf
• The c represents the speed of light having wavelength l and frequency f. This formula is just a special case of v = lf, which states that the speed of a traveling wave is equal to the product of its wavelength and its frequency.
International-mindedness:
• Electromagnetic waves are used extensively for national and international communication
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?
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)
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


4.3 – Wave characteristics


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.
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.
Understandings:
• Wavefronts and rays Concepts
• Amplitude and intensity Concept
• Superposition Concept Simulations Fourier waves - super superposition!
• Polarization Concept Concept Simulations How do 3D glasses work?
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
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
Data Booklet reference:
I µ A2
I µ x-2
I = I0 cosq
• The I represents the intensity of the wave (which is power per unit area) and the A represents the amplitude of the traveling wave.
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 reality?
Utilization:
• A number of modern technologies, such as LCD displays, rely on polarization for their operation
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


4.4 – Wave behavior


Essential idea: Waves interact with media and each other in a number of ways that can be unexpected and useful.
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.
Understandings:
• Reflection and refraction Light concepts
• Snell’s law, critical angle and total internal reflection Concept Bending light
• Diffraction through a single-slit and around objects Concept Ripple tank
• Interference patterns Water-wave interference Sound-wave interference
• Double-slit interference Concept Slit experiments
• Path difference Sample
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
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
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
Theory of knowledge:
• Huygens and Newton proposed two competing theories of the behaviour of light. How does the scientific community decide between competing theories?
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.
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 foot-print


4.5 – Standing waves


Essential idea: When travelling waves meet they can superpose to form standing waves in which energy may not be transferred.
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.
Understandings:
• The nature of standing waves Concept USNA water tank Tacoma Narrows movie
• Boundary conditions Concept Normal modes of vibration Standing waves in water droplets in space
• Nodes and antinodes Concept Resonance and the driving force 2D Reuben's tube Sand nodes
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
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 questions
International-mindedness:
• The art of music, which has its scientific basis in these ideas, is universal to all cultures, past and present. Many musical instruments rely heavily on the generation and manipulation of standing waves.
Theory of knowledge:
• There are close links between standing waves in strings and Schrodinger’s theory for the probability amplitude of electrons in the atom. Application to superstring theory requires standing wave patterns in 11 dimensions. What is the role of reason and imagination in enabling scientists to visualize scenarios that are beyond our physical capabilities?
Utilization:
• Students studying music should be encouraged to bring their own experiences of this art form to the physics classroom
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 4 PROBLEM SET

This is the complete problem set for Topic 4 - the same one I hand out. If you lose yours, you can download this one to replace it.




TOPIC 4 FORMATIVE ASSESSMENTS

These are the Formative Assessments (practice) that you will do in order to prepare yourself for the Summative Assessments (evidence of proficiency). You can expect to receive a mark of at least Proficient on the Summative Assessment if you understand everything on these Formative Assessments.




TOPIC 4 PROJECTS

Project marks are meant to replace summative assessment marks. Projects are your last opportunity to demonstrate your proficiency in meeting the standards of the assessment criteria.


EXTENSION NOTES FOR ENRICHMENT