PHYSICS 20
Unit 4: Oscillatory Motion and Mechanical Waves
Unit Themes and Emphases
- Change, Energy and Matter
- Scientific Inquiry
- Nature of Science
Focusing Questions
- Where do we observe oscillatory motion?
- How do mechanical waves transmit energy?
- How can an understanding of the natural world improve how society, technology and the environment interact?
Unit D: Oscillatory Motion and Mechanical Waves
Themes: Energy and Matter
Overview:
In this unit, students investigate simple harmonic motion and mechanical waves.This unit builds on:
- Science 10, Unit B: Energy Flow in Technological Systems
- Physics 20, Unit A: Kinematics; Unit B: Dynamics; and Unit C: Circular Motion, Work and Energy
Unit D will require approximately 30% of the time allotted for Physics 20.
Focusing Questions:
- What are examples of oscillatory motion in the world around us?
- How do mechanical waves transmit energy?
- How is structural design and the development of technologies influenced by our understanding of wave properties?
General Outcomes:
There are two major outcomes in this unit.Students will:
D1. describe the conditions that produce oscillatory motion
D2. describe the properties of mechanical waves and explain how mechanical waves transmit energy.
Key Concepts:
The following concepts are developed in this unit and may also be addressed in other units or in other courses. The intended level and scope of treatment is defined by the outcomes.- oscillatory motion
- simple harmonic motion
- restoring force
- oscillating spring, pendulum
- mechanical resonance
- mechanical waves—longitudinal and transverse
- universal wave equation
- reflection
- interference
- acoustic resonance
- Doppler effect
General Outcome 1
1. describe the conditions that produce oscillatory motionSpecific Outcomes for Knowledge
Students will:
20–D1.1k describe oscillatory motion in terms of period and frequency
20–D1.2k define simple harmonic motion as a motion due to a restoring force that is directly proportional and opposite to the displacement from an equilibrium position
20–D1.3k explain, quantitatively, the relationships among displacement, acceleration, velocity and time for simple harmonic motion, as illustrated by a frictionless, horizontal mass-spring system or a pendulum, using the small-angle approximation
20–D1.4k determine, quantitatively, the relationships among kinetic, gravitational potential and total mechanical energies of a mass executing simple harmonic motion
20–D1.5k define mechanical resonance.
20–D1.2k define simple harmonic motion as a motion due to a restoring force that is directly proportional and opposite to the displacement from an equilibrium position
20–D1.3k explain, quantitatively, the relationships among displacement, acceleration, velocity and time for simple harmonic motion, as illustrated by a frictionless, horizontal mass-spring system or a pendulum, using the small-angle approximation
20–D1.4k determine, quantitatively, the relationships among kinetic, gravitational potential and total mechanical energies of a mass executing simple harmonic motion
20–D1.5k define mechanical resonance.
Specific Outcomes for Science, Technology and Society (STS) (Nature of Science Emphasis)
Students will:
20–D1.1sts explain that the goal of science is knowledge about the natural world (NS1)
• analyze, qualitatively, the forces in real-life examples of simple harmonic motion:
- action of springs in vehicle suspensions
- mechanical resonance in cars, bridges and buildings
- seismic waves in Earth’s crust
• relate the fundamental frequency and amplitude of a vibrating drum membrane to its properties.
Note: Some of the outcomes are supported by examples. The examples are written in italics and do not form part of the required program but are provided as an illustration of how the outcomes might be developed.
• analyze, qualitatively, the forces in real-life examples of simple harmonic motion:
- action of springs in vehicle suspensions
- mechanical resonance in cars, bridges and buildings
- seismic waves in Earth’s crust
• relate the fundamental frequency and amplitude of a vibrating drum membrane to its properties.
Note: Some of the outcomes are supported by examples. The examples are written in italics and do not form part of the required program but are provided as an illustration of how the outcomes might be developed.
Specific Outcomes for Skills (Nature of Science Emphasis)
Initiating and PlanningStudents will:
20–D1.1s formulate questions about observed relationships and plan investigations of questions, ideas, problems and issues
• design an experiment to demonstrate that simple harmonic motion can be observed within certain limits, relating the frequency and period of the motion to the physical characteristics of the system;
e.g., a frictionless horizontal mass-spring system or a pendulum (IP–NS2)
• predict the conditions required for mechanical resonance (IP–NS3).
• design an experiment to demonstrate that simple harmonic motion can be observed within certain limits, relating the frequency and period of the motion to the physical characteristics of the system;
e.g., a frictionless horizontal mass-spring system or a pendulum (IP–NS2)
• predict the conditions required for mechanical resonance (IP–NS3).
Performing and Recording
Students will:
20–D1.2s conduct investigations into relationships among observable variables and use a broad range of tools and techniques to gather and record data and information
• perform an experiment to determine the relationship between the length of a pendulum and its period of oscillation (PR–NS3)
• perform an experiment to illustrate the phenomenon of mechanical resonance (PR–NS3)
• perform an experiment to determine the spring constant of a spring (PR–NS3).
• perform an experiment to determine the relationship between the length of a pendulum and its period of oscillation (PR–NS3)
• perform an experiment to illustrate the phenomenon of mechanical resonance (PR–NS3)
• perform an experiment to determine the spring constant of a spring (PR–NS3).
Analyzing and Interpreting
Students will:
20–D1.3s analyze data and apply mathematical and conceptual models to develop and assess possible solutions
• relate the length of a pendulum to its period of oscillation (AI–NS2) [ICT C7–4.2]
• ask if the mass of the pendulum bob is a factor in the pendulum’s period of oscillation (AI–NS5).
• relate the length of a pendulum to its period of oscillation (AI–NS2) [ICT C7–4.2]
• ask if the mass of the pendulum bob is a factor in the pendulum’s period of oscillation (AI–NS5).
Communication and Teamwork
Students will:
20–D1.4s work collaboratively in addressing problems and apply the skills and conventions of science in communicating information and ideas and in assessing results
• select and use appropriate numeric, symbolic, graphical or linguistic modes of representation to communicate findings and conclusions (CT–NS2).
Note: Some of the outcomes are supported by examples. The examples are written in italics and do not form part of the required program but are provided as an illustration of how the outcomes might be developed. • select and use appropriate numeric, symbolic, graphical or linguistic modes of representation to communicate findings and conclusions (CT–NS2).
Links to Mathematics
The following mathematics outcomes are related to the content of Unit D but are not considered prerequisites.Concept - Mathematics Course, Strand and Specific Outcome
Data Collection and Analysis
Grade 9 Mathematics, Statistics and Probability (Data Analysis), Specific Outcome 3
Measurement andUnit Conversions
Mathematics 10C, Measurement, Specific Outcomes 1 and 2;
Mathematics 10-3, Measurement, Specific Outcome 1;
Mathematics 20-3, Algebra, Specific Outcome 3
Trigonometry
Mathematics 10C, Measurement, Specific Outcome 4;
Mathematics 10-3, Geometry, Specific Outcomes 2 and 4
Rate and Proportions
Mathematics 20-2, Measurement, Specific Outcome 1
Graph Analysis
Mathematics10C, Relations and Functions, Specific Outcomes 1, 4 and 7;
Mathematics 20-3, Statistics, Specific Outcome 1
Mathematics 30-1, Trigonometry, Specific Outcome 4
Mathematics 30-2, Relations and Functions, Outcome 8
Solving Equations
Grade 9 Mathematics, Number, Specific Outcome 6;
Mathematics 20-2, Number and Logic, Specific Outcome 4;
Mathematics 20-1, Algebra and Number, Specific Outcomes 3 and 6;
Mathematics 30-2, Relations and Functions, Specific Outcome 3
Slope
Mathematics10C, Relations and Functions, Specific Outcomes 3 and 5;
Mathematics 20-3, Algebra, Specific Outcome 2
Powers
Mathematics10C, Algebra and Number, Specific Outcome 3
Note: The use of systems of equations, the quadratic formula and trigonometric ratios for angles greater than 90º is not required in this unit.
Chapter 8: Mechanical waves transmit energy in a variety of ways
Unit Themes and Emphases
- Mechanical waves – longitudinal and transverse
- Universal wave equation
- Reflection
- Interference
- Acoustical resonance
- Doppler effect
Knowledge
- Describe how transverse and longitudinal waves move through a medium
- Explain how the speed, wavelength, frequency, and amplitude of a wave are related.
- Describe how interference patterns can be used to determine the properties of the waves.
- Explain the Doppler effect.
- Describe the difference between transverse and longitudinal waves.
- Describe how waves are reflected.
- Explain the relationship between rays and waves.
- Apply the universal wave equation to explain how frequency, wavelength, and wave velocity are related.
- Explain the effects of constructive and destructive interference
STS
- Explain that the goal of technology is to provide solutions to practical problems.
8.1 The Properties of Waves
Waves have many properties that can be used to analyze the nature of the wave and the way it behaves as it moves through a medium. Some of these properties are qualitative (crest, trough, wave front, medium, incident wave, reflected wave, wave train) while others are quantitative (amplitude, wavelength, frequency, wave velocity).Medium – the substance that the wave moves through.
Wave – a disturbance of energy that moves through a medium.
Equilibrium position – the position of a medium before a wave enters.
Crest – the part of a transverse wave above the equilibrium position (positive amplitude).
Trough – the part of a transverse wave below the equilibrium position (negative amplitude).
Amplitude – the distance a wave has moved from the equilibrium point. Think the height of the wave.
Wavelength – the horizontal length of a wave. The distance from crest to crest or trough to trough or node to second node.
Wave front – the front of a wave. Reduces a wave to a simple line.
CIRCULAR WAVE
Incident wave – the incoming (original) wave.Reflected wave – the wave that bounces off of a reflective surface (light that bounced off of a mirror).
MEDIA WAVES ANIMATION
Wave train – a group of waves moving together.Point source – a single point from which a wave emerges.
Ray – an arrow that shows the direction of movement of a wave.
f - frequency, Hz
λ - wavelength, m
8.2 Transverse and Longitudinal Waves
Waves can move through a medium either as transverse or longitudinal waves. The relationship among frequency, wavelength, and wave velocity is given by the universal wave equation.Pulse -
LONGITUDINAL WAVE
TRANSVERSE WAVE
8.3 Superposition and Interference
When two, or more, waves travel in different directions through the same point in space their amplitudes combine according to the principle of superposition. Depending on the properties of the waves, they may form an interference pattern. Interference patterns can often be used to determine the properties of the waves from which they are formed.SUPERPOSITION
2 POINT SOURCE INTERFERENCE
Interference – the effect of two pulses (or two waves) crossing within a medium; the medium takes on a shape that is different from the shape of either pulse alonePrinciple of superposition – the displacement of the combined pulse at each point of interference is the sum of the displacements of the individual pulses
Constructive interference – the overlap of pulses to create a pulse of greater amplitude
CONSTRUCTIVE INTERFERENCE
Destructive interference – the overlap of pulses to create a pulse of lesser amplitudeDESTRUCTIVE INTERFERENCE
Node – a point on a spring or other medium at which only destructive interference occurs; a point that never vibrates between supercrest and supertroughs; in a standing wave nodes occur at intervals ofAntinode – a point in an interference pattern that oscillates with maximum amplitude; in a standing wave antinodes occur at intervals of
Standing wave – a condition in a spring or other medium in which a wave seems to oscillate around stationary points called nodes. The wavelength of a standing wave is the distance between alternate nodes or alternate antinodes.
Resonance – an increase in the amplitude of a wave due to a transfer of energy in phase with the natural frequency of the wave
Closed pipe
Fundamental frequency – the lowest frequency produced by a particular instrument; corresponds to the standing wave having a single antinode, with a node at each end of the string
Overtone – any frequency of vibration of a string that may exist simultaneously with the fundamental frequency
Open pipe
Interference pattern – a pattern of maxima and minima resulting from the interaction of waves, as crests and troughs overlap while the waves move through each other
Maximum - a line of points linking antinodes that occur as the result of constructive interference between waves
Minimum – a line of points linking nodes that occur as the result of destructive interference between waves
Phase shift – the result of waves from one source having to travel farther to reach a particular point in the interference pattern that waves from the other source
OPEN PIPE RESONANCE
SLIDE WHISTLE RESONANCE
8.4 The Doppler Effect
When a sound source moves either toward or away from a sensor (ear or microphone), the frequency of the sound that is detected will be different from the frequency emitted by the source.When an object is traveling at the speed of sound it creates a shock wave known as a sonic boom.
DOPPLER ANIMATION
| f = | v | ×fo |
| v ± vs |
v - velocity of wave, m/s
vs - velocity of source, m/s
fo - original frequency, Hz
Program of Studies
Alberta Physics 20
Program of Studies
Alberta Physics 20
Program of Studies
Contact me:
BCHS Barrhead AB
Steven Montgomery
steven.montgomery@pembinahills.caBCHS Barrhead AB
Textbook
Physics 20 & 20 Textbook (2009)
Physics 20 & 20 Textbook (2009)