Wave Motion. Chapter 14 of Essential University Physics, Richard Wolfson, 3 rd Edition
|
|
- Claire Tucker
- 5 years ago
- Views:
Transcription
1 Wave Motion Chapter 14 of Essential University Physics, Richard Wolfson, 3 rd Edition 1
2 Waves: propagation of energy, not particles 2
3 Longitudinal Waves: disturbance is along the direction of wave propagation 3
4 Transverse Waves: disturbance is perpendicular to the direction of wave propagation 4
5 Waves with Longitudinal Transverse Motions 5
6 Amplitude of a Wave pressure height longitudinal displacement transverse displacement 6
7 Waveforms a pulse a wave train a continuous wave 7
8 PhET 8
9 Wavelength in a continuous wave 9
10 Wave Speed vv = λλ TT 10
11 PhET 11
12 Two Snapshots of a Wave Pulse tt = 0 yy = ff xx tt 0 yy = ff xx vv tt 12
13 PhET 13
14 Fingerprint of a Wave: ψψ(xx, tt) = ff xx vv tt 14
15 A Harmonic Wave tt = 0 ψψ xx, tt = 0 = AA cccccc 2 ππ xx λλ tt 0 ψψ xx, tt = AA cccccc 2 ππ xx vv tt λλ 15
16 PhET 16
17 A Couple of Definitions ψψ xx, tt = AA cccccc 2 ππ xx vv tt λλ Wave Number Angular Frequency kk 2 ππ λλ ωω 2 ππ TT = 2 ππ ff ψψ xx, tt = AA cccccc kk xx ωω tt vv = ωω kk 17
18 Propagation towards Positive x-direction ψψ xx, tt = AA cccccc kk xx ωω tt Propagation towards Negative x-direction ψψ xx, tt = AA cccccc kk xx + ωω tt 18
19 Got It?
20 The Wave Equation ψψ(xx, tt) = AA cccccc kk xx ωω tt ψψ = kk AA ssssss kk xx ωω tt ψψ = ωω AA ssssss kk xx ωω tt 2 ψψ xx 2 = kk2 AA cccccc kk xx ωω tt 2 ψψ tt 2 = ωω2 AA cccccc kk xx ωω tt 1 2 ψψ kk 2 xx 2 = 1 2 ψψ ωω 2 tt 2 2 ψψ xx 2 = 1 2 ψψ vv 2 tt 2 20
21 Waves on a String 21
22 An example on how the properties of the carrying medium determines the wave speed: 22
23 Wave Speed FF nnnnnn 2 FF θθ FF = mm aa mm 2 θθ RR μμ aa = vv2 RR 2 FF θθ 2 θθ RR μμ vv2 RR vv = FF μμ 23
24 Example 14.2 mm = 5.0 kkkk FF =?? xx = 43 mm tt = 1.4 ss vv = FF μμ 24
25 Got It?
26 Wave Power yy xx, tt = AA cccccc kk xx ωω tt PP = FF. vv = FF vv ssssss θθ vv = tttttt θθ = xx = ωω AA ssssss kk xx ωω tt = kk AA ssssss kk xx ωω tt FF vv tttttt θθ = FF ωω kk AA 2 ssssss 2 kk xx ωω tt = μμ vv ωω 2 AA 2 ssssss 2 kk xx ωω tt PP = 1 2 μμ vv ωω2 AA 2 PP = μμ vv ωω 2 AA 2 ssssss 2 kk xx ωω tt 26
27 Wave Intensity II PPPPPPPPPP AAAAAAAA II = PPPPPPPPPP 4 ππ rr 2 27
28 Example of Wave Intensities 28
29 Example 14.3 PP 1 = 9.2 WW xx 1 = 1.9 mm xx 2 =?? PP 2 = 4.9 WW II 1 = II 2 II = PPPPPPPPPP 4 ππ rr 2 II 1 = PP 1 4 ππ xx 1 2 II 2 = PP 2 4 ππ xx 2 2 PP 1 4 ππ xx 1 2 = PP 2 4 ππ xx 2 2 xx 2 = xx 1 PP 2 PP 1 29
30 Got It?
31 Sound Waves vv = γγ PP ρρ γγ is a constant characteristic of the gas 31
32 Audible Frequencies for Human Ears ββ dddd 10 log 10 II II oo II oo WW mm 2 32
33 Example 14.4 ββ 1 = 75 dddd ββ 2 = 60 dddd PP 2 PP 1 =?? PP 2 PP 1 = II 2 II 1 II = II oo 10 ββ 10 ββ 2 10 II 2 = II oo 10 II 1 II oo 10 ββ 1 10 = 10 ββ 2 ββ
34 Interference or what happened when two waves are present in the same region of space at a particular time? Just add them up!! When wave crests coincide with crests, the interference is constructive. When crests coincide with troughs, the interference is destructive. 34
35 2016 Pearson Education, Inc. Co-Propagating Waves Constructive Destructive
36 An application of destructive interference: getting waves to cancel each other: 36
37 2016 Pearson Education, Inc. Adding Multiple Harmonic Waves: Fourier Analysis
38 Sound 2016 Pearson Education, Inc.
39 Dispersion: vv ωω No dispersion With dispersion 39
40 2016 Pearson Education, Inc. Beats: two co-propagating waves of slightly different frequencies tt yy 1 tt = AA cccccc ωω 1 tt yy 2 tt = AA cccccc ωω 2 tt yy 1 tt + yy 2 tt = 2 AA cccccc 1 2 ωω 1 ωω 2 tt cccccc 1 2 ωω 1 + ωω 2 tt
41 41
42 Interference in 2D yy 1 rr 1 = AA cccccc kk rr 1 yy 2 rr 2 = AA cccccc kk rr 2 Constructive Interference: kk rr 1 rr 2 = ππ 2 mm Destructive Interference: kk rr 1 rr 2 = ππ 2 mm
43 Reflection and Refraction PhET 43
44 Partial Reflection and Transmission 44
45 2016 Pearson Education, Inc. Standing Waves: two counter-propagating waves yy 1 xx, tt = AA cccccc kk xx ωω tt yy 2 xx, tt = AA cccccc kk xx + ωω tt yy 1 tt + yy 2 tt = 2 AA cccc ss ωω tt cccccc kk xx
46 46
47 Doppler Effect λλ = λλ uu TT = λλ uu λλ vv 47
CHAPTER 5 Wave Properties of Matter and Quantum Mechanics I
CHAPTER 5 Wave Properties of Matter and Quantum Mechanics I 1 5.1 X-Ray Scattering 5.2 De Broglie Waves 5.3 Electron Scattering 5.4 Wave Motion 5.5 Waves or Particles 5.6 Uncertainty Principle Topics 5.7
More informationWork, Energy, and Power. Chapter 6 of Essential University Physics, Richard Wolfson, 3 rd Edition
Work, Energy, and Power Chapter 6 of Essential University Physics, Richard Wolfson, 3 rd Edition 1 With the knowledge we got so far, we can handle the situation on the left but not the one on the right.
More informationRotational Motion. Chapter 10 of Essential University Physics, Richard Wolfson, 3 rd Edition
Rotational Motion Chapter 10 of Essential University Physics, Richard Wolfson, 3 rd Edition 1 We ll look for a way to describe the combined (rotational) motion 2 Angle Measurements θθ ss rr rrrrrrrrrrrrrr
More informationGravitation. Chapter 8 of Essential University Physics, Richard Wolfson, 3 rd Edition
Gravitation Chapter 8 of Essential University Physics, Richard Wolfson, 3 rd Edition 1 What you are about to learn: Newton's law of universal gravitation About motion in circular and other orbits How to
More informationINTRODUCTION TO QUANTUM MECHANICS
4 CHAPTER INTRODUCTION TO QUANTUM MECHANICS 4.1 Preliminaries: Wave Motion and Light 4.2 Evidence for Energy Quantization in Atoms 4.3 The Bohr Model: Predicting Discrete Energy Levels in Atoms 4.4 Evidence
More informationUnit WorkBook 4 Level 4 ENG U8 Mechanical Principles 2018 UniCourse Ltd. All Rights Reserved. Sample
2018 UniCourse Ltd. A Rights Reserved. Pearson BTEC Levels 4 Higher Nationals in Engineering (RQF) Unit 8: Mechanical Principles Unit Workbook 4 in a series of 4 for this unit Learning Outcome 4 Translational
More information(1) Correspondence of the density matrix to traditional method
(1) Correspondence of the density matrix to traditional method New method (with the density matrix) Traditional method (from thermal physics courses) ZZ = TTTT ρρ = EE ρρ EE = dddd xx ρρ xx ii FF = UU
More informationClass Average = 71. Counts Scores
30 Class Average = 71 25 20 Counts 15 10 5 0 0 20 10 30 40 50 60 70 80 90 100 Scores Chapter 12 Mechanical Waves and Sound To describe mechanical waves. To study superposition, standing waves, and interference.
More informationCHAPTER 2 Special Theory of Relativity
CHAPTER 2 Special Theory of Relativity Fall 2018 Prof. Sergio B. Mendes 1 Topics 2.0 2.1 2.2 2.3 2.4 2.5 2.6 2.7 2.8 2.9 2.10 2.11 2.12 2.13 2.14 Inertial Frames of Reference Conceptual and Experimental
More informationQuantum Mechanics. An essential theory to understand properties of matter and light. Chemical Electronic Magnetic Thermal Optical Etc.
Quantum Mechanics An essential theory to understand properties of matter and light. Chemical Electronic Magnetic Thermal Optical Etc. Fall 2018 Prof. Sergio B. Mendes 1 CHAPTER 3 Experimental Basis of
More informationCHAPTER 4 Structure of the Atom
CHAPTER 4 Structure of the Atom Fall 2018 Prof. Sergio B. Mendes 1 Topics 4.1 The Atomic Models of Thomson and Rutherford 4.2 Rutherford Scattering 4.3 The Classic Atomic Model 4.4 The Bohr Model of the
More information(1) Introduction: a new basis set
() Introduction: a new basis set In scattering, we are solving the S eq. for arbitrary VV in integral form We look for solutions to unbound states: certain boundary conditions (EE > 0, plane and spherical
More informationSection 1 Simple Harmonic Motion. The student is expected to:
Section 1 Simple Harmonic Motion TEKS The student is expected to: 7A examine and describe oscillatory motion and wave propagation in various types of media Section 1 Simple Harmonic Motion Preview Objectives
More informationVariations. ECE 6540, Lecture 02 Multivariate Random Variables & Linear Algebra
Variations ECE 6540, Lecture 02 Multivariate Random Variables & Linear Algebra Last Time Probability Density Functions Normal Distribution Expectation / Expectation of a function Independence Uncorrelated
More informationHaar Basis Wavelets and Morlet Wavelets
Haar Basis Wavelets and Morlet Wavelets September 9 th, 05 Professor Davi Geiger. The Haar transform, which is one of the earliest transform functions proposed, was proposed in 90 by a Hungarian mathematician
More informationHeat, Work, and the First Law of Thermodynamics. Chapter 18 of Essential University Physics, Richard Wolfson, 3 rd Edition
Heat, Work, and the First Law of Thermodynamics Chapter 18 of Essential University Physics, Richard Wolfson, 3 rd Edition 1 Different ways to increase the internal energy of system: 2 Joule s apparatus
More informationProducing a Sound Wave. Chapter 14. Using a Tuning Fork to Produce a Sound Wave. Using a Tuning Fork, cont.
Producing a Sound Wave Chapter 14 Sound Sound waves are longitudinal waves traveling through a medium A tuning fork can be used as an example of producing a sound wave Using a Tuning Fork to Produce a
More informationBaccalieu Collegiate. Physics Course Outline
Baccalieu Collegiate Physics 2204 Course Outline Course Content: Unit 1: Kinematics Motion is a common theme in our everyday lives: birds fly, babies crawl, and we, ourselves, seem to be in a constant
More informationProf. Dr. Rishi Raj Design of an Impulse Turbine Blades Hasan-1
Prof. Dr. Rishi Raj Design of an Impulse Turbine Blades Hasan-1 The main purpose of this project, design of an impulse turbine is to understand the concept of turbine blades by defining and designing the
More informationPhysics 371 Spring 2017 Prof. Anlage Review
Physics 71 Spring 2017 Prof. Anlage Review Special Relativity Inertial vs. non-inertial reference frames Galilean relativity: Galilean transformation for relative motion along the xx xx direction: xx =
More informationOscillatory Motion and Wave Motion
Oscillatory Motion and Wave Motion Oscillatory Motion Simple Harmonic Motion Wave Motion Waves Motion of an Object Attached to a Spring The Pendulum Transverse and Longitudinal Waves Sinusoidal Wave Function
More informationSection 1 Simple Harmonic Motion. Chapter 11. Preview. Objectives Hooke s Law Sample Problem Simple Harmonic Motion The Simple Pendulum
Section 1 Simple Harmonic Motion Preview Objectives Hooke s Law Sample Problem Simple Harmonic Motion The Simple Pendulum Section 1 Simple Harmonic Motion Objectives Identify the conditions of simple harmonic
More informationWave Motions and Sound
EA Notes (Scen 101), Tillery Chapter 5 Wave Motions and Sound Introduction Microscopic molecular vibrations determine temperature (last Chapt.). Macroscopic vibrations of objects set up what we call Sound
More informationYang-Hwan Ahn Based on arxiv:
Yang-Hwan Ahn (CTPU@IBS) Based on arxiv: 1611.08359 1 Introduction Now that the Higgs boson has been discovered at 126 GeV, assuming that it is indeed exactly the one predicted by the SM, there are several
More informationThornton & Rex, 4th ed. Fall 2018 Prof. Sergio B. Mendes 1
Modern Physics for Scientists and Engineers Thornton & Rex, 4th ed. Fall 2018 Prof. Sergio B. Mendes 1 CHAPTER 1 The Birth of Modern Physics Fall 2018 Prof. Sergio B. Mendes 2 Topics 1) Classical Physics
More informationAngular Momentum, Electromagnetic Waves
Angular Momentum, Electromagnetic Waves Lecture33: Electromagnetic Theory Professor D. K. Ghosh, Physics Department, I.I.T., Bombay As before, we keep in view the four Maxwell s equations for all our discussions.
More informationModule 7 (Lecture 25) RETAINING WALLS
Module 7 (Lecture 25) RETAINING WALLS Topics Check for Bearing Capacity Failure Example Factor of Safety Against Overturning Factor of Safety Against Sliding Factor of Safety Against Bearing Capacity Failure
More informationNational 5 Mathematics. Practice Paper E. Worked Solutions
National 5 Mathematics Practice Paper E Worked Solutions Paper One: Non-Calculator Copyright www.national5maths.co.uk 2015. All rights reserved. SQA Past Papers & Specimen Papers Working through SQA Past
More informationECE 6540, Lecture 06 Sufficient Statistics & Complete Statistics Variations
ECE 6540, Lecture 06 Sufficient Statistics & Complete Statistics Variations Last Time Minimum Variance Unbiased Estimators Sufficient Statistics Proving t = T(x) is sufficient Neyman-Fischer Factorization
More informationElastic light scattering
Elastic light scattering 1. Introduction Elastic light scattering in quantum mechanics Elastic scattering is described in quantum mechanics by the Kramers Heisenberg formula for the differential cross
More informationTransverse wave - the disturbance is perpendicular to the propagation direction (e.g., wave on a string)
1 Part 5: Waves 5.1: Harmonic Waves Wave a disturbance in a medium that propagates Transverse wave - the disturbance is perpendicular to the propagation direction (e.g., wave on a string) Longitudinal
More informationFluids in Rigid-Body Motion
Fluids in Rigid-Body Motion 9. 14. 2016 Hyunse Yoon, Ph.D. Associate Research Scientist IIHR-Hydroscience & Engineering Newton s 2 nd Law of Motion In general, for a body of mass mm, mmaa = FF where, aa
More informationTECHNICAL NOTE AUTOMATIC GENERATION OF POINT SPRING SUPPORTS BASED ON DEFINED SOIL PROFILES AND COLUMN-FOOTING PROPERTIES
COMPUTERS AND STRUCTURES, INC., FEBRUARY 2016 TECHNICAL NOTE AUTOMATIC GENERATION OF POINT SPRING SUPPORTS BASED ON DEFINED SOIL PROFILES AND COLUMN-FOOTING PROPERTIES Introduction This technical note
More informationPhotons in the universe. Indian Institute of Technology Ropar
Photons in the universe Photons in the universe Element production on the sun Spectral lines of hydrogen absorption spectrum absorption hydrogen gas Hydrogen emission spectrum Element production on the
More informationPHL424: Feynman diagrams
PHL424: Feynman diagrams In 1940s, R. Feynman developed a diagram technique to describe particle interactions in space-time. Feynman diagram example Richard Feynman time Particles are represented by lines
More informationModeling of a non-physical fish barrier
University of Massachusetts - Amherst ScholarWorks@UMass Amherst International Conference on Engineering and Ecohydrology for Fish Passage International Conference on Engineering and Ecohydrology for Fish
More information13.3 Interference and Superposition. Interference and Superposition Constructive Interference Destructive Interference Standing Waves
13.3 Interference and Superposition Interference and Superposition Constructive Interference Destructive Interference Standing Waves Interference and Superposition When raindrops fall into still water,
More informationPhysics General Physics. Lecture 25 Waves. Fall 2016 Semester Prof. Matthew Jones
Physics 22000 General Physics Lecture 25 Waves Fall 2016 Semester Prof. Matthew Jones 1 Final Exam 2 3 Mechanical Waves Waves and wave fronts: 4 Wave Motion 5 Two Kinds of Waves 6 Reflection of Waves When
More informationChapter 22 : Electric potential
Chapter 22 : Electric potential What is electric potential? How does it relate to potential energy? How does it relate to electric field? Some simple applications What does it mean when it says 1.5 Volts
More information4. What is the speed (in cm s - 1 ) of the tip of the minute hand?
Topic 4 Waves PROBLEM SET Formative Assessment NAME: TEAM: THIS IS A PRACTICE ASSESSMENT. Show formulas, substitutions, answers, and units! Topic 4.1 Oscillations A mass is attached to a horizontal spring.
More informationLecture 17. Mechanical waves. Transverse waves. Sound waves. Standing Waves.
Lecture 17 Mechanical waves. Transverse waves. Sound waves. Standing Waves. What is a wave? A wave is a traveling disturbance that transports energy but not matter. Examples: Sound waves (air moves back
More informationPhysics 123 Unit #3 Review
Physics 123 Unit #3 Review I. Definitions and Facts longitudinal wave transverse wave traveling wave standing wave wave front wavelength wave number frequency angular frequency period crest trough node
More informationChapter 15. Mechanical Waves
Chapter 15 Mechanical Waves A wave is any disturbance from an equilibrium condition, which travels or propagates with time from one region of space to another. A harmonic wave is a periodic wave in which
More informationWaves Review Checklist Pulses 5.1.1A Explain the relationship between the period of a pendulum and the factors involved in building one
5.1.1 Oscillating Systems Waves Review Checklist 5.1.2 Pulses 5.1.1A Explain the relationship between the period of a pendulum and the factors involved in building one Four pendulums are built as shown
More informationExam tomorrow on Chapter 15, 16, and 17 (Oscilla;ons and Waves 1 &2)
Exam tomorrow on Chapter 15, 16, and 17 (Oscilla;ons and Waves 1 &2) What to study: Quiz 6 Homework problems for Chapters 15 & 16 Material indicated in the following review slides Other Specific things:
More informationPhys101 Lectures 28, 29. Wave Motion
Phys101 Lectures 8, 9 Wave Motion Key points: Types of Waves: Transverse and Longitudinal Mathematical Representation of a Traveling Wave The Principle of Superposition Standing Waves; Resonance Ref: 11-7,8,9,10,11,16,1,13,16.
More informationPhysics 1C. Lecture 12C
Physics 1C Lecture 12C Simple Pendulum The simple pendulum is another example of simple harmonic motion. Making a quick force diagram of the situation, we find:! The tension in the string cancels out with
More informationUniversity of North Georgia Department of Mathematics
Instructor: Berhanu Kidane Course: Precalculus Math 13 University of North Georgia Department of Mathematics Text Books: For this course we use free online resources: See the folder Educational Resources
More informationPhysics 141 Second Mid-Term Examination Spring 2015 March 31, 2015
Physics 141 Second Mid-Term Examination Spring 2015 March 31, 2015 Your Number Solutions LAST Name (print) FIRST Name (print) Signature: UIN #: Your Section: Barkan 9 am Barkan 11 am Goeckner 3 pm PROBLEM
More informationAfter successfully answering these questions, the students will be able to
Pre-Lab Questions 4 Topic: Simple Pendulum Objective: 1. To enable the students to identify the physical parameters of a simple pendulum. 2. To enable the students to identify the independent and dependant
More informationFor more info:
Waves:- Wave motion:- Wave motion is the disturbance, set up in the medium, due to the repeated periodic motion of the particles of the medium and travels from the particle to particle, the particles themselves
More informationModule 7 (Lecture 27) RETAINING WALLS
Module 7 (Lecture 27) RETAINING WALLS Topics 1.1 RETAINING WALLS WITH METALLIC STRIP REINFORCEMENT Calculation of Active Horizontal and vertical Pressure Tie Force Factor of Safety Against Tie Failure
More informationReview for Exam Hyunse Yoon, Ph.D. Assistant Research Scientist IIHR-Hydroscience & Engineering University of Iowa
57:020 Fluids Mechanics Fall2013 1 Review for Exam3 12. 11. 2013 Hyunse Yoon, Ph.D. Assistant Research Scientist IIHR-Hydroscience & Engineering University of Iowa 57:020 Fluids Mechanics Fall2013 2 Chapter
More informationCold atoms in optical lattices
Cold atoms in optical lattices www.lens.unifi.it Tarruel, Nature Esslinger group Optical lattices the big picture We have a textbook model, which is basically exact, describing how a large collection of
More information1 f. result from periodic disturbance same period (frequency) as source Longitudinal or Transverse Waves Characterized by
result from periodic disturbance same period (frequency) as source Longitudinal or Transverse Waves Characterized by amplitude (how far do the bits move from their equilibrium positions? Amplitude of MEDIUM)
More informationRadiation. Lecture40: Electromagnetic Theory. Professor D. K. Ghosh, Physics Department, I.I.T., Bombay
Radiation Zone Approximation We had seen that the expression for the vector potential for a localized cuent distribution is given by AA (xx, tt) = μμ 4ππ ee iiiiii dd xx eeiiii xx xx xx xx JJ (xx ) In
More informationThe Bose Einstein quantum statistics
Page 1 The Bose Einstein quantum statistics 1. Introduction Quantized lattice vibrations Thermal lattice vibrations in a solid are sorted in classical mechanics in normal modes, special oscillation patterns
More informationHomework Book. Wave Properties. Huijia Physics Homework Book 1 Semester 2. Name: Homeroom: Physics Class:
Homework Book Wave Properties Huijia Physics Homework Book 1 Semester 2 Name: Homeroom: Physics Class: Week 1 Reflection, Refraction, wave equations 1. If the wavelength of an incident wave is 1.5cm and
More informationInteraction with matter
Interaction with matter accelerated motion: ss = bb 2 tt2 tt = 2 ss bb vv = vv 0 bb tt = vv 0 2 ss bb EE = 1 2 mmvv2 dddd dddd = mm vv 0 2 ss bb 1 bb eeeeeeeeeeee llllllll bbbbbbbbbbbbbb dddddddddddddddd
More informationLecture 14 1/38 Phys 220. Final Exam. Wednesday, August 6 th 10:30 am 12:30 pm Phys multiple choice problems (15 points each 300 total)
Lecture 14 1/38 Phys 220 Final Exam Wednesday, August 6 th 10:30 am 12:30 pm Phys 114 20 multiple choice problems (15 points each 300 total) 75% will be from Chapters 10-16 25% from Chapters 1-9 Students
More informationSchedule for the remainder of class
Schedule for the remainder of class 04/25 (today): Regular class - Sound and the Doppler Effect 04/27: Cover any remaining new material, then Problem Solving/Review (ALL chapters) 04/29: Problem Solving/Review
More informationPHYSICS. Chapter 16 Lecture FOR SCIENTISTS AND ENGINEERS A STRATEGIC APPROACH 4/E RANDALL D. KNIGHT Pearson Education, Inc.
PHYSICS FOR SCIENTISTS AND ENGINEERS A STRATEGIC APPROACH 4/E Chapter 16 Lecture RANDALL D. KNIGHT 2017 Pearson Education, Inc. Chapter 16 Traveling Waves IN THIS CHAPTER, you will learn the basic properties
More information2016 AP Physics Unit 6 Oscillations and Waves.notebook December 09, 2016
AP Physics Unit Six Oscillations and Waves 1 2 A. Dynamics of SHM 1. Force a. since the block is accelerating, there must be a force acting on it b. Hooke's Law F = kx F = force k = spring constant x =
More informationMathematics Ext 2. HSC 2014 Solutions. Suite 403, 410 Elizabeth St, Surry Hills NSW 2010 keystoneeducation.com.
Mathematics Ext HSC 4 Solutions Suite 43, 4 Elizabeth St, Surry Hills NSW info@keystoneeducation.com.au keystoneeducation.com.au Mathematics Extension : HSC 4 Solutions Contents Multiple Choice... 3 Question...
More informationChapter 17. Superposition & Standing Waves
Chapter 17 Superposition & Standing Waves Superposition & Standing Waves Superposition of Waves Standing Waves MFMcGraw-PHY 2425 Chap 17Ha - Superposition - Revised: 10/13/2012 2 Wave Interference MFMcGraw-PHY
More informationCLASS 2 CLASS 2. Section 13.5
CLASS 2 CLASS 2 Section 13.5 Simple Pendulum The simple pendulum is another example of a system that exhibits simple harmonic motion The force is the component of the weight tangent to the path of motion
More informationMath 171 Spring 2017 Final Exam. Problem Worth
Math 171 Spring 2017 Final Exam Problem 1 2 3 4 5 6 7 8 9 10 11 Worth 9 6 6 5 9 8 5 8 8 8 10 12 13 14 15 16 17 18 19 20 21 22 Total 8 5 5 6 6 8 6 6 6 6 6 150 Last Name: First Name: Student ID: Section:
More informationFineman CP Physics Final Study Guide
All Science Tests are on Wednesday, June 17 th. Students who take more than one Science class will take their second science final on Thursday, June 18 from 8:00-10:00 AM in the Library. The CP Physics
More informationContent of the course 3NAB0 (see study guide)
Content of the course 3NAB0 (see study guide) 17 November diagnostic test! Week 1 : 14 November Week 2 : 21 November Introduction, units (Ch1), Circuits (Ch25,26) Heat (Ch17), Kinematics (Ch2 3) Week 3:
More informationGeneral Physics I. Lecture 14: Sinusoidal Waves. Prof. WAN, Xin ( 万歆 )
General Physics I Lecture 14: Sinusoidal Waves Prof. WAN, Xin ( 万歆 ) xinwan@zju.edu.cn http://zimp.zju.edu.cn/~xinwan/ Motivation When analyzing a linear medium that is, one in which the restoring force
More informationTime Domain Analysis of Linear Systems Ch2. University of Central Oklahoma Dr. Mohamed Bingabr
Time Domain Analysis of Linear Systems Ch2 University of Central Oklahoma Dr. Mohamed Bingabr Outline Zero-input Response Impulse Response h(t) Convolution Zero-State Response System Stability System Response
More informationChapter 16 Traveling Waves
Chapter 16 Traveling Waves GOALS When you have mastered the contents of this chapter, you will be able to achieve the following goals: Definitions Define each of the following terms as it is used in physics,
More informationGrover s algorithm. We want to find aa. Search in an unordered database. QC oracle (as usual) Usual trick
Grover s algorithm Search in an unordered database Example: phonebook, need to find a person from a phone number Actually, something else, like hard (e.g., NP-complete) problem 0, xx aa Black box ff xx
More informationWhat is a Wave. Why are Waves Important? Power PHYSICS 220. Lecture 19. Waves
PHYSICS 220 Lecture 19 Waves What is a Wave A wave is a disturbance that travels away from its source and carries energy. A wave can transmit energy from one point to another without transporting any matter
More information-Electromagnetic. Waves - disturbance that propagates through space & time - usually with transfer of energy -Mechanical.
Waves Waves - disturbance that propagates through space & time - usually with transfer of energy -Mechanical requires a medium -Electromagnetic no medium required Mechanical waves: sound, water, seismic.
More informationEXAMEN GÉNÉRAL DE SYNTHÈSE ÉPREUVE ÉCRITE Programme de doctorat en génie physique. Jeudi 18 juin Salle B-508.
EXAMEN GÉNÉRAL DE SYNTHÈSE ÉPREUVE ÉCRITE Programme de doctorat en génie physique Salle B-58 de 9h3 à 3h3 NOTES : No documentation allowed. A non-programmable calculator is allowed. The candidate can answer
More informationFineman Honors Physics Final Study Guide
All Science Tests are on Wednesday, June 17 th. Students who take more than one Science class will take their second science final on Thursday, June 18 from 8:00-10:00 AM in the Library. The Honors Physics
More informationProblem 3.1 (Verdeyen 5.13) First, I calculate the ABCD matrix for beam traveling through the lens and space.
Problem 3. (Verdeyen 5.3) First, I calculate the ABCD matrix for beam traveling through the lens and space. T = dd 0 0 dd 2 ff 0 = dd 2 dd ff 2 + dd ( dd 2 ff ) dd ff ff Aording to ABCD law, we can have
More informationCharge carrier density in metals and semiconductors
Charge carrier density in metals and semiconductors 1. Introduction The Hall Effect Particles must overlap for the permutation symmetry to be relevant. We saw examples of this in the exchange energy in
More informationPHY103A: Lecture # 4
Semester II, 2017-18 Department of Physics, IIT Kanpur PHY103A: Lecture # 4 (Text Book: Intro to Electrodynamics by Griffiths, 3 rd Ed.) Anand Kumar Jha 10-Jan-2018 Notes The Solutions to HW # 1 have been
More informationGraduate School of Engineering, Kyoto University, Kyoto daigaku-katsura, Nishikyo-ku, Kyoto, Japan.
On relationship between contact surface rigidity and harmonic generation behavior in composite materials with mechanical nonlinearity at fiber-matrix interface (Singapore November 2017) N. Matsuda, K.
More informationStanding waves [49 marks]
Standing waves [49 marks] 1. The graph shows the variation with time t of the velocity v of an object undergoing simple harmonic motion (SHM). At which velocity does the displacement from the mean position
More informationControl of Mobile Robots
Control of Mobile Robots Regulation and trajectory tracking Prof. Luca Bascetta (luca.bascetta@polimi.it) Politecnico di Milano Dipartimento di Elettronica, Informazione e Bioingegneria Organization and
More informationSound Waves. Sound waves are longitudinal waves traveling through a medium Sound waves are produced from vibrating objects.
Sound Waves Sound waves are longitudinal waves traveling through a medium Sound waves are produced from vibrating objects Introduction Sound Waves: Molecular View When sound travels through a medium, there
More informationTRIAL HIGHER SCHOOL CERTIFICATE EXAMINATION 2017 MATHEMATICS
Name: Class: TRIAL HIGHER SCHOOL CERTIFICATE EXAMINATION 2017 MATHEMATICS General Instructions: Total Marks 100 Reading Time: 5 minutes. Section I: 10 marks Working Time: 3 hours. Attempt Question 1 10.
More informationOscillation the vibration of an object. Wave a transfer of energy without a transfer of matter
Oscillation the vibration of an object Wave a transfer of energy without a transfer of matter Equilibrium Position position of object at rest (mean position) Displacement (x) distance in a particular direction
More informationSimple Harmonic Motion
1. Object Simple Harmonic Motion To determine the period of motion of objects that are executing simple harmonic motion and to check the theoretical prediction of such periods. 2. Apparatus Assorted weights
More informationRaymond A. Serway Chris Vuille. Chapter Thirteen. Vibrations and Waves
Raymond A. Serway Chris Vuille Chapter Thirteen Vibrations and Waves Periodic Motion and Waves Periodic motion is one of the most important kinds of physical behavior Will include a closer look at Hooke
More information(2) Orbital angular momentum
(2) Orbital angular momentum Consider SS = 0 and LL = rr pp, where pp is the canonical momentum Note: SS and LL are generators for different parts of the wave function. Note: from AA BB ii = εε iiiiii
More informationSpecialist Mathematics 2019 v1.2
181314 Mensuration circumference of a circle area of a parallelogram CC = ππππ area of a circle AA = ππrr AA = h area of a trapezium AA = 1 ( + )h area of a triangle AA = 1 h total surface area of a cone
More informationGradient expansion formalism for generic spin torques
Gradient expansion formalism for generic spin torques Atsuo Shitade RIKEN Center for Emergent Matter Science Atsuo Shitade, arxiv:1708.03424. Outline 1. Spintronics a. Magnetoresistance and spin torques
More informationSolid Rocket Motor Combustion Instability Modeling in COMSOL Multiphysics
Solid Rocket Motor Combustion Instability Modeling in COMSOL Multiphysics Sean R. Fischbach Mashall Space Flight Center / Qualis Corp. / Jacobs ESSSA Group *MSFC Huntsville sean.r.fischbach@nasa.gov Outline
More informationDoppler Correction after Inelastic Heavy Ion Scattering 238 U Ta system at the Coulomb barrier
Doppler-Corrected e - and γ-ray Spectroscopy Physical Motivation In-beam conversion electron spectroscopy complements the results obtained from γ-spectroscopy A method for determining the multipolarity
More informationCHAPTER 11 VIBRATIONS AND WAVES
CHAPTER 11 VIBRATIONS AND WAVES http://www.physicsclassroom.com/class/waves/u10l1a.html UNITS Simple Harmonic Motion Energy in the Simple Harmonic Oscillator The Period and Sinusoidal Nature of SHM The
More informationMATHEMATICAL MODEL OF ULTRASOUND TRANSMISSION IN GRADIENT MATERIALS SYNTHESIZED IN ARC SURFACING UNDER CONTACT LOADING
Materials Physics and Mechanics 32 (207) 86-93 Received: May 7, 207 MATHEMATICAL MODEL OF ULTRASOUND TRANSMISSION IN GRADIENT MATERIALS SYNTHESIZED IN ARC SURFACING UNDER CONTACT LOADING V.D. Sarychev,
More information10.4 The Cross Product
Math 172 Chapter 10B notes Page 1 of 9 10.4 The Cross Product The cross product, or vector product, is defined in 3 dimensions only. Let aa = aa 1, aa 2, aa 3 bb = bb 1, bb 2, bb 3 then aa bb = aa 2 bb
More informationSecondary 3H Unit = 1 = 7. Lesson 3.3 Worksheet. Simplify: Lesson 3.6 Worksheet
Secondary H Unit Lesson Worksheet Simplify: mm + 2 mm 2 4 mm+6 mm + 2 mm 2 mm 20 mm+4 5 2 9+20 2 0+25 4 +2 2 + 2 8 2 6 5. 2 yy 2 + yy 6. +2 + 5 2 2 2 0 Lesson 6 Worksheet List all asymptotes, holes and
More informationJasmin Smajic1, Christian Hafner2, Jürg Leuthold2, March 23, 2015
Jasmin Smajic, Christian Hafner 2, Jürg Leuthold 2, March 23, 205 Time Domain Finite Element Method (TD FEM): Continuous and Discontinuous Galerkin (DG-FEM) HSR - University of Applied Sciences of Eastern
More information(Total 1 mark) IB Questionbank Physics 1
1. A transverse wave travels from left to right. The diagram below shows how, at a particular instant of time, the displacement of particles in the medium varies with position. Which arrow represents the
More informationis a What you Hear The Pressure Wave sets the Ear Drum into Vibration.
is a What you Hear The ear converts sound energy to mechanical energy to a nerve impulse which is transmitted to the brain. The Pressure Wave sets the Ear Drum into Vibration. electroencephalogram v S
More information