# 1/26/2016. Chapter 21 Superposition. Chapter 21 Preview. Chapter 21 Preview

Save this PDF as:

Size: px
Start display at page:

## Transcription

1 Chapter 21 Superposition Chapter Goal: To understand and use the idea of superposition. Slide 21-2 Chapter 21 Preview Slide 21-3 Chapter 21 Preview Slide

2 Chapter 21 Preview Slide 21-5 Chapter 21 Preview Slide 21-6 Chapter 21 Preview Slide

3 Chapter 21 Reading Quiz Slide 21-8 Reading Question 21.1 When a wave pulse on a string reflects from a hard boundary, how is the reflected pulse related to the incident pulse? A. Shape unchanged, amplitude unchanged. B. Shape inverted, amplitude unchanged. C. Shape unchanged, amplitude reduced. D. Shape inverted, amplitude reduced. E. Amplitude unchanged, speed reduced. Slide 21-9 Reading Question 21.2 There are some points on a standing wave that never move. What are these points called? A. Harmonics. B. Normal Modes. C. Nodes. D. Anti-nodes. E. Interference. Slide

4 Reading Question 21.3 Two sound waves of nearly equal frequencies are played simultaneously. What is the name of the acoustic phenomena you hear if you listen to these two waves? A. Beats. B. Diffraction. C. Harmonics. D. Chords. E. Interference. Slide Reading Question 21.4 The various possible standing waves on a string are called the A. Antinodes. B. Resonant nodes. C. Normal modes. D. Incident waves. Slide Reading Question 21.5 The frequency of the third harmonic of a string is A. One-third the frequency of the fundamental. B. Equal to the frequency of the fundamental. C. Three times the frequency of the fundamental. D. Nine times the frequency of the fundamental. Slide

5 Chapter 21 Content, Examples, and QuickCheck Questions Slide Particles vs. Waves Two particles flying through the same point at the same time will collide and bounce apart, as in Figure (a). But waves, unlike particles, can pass directly through each other, as in Figure (b). Slide The Principle of Superposition If wave 1 displaces a particle in the medium by D 1 and wave 2 simultaneously displaces it by D 2, the net displacement of the particle is D 1 + D 2. Slide

6 Standing Waves Shown is a time-lapse photograph of a standing wave on a vibrating string. It s not obvious from the photograph, but this is actually a superposition of two waves. To understand this, consider two sinusoidal waves with the same frequency, wavelength, and amplitude traveling in opposite directions. Slide Standing Waves Antinode Node Slide Standing Waves The figure has collapsed several graphs into a single graphical representation of a standing wave. A striking feature of a standing-wave pattern is the existence of nodes, points that never move! The nodes are spaced λ/2 apart. Halfway between the nodes are the antinodes where the particles in the medium oscillate with maximum displacement. Slide

7 Standing Waves In Chapter 20 you learned that the intensity of a wave is proportional to the square of the amplitude: I A 2. Intensity is maximum at points of constructive interference and zero at points of destructive interference. Slide QuickCheck 21.3 What is the wavelength of this standing wave? A m. B. 0.5 m. C. 1.0 m. D. 2.0 m. E. Standing waves don t have a wavelength. Slide QuickCheck 21.3 What is the wavelength of this standing wave? A m. B. 0.5 m. C. 1.0 m. D. 2.0 m. E. Standing waves don t have a wavelength. Slide

8 The Mathematics of Standing Waves A sinusoidal wave traveling to the right along the x-axis with angular frequency ω = 2πf, wave number k = 2π/λ and amplitude a is: An equivalent wave traveling to the left is: We previously used the symbol A for the wave amplitude, but here we will use a lowercase a to represent the amplitude of each individual wave and reserve A for the amplitude of the net wave. Slide The Mathematics of Standing Waves According to the principle of superposition, the net displacement of the medium when both waves are present is the sum of D R and D L : We can simplify this by using a trigonometric identity, and arrive at: Where the amplitude function A(x) is defined as: The amplitude reaches a maximum value of A max = 2a at points where sin kx = 1. Slide The Mathematics of Standing Waves Shown is the graph of D(x,t) at several instants of time. The nodes occur at x m = mλ/2, where m is an integer. Slide

9 Example 21.1 Node Spacing on a String Slide Example 21.1 Node Spacing on a String Slide Example 21.1 Node Spacing on a String Slide

10 Waves on a String with a Discontinuity A string with a large linear density is connected to one with a smaller linear density. The tension is the same in both strings, so the wave speed is slower on the left, faster on the right. When a wave encounters such a discontinuity, some of the wave s energy is transmitted forward and some is reflected. Slide Waves on a String with a Discontinuity Below, a wave encounters discontinuity at which the wave speed decreases. In this case, the reflected pulse is inverted. We say that the reflected wave has a phase change of π upon reflection. Slide Waves on a String with a Boundary When a wave reflects from a boundary, the reflected wave is inverted, but has the same amplitude. Slide

11 Creating Standing Waves The figure shows a string of length L tied at x = 0 and x = L. Reflections at the ends of the string cause waves of equal amplitude and wavelength to travel in opposite directions along the string. These are the conditions that cause a standing wave! Slide Standing Waves on a String For a string of fixed length L, the boundary conditions can be satisfied only if the wavelength has one of the values: Because λf = v for a sinusoidal wave, the oscillation frequency corresponding to wavelength λ m is: The lowest allowed frequency is called the fundamental frequency: f 1 = v/2l. Slide Standing Waves on a String Shown are the first four possible standing waves on a string of fixed length L. These possible standing waves are called the modes of the string, or sometimes the normal modes. Each mode, numbered by the integer m, has a unique wavelength and frequency. Slide

12 Standing Waves on a String m is the number of antinodes on the standing wave. The fundamental mode, with m = 1, has λ 1 = 2L. The frequencies of the normal modes form a series: f 1, 2f 1, 3f 1, The fundamental frequency f 1 can be found as the difference between the frequencies of any two adjacent modes: f 1 = f = f m+1 f m. Below is a time-exposure photograph of the m = 3 standing wave on a string. Slide QuickCheck 21.4 What is the mode number of this standing wave? A. 4. B. 5. C. 6. D. Can t say without knowing what kind of wave it is. Slide QuickCheck 21.4 What is the mode number of this standing wave? A. 4. B. 5. C. 6. D. Can t say without knowing what kind of wave it is. Slide

13 QuickCheck 21.5 A standing wave on a string vibrates as shown. Suppose the string tension is reduced to 1/4 its original value while the frequency and length are kept unchanged. Which standing wave pattern is produced? Slide QuickCheck 21.5 A standing wave on a string vibrates as shown. Suppose the string tension is reduced to 1/4 its original value while the frequency and length are kept unchanged. Which standing wave pattern is produced? The frequency is f m = m v. 2L Quartering the tension reduces v by one half. Thus m must double to keep the frequency constant. Slide Standing Electromagnetic Waves Standing electromagnetic waves can be established between two parallel mirrors that reflect light back and forth. A typical laser cavity has a length L 30 cm, and visible light has a wavelength λ 600 nm. The standing light wave in a typical laser cavity has a mode number m that is 2L/λ 1,000,000! Slide

14 Example 21.3 The Standing Light Wave Inside a Laser Slide Example 21.3 The Standing Light Wave Inside a Laser Slide Standing Sound Waves A long, narrow column of air, such as the air in a tube or pipe, can support a longitudinal standing sound wave. A closed end of a column of air must be a displacement node, thus the boundary conditions nodes at the ends are the same as for a standing wave on a string. It is often useful to think of sound as a pressure wave rather than a displacement wave: The pressure oscillates around its equilibrium value. The nodes and antinodes of the pressure wave are interchanged with those of the displacement wave. Slide

15 Standing Sound Wave Time Sequence Slide 1 of 3 Shown is the m = 2 standing sound wave in a closed-closed tube of air at t = 0. Slide Standing Sound Wave Time Sequence Slide 2 of 3 Shown is the m = 2 standing sound wave in a closed-closed tube of air a quarter-cycle after t = 0. Slide Standing Sound Wave Time Sequence Slide 3 of 3 Shown is the m = 2 standing sound wave in a closed-closed tube of air a half-cycle after t = 0. Slide

16 Standing Sound Waves Shown are the displacement x and pressure graphs for the m = 2 mode of standing sound waves in a closed-closed tube. The nodes and antinodes of the pressure wave are interchanged with those of the displacement wave. Slide Example 21.4 Singing in the Shower Slide Standing Sound Waves Shown are displacement and pressure graphs for the first three standingwave modes of a tube closed at both ends: Slide

17 Standing Sound Waves Shown are displacement and pressure graphs for the first three standingwave modes of a tube open at both ends: Slide Standing Sound Waves Shown are displacement and pressure graphs for the first three standingwave modes of a tube open at one end but closed at the other: Slide QuickCheck 21.6 An open-open tube of air has length L. Which is the displacement graph of the m = 3 standing wave in this tube? Slide

18 QuickCheck 21.6 An open-open tube of air has length L. Which is the displacement graph of the m = 3 standing wave in this tube? Slide QuickCheck 21.7 An open-closed tube of air of length L has the closed end on the right. Which is the displacement graph of the m = 3 standing wave in this tube? Slide QuickCheck 21.7 An open-closed tube of air of length L has the closed end on the right. Which is the displacement graph of the m = 3 standing wave in this tube? Slide

19 Musical Instruments Instruments such as the harp, the piano, and the violin have strings fixed at the ends and tightened to create tension. A disturbance generated on the string by plucking, striking, or bowing it creates a standing wave on the string. The fundamental frequency is the musical note you hear when the string is sounded: where T s is the tension in the string and µ is its linear density. Slide Musical Instruments With a wind instrument, blowing into the mouthpiece creates a standing sound wave inside a tube of air. The player changes the notes by using her fingers to cover holes or open valves, changing the length of the tube and thus its fundamental frequency: In both of these equations, v is the speed of sound in the air inside the tube. Overblowing wind instruments can sometimes produce higher harmonics such as f 2 = 2f 1 and f 3 = 3f 1. for an open-open tube instrument, such as a flute for an open-closed tube instrument, such as a clarinet Slide QuickCheck 21.8 At room temperature, the fundamental frequency of an open-open tube is 500 Hz. If taken outside on a cold winter day, the fundamental frequency will be A. Less than 500 Hz. B. 500 Hz. C. More than 500 Hz. Slide

20 QuickCheck 21.8 At room temperature, the fundamental frequency of an open-open tube is 500 Hz. If taken outside on a cold winter day, the fundamental frequency will be A. Less than 500 Hz. B. 500 Hz. C. More than 500 Hz. Slide Example 21.6 Flutes and Clarinets Slide Example 21.6 Flutes and Clarinets Slide

21 Interference in One Dimension The pattern resulting from the superposition of two waves is often called interference. In this section we will look at the interference of two waves traveling in the same direction. Slide Interference in One Dimension A sinusoidal wave traveling to the right along the x-axis has a displacement: D = a sin(kx ωt + φ 0 ) The phase constant φ 0 tells us what the source is doing at t = 0. Slide Constructive Interference D 1 = a sin(kx 1 ωt + φ 10 ) D 2 = a sin(kx 2 ωt + φ 20 ) D = D 1 + D 2 The two waves are in phase, meaning that D 1 (x) = D 2 (x) The resulting amplitude is A = 2a for maximum constructive interference. Slide

22 Destructive Interference D 1 = a sin(kx 1 ωt + φ 10 ) D 2 = a sin(kx 2 ωt + φ 20 ) D = D 1 + D 2 The two waves are out of phase, meaning that D 1 (x) = D 2 (x). The resulting amplitude is A = 0 for perfect destructive interference. Slide The Mathematics of Interference As two waves of equal amplitude and frequency travel together along the x-axis, the net displacement of the medium is: We can use a trigonometric identity to write the net displacement as: Where φ = φ 1 + φ 2 is the phase difference between the two waves. Slide The Mathematics of Interference The amplitude has a maximum value A = 2a if cos( φ/2) = ±1. This is maximum constructive interference, when: where m is an integer. Similarly, the amplitude is zero if cos( φ/2) = 0. This is perfect destructive interference, when: Slide

23 Interference in One Dimension Shown are two identical sources located one wavelength apart: x = λ The two waves are in step with φ = 2π, so we have maximum constructive interference with A = 2a. Slide Interference in One Dimension Shown are two identical sources located half a wavelength apart: x = λ/2 The two waves have phase difference φ = π, so we have perfect destructive interference with A = 0. Slide Example 21.7 Interference Between Two Sound Waves Slide

24 Example 21.7 Interference Between Two Sound Waves Slide Example 21.7 Interference Between Two Sound Waves Slide Example 21.7 Interference Between Two Sound Waves Slide

25 The Mathematics of Interference It is entirely possible, of course, that the two waves are neither exactly in phase nor exactly out of phase. Shown are the calculated interference of two waves that differ in phase by 40, 90 and 160. Slide QuickCheck 21.9 Two loudspeakers emit sound waves with the same wavelength and the same amplitude. The waves are shown displaced, for clarity, but assume that both are traveling along the same axis. At the point where the dot is, A. the interference is constructive. B. the interference is destructive. C. the interference is somewhere between constructive and destructive. D. There s not enough information to tell about the interference. Slide QuickCheck 21.9 Two loudspeakers emit sound waves with the same wavelength and the same amplitude. The waves are shown displaced, for clarity, but assume that both are traveling along the same axis. At the point where the dot is, A. the interference is constructive. B. the interference is destructive. C. the interference is somewhere between constructive and destructive. D. There s not enough information to tell about the interference. Slide

26 QuickCheck Two loudspeakers emit sound waves with the same wavelength and the same amplitude. Which of the following would cause there to be destructive interference at the position of the dot? A. Move speaker 2 forward (right) 1.0 m. B. Move speaker 2 forward (right) 0.5 m. C. Move speaker 2 backward (left) 0.5 m. D. Move speaker 2 backward (left) 1.0 m. E. Nothing. Destructive interference is not possible in this situation. Slide QuickCheck Two loudspeakers emit sound waves with the same wavelength and the same amplitude. Which of the following would cause there to be destructive interference at the position of the dot? A. Move speaker 2 forward (right) 1.0 m. Move this peak back 1/4 wavelength to B. Move speaker 2 forward (right) 0.5 m. align with the trough C. Move speaker 2 backward (left) 0.5 m. of wave 1. D. Move speaker 2 backward (left) 1.0 m. E. Nothing. Destructive interference is not possible in this situation. Slide Example 21.8 More Interference of Sound Waves Slide

27 Example 21.8 More Interference of Sound Waves Slide Example 21.8 More Interference of Sound Waves Slide Application: Thin-Film Optical Coatings Thin transparent films, placed on glass surfaces, such as lenses, can control reflections from the glass. Antireflection coatings on the lenses in cameras, microscopes, and other optical equipment are examples of thin-film coatings. Slide

28 Application: Thin-Film Optical Coatings The phase difference between the two reflected waves is: where n is the index of refraction of the coating, d is the thickness, and λ is the wavelength of the light in vacuum or air. For a particular thin-film, constructive or destructive interference depends on the wavelength of the light: Slide Example 21.9 Designing an Antireflection Coating Slide Example 21.9 Designing an Antireflection Coating Slide

29 Example 21.9 Designing an Antireflection Coating Slide A Circular or Spherical Wave A circular or spherical wave can be written: D(r, t) = a sin(kr ωt + φ 0 ) where r is the distance measured outward from the source. The amplitude a of a circular or spherical wave diminishes as r increases. Slide Interference in Two and Three Dimensions Two overlapping water waves create an interference pattern. Slide

30 Interference in Two and Three Dimensions = Points of constructive interference. A crest is aligned with a crest, or a trough with a trough. = Points of destructive interference. A crest is aligned with a trough of another wave. Slide Interference in Two and Three Dimensions The mathematical description of interference in two or three dimensions is very similar to that of onedimensional interference. The conditions for constructive and destructive interference are: where r is the path-length difference. Slide Interference in Two and Three Dimensions The figure shows two identical sources that are in phase. The path-length difference r determines whether the interference at a particular point is constructive or destructive. Slide

31 Interference in Two and Three Dimensions Slide QuickCheck Two in-phase sources emit sound waves of equal wavelength and intensity. At the position of the dot, A. The interference is constructive. B. The interference is destructive. C. The interference is somewhere between constructive and destructive. D. There s not enough information to tell about the interference. Slide QuickCheck Two in-phase sources emit sound waves of equal wavelength and intensity. At the position of the dot, A. The interference is constructive. B. The interference is destructive. C. The interference is somewhere between constructive and destructive. D. There s not enough information to tell about the interference. Slide

32 QuickCheck Two in-phase sources emit sound waves of equal wavelength and intensity. How many antinodal lines (lines of constructive interference) are in the interference pattern? A. 1 B. 2 C. 3 D. 4 E. 5 Slide QuickCheck Two in-phase sources emit sound waves of equal wavelength and intensity. How many antinodal lines (lines of constructive interference) are in the interference pattern? A. 1 B. 2 C. 3 D. 4 E. 5 Sources are 1.5λ apart, so no point can have r more than 1.5λ. Slide Problem-Solving Strategy: Interference of Two Waves Slide

33 Problem-Solving Strategy: Interference of Two Waves Slide Example Two-Dimensional Interference Between Two Loudspeakers Slide Example Two-Dimensional Interference Between Two Loudspeakers Slide

34 Example Two-Dimensional Interference Between Two Loudspeakers Slide Example Two-Dimensional Interference Between Two Loudspeakers Slide Example Two-Dimensional Interference Between Two Loudspeakers Slide

35 Picturing Interference: Two Identical Sources Slide Picturing Interference: Two Out-of-Phase Sources Slide Beats The figure shows the history graph for the superposition of the sound from two sources of equal amplitude a, but slightly different frequency. Slide

36 Beats With beats, the sound intensity rises and falls twice during one cycle of the modulation envelope. Each loud-soft-loud is one beat, so the beat frequency f beat, which is the number of beats per second, is twice the modulation frequency f mod. The beat frequency is: where, to keep f beat from being negative, we will always let f 1 be the larger of the two frequencies. The beat frequency is simply the difference between the two individual frequencies. Slide Visual Beats Shown is a graphical example of beats. Two fences of slightly different frequencies are superimposed on each other. The center part of the figure has two beats per inch: f beat = = 2 Slide QuickCheck You hear 2 beats per second when two sound sources, both at rest, play simultaneously. The beats disappear if source 2 moves toward you while source 1 remains at rest. The frequency of source 1 is 500 Hz. The frequency of source 2 is A. 496 Hz. B. 498 Hz. C. 500 Hz. D. 502 Hz. E. 504 Hz. Slide

37 QuickCheck You hear 2 beats per second when two sound sources, both at rest, play simultaneously. The beats disappear if source 2 moves toward you while source 1 remains at rest. The frequency of source 1 is 500 Hz. The frequency of source 2 is A. 496 Hz. B. 498 Hz. C. 500 Hz. D. 502 Hz. E. 504 Hz. Slide Example Detecting Bats with Beats Slide Example Detecting Bats with Beats Slide

38 Example Detecting Bats with Beats Slide Chapter 21 Summary Slides Slide General Principles Principle of Superposition The displacement of a medium when more than one wave is present is the sum of the displacements due to each individual wave. Slide

39 Important Concepts Slide Important Concepts Slide

### Chapter 21. Superposition

Chapter 21. Superposition The combination of two or more waves is called a superposition of waves. Applications of superposition range from musical instruments to the colors of an oil film to lasers. Chapter

### 20-1. Sections Covered in the Text: Chapter 21, except The Principle of Superposition

Superposition Sections Covered in the Text: Chapter 21, except 21.8 In Note 18 we saw that a wave has the attributes of displacement, amplitude, frequency, wavelength and speed. We can now consider the

### Interference: Two Spherical Sources

Interference: Two Spherical Sources Superposition Interference Waves ADD: Constructive Interference. Waves SUBTRACT: Destructive Interference. In Phase Out of Phase Superposition Traveling waves move through

### Lecture Presentation Chapter 16 Superposition and Standing Waves

Lecture Presentation Chapter 16 Superposition and Standing Waves Suggested Videos for Chapter 16 Prelecture Videos Constructive and Destructive Interference Standing Waves Physics of Your Vocal System

### Chapter4: Superposition and Interference

Chapter4: Superposition and Interference Sections Superposition Principle Superposition of Sinusoidal Waves Interference of Sound Waves Standing Waves Beats: Interference in Time Nonsinusoidal Wave Patterns

### Chapter 18 4/14/11. Superposition Principle. Superposition and Interference. Superposition Example. Superposition and Standing Waves

Superposition Principle Chapter 18 Superposition and Standing Waves If two or more traveling waves are moving through a medium, the resultant value of the wave function at any point is the algebraic sum

### Nicholas J. Giordano. Chapter 12 Waves

Nicholas J. Giordano www.cengage.com/physics/giordano Chapter 12 Waves Wave Motion A wave is a moving disturbance that transports energy from one place to another without transporting matter Questions

### NOTES Unit 13: Waves and Optics Wave Motion and Sound

Unit 13: Waves and Optics Wave Motion and Sound OBJECTIVES: Big Idea 6: Waves can transfer energy and momentum from one location to another without the permanent transfer of mass and serve as a mathematical

### Chapter 15 Wave Motion. Copyright 2009 Pearson Education, Inc.

Chapter 15 Wave Motion Characteristics of Wave Motion Types of Waves: Transverse and Longitudinal Energy Transported by Waves Mathematical Representation of a Traveling Wave The Wave Equation Units of

### Waves I: Generalities, Superposition & Standing Waves

Chapter 5 Waves I: Generalities, Superposition & Standing Waves 5.1 The Important Stuff 5.1.1 Wave Motion Wave motion occurs when the mass elements of a medium such as a taut string or the surface of a

### A Simple Introduction to Interference

Course PHYSICS260 Assignment 4 Due at 11:00pm on Wednesday, February 27, 2008 A Simple Introduction to Interference Description: Interference is discussed for pulses on strings and then for sinusoidal

### Physics 2A (Fall 2012) Chapters 15: Traveling Waves and Sound and 16: Superposition and Standing Waves

Physics 2A (Fall 2012) Chapters 15: Traeling Waes and Sound and 16: Superposition and Standing Waes There is only one corner of the unierse that you can be certain of improing, and that s your own. Aldous

### Constructive and Destructive Interference Conceptual Question

Chapter 16 - solutions Constructive and Destructive Interference Conceptual Question Description: Conceptual question on whether constructive or destructive interference occurs at various points between

### University Physics 226N/231N Old Dominion University Wave Motion, Interference, Reflection (Chapter 14)

University Physics 226N/231N Old Dominion University Wave Motion, Interference, Reflection (Chapter 14) Dr. Todd Satogata (ODU/Jefferson Lab) http://www.toddsatogata.net/2012-odu Monday November 26, 2012

### Waves. Types of Waves. Waves and Wave Properties Serway Ch. 13: Section 8 thru 13 Physics B Lesson 42: Wave Basics.

Waves Waves and Wave Properties Serway Ch. 13: Section 8 thru 13 www.archive.org Physics B Lesson 42: Wave Basics Mechanical Caused by vibrations in a medium Examples: Sound Waves in a string Water waves

### Sound Waves. PHYS102 Previous Exam Problems CHAPTER. Sound waves Interference of sound waves Intensity & level Resonance in tubes Doppler effect

PHYS102 Previous Exam Problems CHAPTER 17 Sound Waves Sound waves Interference of sound waves Intensity & level Resonance in tubes Doppler effect If the speed of sound in air is not given in the problem,

You may not realize it, but you are surrounded by waves. The waviness of a water wave is readily apparent, from the ripples on a pond to ocean waves large enough to surf. It s less apparent that sound

### 1 of 8 1/23/2010 6:15 PM

1 of 8 1/23/2010 6:15 PM Chapter 21 Homework Due: 8:00am on Tuesday, January 26, 2010 Note: To understand how points are awarded, read your instructor's Grading Policy [Return to Standard Assignment View]

### University Physics 226N/231N Old Dominion University Wave Motion (Chapter 14)

University Physics 226N/231N Old Dominion University Wave Motion (Chapter 14) Dr. Todd Satogata (ODU/Jefferson Lab) http://www.toddsatogata.net/2012-odu Wednesday November 14, 2012 Happy Birthday to Travis

### Unit 8. Oscillations: Simple Harmonic Motion and Waves Big Idea 3: The interactions of an object with other objects can be described by forces.

Unit 8. Oscillations: Simple Harmonic Motion and Waves Name: Big Idea 3: The interactions of an object with other objects can be described by forces. Essential Knowledge 3.B.3: Restoring forces can Learning

### Waves. J.S Wetzel, 1993

Waves J.S Wetzel, 1993 A wave is a disturbance traveling through a medium. When we speak of wave motion, we are not speaking of matter in motion as we do in kinematics; we are speaking of the motion of

### physics 1/12/2016 Chapter 20 Lecture Chapter 20 Traveling Waves

Chapter 20 Lecture physics FOR SCIENTISTS AND ENGINEERS a strategic approach THIRD EDITION randall d. knight Chapter 20 Traveling Waves Chapter Goal: To learn the basic properties of traveling waves. Slide

### WAVE MOTION AND SOUND

Part 2 WAVE MOTION AND SOUND The general discussion of wave motion is important because the ideas of wave propagation are ubiquitous. In nearly all areas of science (and therefore real life) energy is

### Waves. Sec Wave Properties. Waves are everywhere in nature. What is a wave? Example: Slinky Wave

Waves PART I Wave Properties Wave Anatomy PART II Wave Math Wave Behavior PART III Sound Waves Light Waves (aka Electromagnetic Waves or Radiation) 1 Sec. 14.1 Wave Properties Objectives Identify how waves

### Unit 6 Practice Test: Sound

Unit 6 Practice Test: Sound Name: Multiple Guess Identify the letter of the choice that best completes the statement or answers the question. 1. A mass attached to a spring vibrates back and forth. At

### Cutnell/Johnson Physics

Cutnell/Johnson Physics Classroom Response System Questions Chapter 17 The Principle of Linear Superposition and Interference Phenomena Interactive Lecture Questions 17.1.1. The graph shows two waves at

### Physics 53. Wave Motion 1

Physics 53 Wave Motion 1 It's just a job. Grass grows, waves pound the sand, I beat people up. Muhammad Ali Overview To transport energy, momentum or angular momentum from one place to another, one can

### Waves Introduction A wave is a disturbance in a medium that caries energy without a net movement of particles.

Waves Introduction A wave is a disturbance in a medium that caries energy without a net movement of particles. A wave: transfers energy. usually involves a periodic, repetitive movement. does not result

### AP1 Waves. (A) frequency (B) wavelength (C) speed (D) intensity. Answer: (A) and (D) frequency and intensity.

1. A fire truck is moving at a fairly high speed, with its siren emitting sound at a specific pitch. As the fire truck recedes from you which of the following characteristics of the sound wave from the

### What is the essence of waviness? The Wave Model. Waves: examples. Particles. Wave. 1. Ripples on a pond. Think of a leaf, or a cork on the water

Chapter 20: Traveling Waves 20.1 The wave model 20.2 One-dimensional waves 20.3 Sinusoidal waves 20.4 Waves in 2- & 3-dimensions 20.5 Sound and Light Waves 20.6 Power and Intensity 20.7 Doppler Effect

### Chapter 14 Wave Motion

Query 17. If a stone be thrown into stagnating water, the waves excited thereby continue some time to arise in the place where the stone fell into the water, and are propagated from thence in concentric

Chapter 20. Traveling Waves You may not realize it, but you are surrounded by waves. The waviness of a water wave is readily apparent, from the ripples on a pond to ocean waves large enough to surf. It

### Physics 222 Study Guide

Unit 2: Waves & Unit 3: Light Use this course guide to help you prepare for Exam 2. This Guide is designed to give an overview of the main concepts, equations, and vocabulary that will be tested in Unit

### Chapter 3: Sound waves. Sound waves

Sound waves 1. Sound travels at 340 m/s in air and 1500 m/s in water. A sound of 256 Hz is made under water. In the air, A) the frequency remains the same but the wavelength is shorter. B) the frequency

### Waves. Transverse Waves

Waves A wave is a repeated oscillation or disturbance that transfers energy through matter or space. The two primary types of waves are Transverse Longitudinal Transverse Waves In a transverse wave, the

### Superposition and Interference

Superposition and Interference Bởi: OpenStaxCollege These waves result from the superposition of several waves from different sources, producing a complex pattern. (credit: waterborough, Wikimedia Commons)

### β = 10 log(i/i 0 ) I = P/4πr 2 v = λ /T = λf

Chapter 12 Lecture Notes Physics 2414 - Strauss Formulas: v (331 + 0.60T ) m/s I P/A 2 I x 0 β = 10 log(i/i 0 ) I = P/4πr 2 v = λ /T = λf v = FT ml for a stretched string λ n = 2L/n, for a stretched string

### Assignment 6. Problem 1: Creating a Standing Wave

Assignment 6 Problem 1: Creating a Standing Wave The wave is traveling in the +x direction Asin(kx + wt) = Asin(k(x + vt)) since vt is added to position, the wave is traveling in the negative direction.

### Angle of an incident (arriving) ray or particle to a surface; measured from a line perpendicular to the surface (the normal) Angle of incidence

The maximum displacement of particles of the medium from their mean positions during the propagation of a wave Angle of an incident (arriving) ray or particle to a surface; measured from a line perpendicular

### IB PHYSICS HL REVIEW PACKET: WAVES & VIBRATIONS

NAME IB PHYSICS HL REVIEW PACKET: WAVES & VIBRATIONS 1. This question is about waves and wave properties. (a) By making reference to waves, distinguish between a ray and a wavefront.......... (3) The diagram

### Chapter 15: Making Waves

Chapter 15: Making Waves 1. Electromagnetic waves are generally A. transverse waves. B. longitudinal waves. C. a 50/50 combination of transverse and longitudinal waves. D. standing waves. 2. The period

### transverse wave on a string Slinky waves

L 23 Vibrations and Waves [3] updated 10/23/07 resonance clocks pendulum springs harmonic motion mechanical waves sound waves golden rule for waves musical instruments The Doppler effect Doppler radar

### Chapter 13. Mechanical Waves

Chapter 13 Mechanical Waves A harmonic oscillator is a wiggle in time. The oscillating object will move back and forth between +A and A forever. If a harmonic oscillator now moves through space, we create

### Lab 14: Standing Waves

Lab 14: Standing Waves Objectives: To understand superposition of waves To understand how a standing wave is created To understand relationships between physical parameters such as tension and length of

### Objectives 354 CHAPTER 8 WAVES AND VIBRATION

Objectives Describe how a mechanical wave transfers energy through a medium. Explain the difference between a transverse wave and a longitudinal wave. Define amplitude and wavelength. Define frequency

### 1) The time for one cycle of a periodic process is called the A) wavelength. B) period. C) frequency. D) amplitude.

practice wave test.. Name Use the text to make use of any equations you might need (e.g., to determine the velocity of waves in a given material) MULTIPLE CHOICE. Choose the one alternative that best completes

### 11/17/10. Transverse and Longitudinal Waves. Transverse and Longitudinal Waves. Wave Speed. EXAMPLE 20.1 The speed of a wave pulse

You may not realize it, but you are surrounded by waves. The waviness of a water wave is readily apparent, from the ripples on a pond to ocean waves large enough to surf. It s less apparent that sound

### INTERFERENCE, BEATS, AND STANDING WAVES

INTERFERENCE, BEATS, AND STANDING WAVES Harmonic Interference in General Consider a superposition of two signals of some kind displacements of a rope, pressures in a sound wave, voltages in an electric

### SPH3UW Superposition and Interference Page 1 of 6

SPH3UW Superposition and Interference Page 1 of 6 Notes Physics Tool box Constructive Interference: refers to when waves build up each other, resulting in the medium having larger amplitude. Destructive

### Chapter 10: Waves. Waves. Waves (2) Examples of waves. Compression Waves. Shear (transverse) Waves

Chapter 10: Waves Chapter 13 Waves Demo: Shive wave machine 1. disturbances that travel from one place to another (pulse, but is often periodic) -pressure -displacement -light 2. initiated by a source

### Waves review practice questions

Name: ate: 1. The diagram shown represents four waves traveling to the right in the same transmitting medium. 4. Which wave has the greatest amplitude?.... Which type of wave is represented? 5. Which characteristic

### Wave Motion, Superposition, Standing Waves. Professor Michael Burton School of Physics, UNSW. Tunguska Meteorite, Siberia 30 June 1908

Chapters 17+18 Wave Motion, Superposition, Standing Waves Professor Michael Burton School of Physics, UNSW Tunguska Meteorite, Siberia 30 June 1908 I saw a moving light in the sky and felt my face become

### Lesson 19: Mechanical Waves!!

Lesson 19: Mechanical Waves Mechanical Waves There are two basic ways to transmit or move energy from one place to another. First, one can move an object from one location to another via kinetic energy.

### physics 111N oscillations & waves

physics 111N oscillations & waves periodic motion! often a physical system will repeat the same motion over and over! we call this periodic motion, or an oscillation the time it takes for the motion to

### Superposition and Interference

OpenStax-CNX module: m42249 1 Superposition and Interference OpenStax College This work is produced by OpenStax-CNX and licensed under the Creative Commons Attribution License 3.0 Abstract Explain standing

### Waves and Sound. An Introduction to Waves and Wave Properties Wednesday, November 19, 2008

Waves and Sound An Introduction to Waves and Wave Properties Wednesday, November 19, 2008 Mechanical Wave A mechanical wave is a disturbance which propagates through a medium with little or no net displacement

### Waves 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

### Chapter 11. Waves & Sound

Chapter 11 Waves & Sound 11.2 Periodic Waves In the drawing, one cycle is shaded in color. The amplitude A is the maximum excursion of a particle of the medium from the particles undisturbed position.

### General Physics (PHY 2130)

General Physics (PHY 2130) Lecture 28 Waves standing waves Sound definitions standing sound waves and instruments Doppler s effect http://www.physics.wayne.edu/~apetrov/phy2130/ Lightning Review Last lecture:

### Lecture PowerPoints. Chapter 12 Physics: Principles with Applications, 6 th edition Giancoli

Lecture PowerPoints Chapter 12 Physics: Principles with Applications, 6 th edition Giancoli 2005 Pearson Prentice Hall This work is protected by United States copyright laws and is provided solely for

### And although two objects like these bumper boats cannot be in the same place on the water at the same time, water waves can. Why is that?

Physics 1103 Wave Interactions (picture of beach on screen) Today, we go back to the beach to investigate more wave interactions. For example, what makes these waves change direction as they approach the

### S15--AP Phys Q3 SHO-Sound PRACTICE

Name: Class: Date: ID: A S5--AP Phys Q3 SHO-Sound PRACTICE Multiple Choice Identify the choice that best completes the statement or answers the question.. If you are on a train, how will the pitch of the

### Waves. Wave: A traveling disturbance consisting of coordinated vibrations that transmit energy with no net movement of the matter.

Waves Wave: A traveling disturbance consisting of coordinated vibrations that transmit energy with no net movement of the matter. Source: some kind of disturbance from the state of equilibrium. Propagation:

### 1. Examples: Wave motion is generating, when disturbance is generating in a wave source and the disturbance is propagating in time and in space.

Wave motion 1. Examples: Wave motion can be observed when a water surface is disturbed. In this case waves move outwards across the water surface from the point of disturbance. Wave motion along the string.

### Vibrations on a String and Resonance

Vibrations on a String and Resonance Umer Hassan and Muhammad Sabieh Anwar LUMS School of Science and Engineering March 5, 2015 Version 2015-1 How does our radio tune into different channels? Can a music

### Transverse and Longitudinal waves (6.2)

Waves Homework from the book: Exercises: 1, 2, 3, 5-10, 12-16, 20, 25, 33, 34, 36. Questions:3, 9, 14 Problems 2, 11, 17 In the study guide: All the Multiple choice & True False a starting on page 69.

### Standing Waves in Strings

Standing Waves in Strings APPARATUS 1. Buzzer (vibrating at a given frequency) mounted on a board with a pulley 2. Electronic balance 3. 2 Strings, one light and one heavy 4. Set of known masses (slotted

### Resonance. Wave. Wave. There are three types of waves: Tacoma Narrows Bridge Torsional Oscillation. Mechanical Waves 11/2/2009

Resonance Wave Transfers Energy Without Transferring Matter Clip from Mechanical Universe Wave A wave can be described as a disturbance that travels through a medium from one location to another location.

### 2. The graph shows how the displacement varies with time for an object undergoing simple harmonic motion.

Practice Test: 29 marks (37 minutes) Additional Problem: 31 marks (45 minutes) 1. A transverse wave travels from left to right. The diagram on the right shows how, at a particular instant of time, the

### Essential Knowledge 5.G.1: The possible nuclear reactions are constrained by the law of conservation of nucleon number.

Curriculum Framework Essential Knowledge 5.F.1: The continuity equation describes conservation of mass flow rate in fluids. Examples should include volume rate of flow and mass flow rate. Learning Objective

### Physics 53. Wave Motion 2. If at first you don't succeed, try, try again. Then quit. No use being a damn fool about it.

Physics 53 Wave Motion 2 If at first you don't succeed, try, try again. Then quit. No use being a damn fool about it. W.C. Fields Waves in two or three dimensions Our description so far has been confined

### Waves and Sound. AP Physics B

Waves and Sound AP Physics B What is a wave A WAVE is a vibration or disturbance in space. A MEDIUM is the substance that all SOUND WAVES travel through and need to have in order to move. Two types of

### Periodic Wave Phenomena

Name: Periodic Wave Phenomena 1. The diagram shows radar waves being emitted from a stationary police car and reflected by a moving car back to the police car. The difference in apparent frequency between

### Principles of Technology CH 12 Wave and Sound 3

Principles of Technology CH 12 Wave and Sound 3 Name KEY OBJECTIVES At the conclusion of this chapter you will be able to: Define the terms constructive interference, destructive interference, resonance,

### Physics 1120: Waves Solutions

Questions: 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 Physics 1120: Waves Solutions 1. A wire of length 4.35 m and mass 137 g is under a tension of 125 N. What is the speed of a wave in this wire? If the tension

### Waves 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 hecklist 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

### Academic Resource Center: Waves Workshop

Academic Resource Center: Waves Workshop Presentation Outline Understanding concepts Types of waves Transverse Waves Longitudinal Waves Interference Constructive v. Destructive Beating Practice problems

### MAKE SURE TA & TI STAMPS EVERY PAGE BEFORE YOU START

Laboratory Section: Last Revised on September 21, 2016 Partners Names: Grade: EXPERIMENT 11 Velocity of Waves 0. Pre-Laboratory Work [2 pts] 1.) What is the longest wavelength at which a sound wave will

### v = λ f this is the Golden Rule for waves transverse & longitudinal waves Harmonic waves The golden rule for waves Example: wave on a string Review

L 23 Vibrations and Waves [3] resonance clocks pendulum springs harmonic motion mechanical waves sound waves golden rule for waves musical instruments The Doppler effect Doppler radar radar guns Review

### Sections Covered in the Text: Selections from Chapter 20, except Figure Examples of a transverse wave (pulse) on a string.

Traveling Waves Sections Covered in the Text: Selections from Chapter 20, except 20.7 Whole courses in physics are devoted to the study of waves (PHYB20H3S, to name one). Waves occur throughout nature

### Final - Physics 1240 Spring, 2010 version 1. Intensity ratio 1 db db db db db db db db db 7.

Final - Physics 1240 Spring, 2010 version 1 0001-1 SIL difference (in decibels) Intensity ratio 1 db 1.3 2 db 1.6 3 db 2.0 4 db 2.5 5 db 3.2 6 db 4.0 7 db 5.0 8 db 6.3 9 db 7.9 Bubble in questions 1-40

### Waves. In short: 1. A disturbance or variation which travels through a medium 2. Must transfer energy from one location to another.

Waves What is a wave? A disturbance or variation that transfers energy progressively from point to point in a medium and that may take the form of an elastic deformation or of a variation of pressure,

### light and sound, our bodies are not capable of sensing radio waves directly.

Background A wave is a disturbance that carries energy, a disturbance that transports energy from one place to another without the transfer of matter. After a wave passes through a medium, there are no

### Superposition and Standing Waves. Solutions of Selected Problems

Chapter 18 Superposition and Standing Waves. s of Selected Problems 18.1 Problem 18.8 (In the text book) Two loudspeakers are placed on a wall 2.00 m apart. A listener stands 3.00 m from the wall directly

### Interference. Physics 102 Workshop #3. General Instructions

Interference Physics 102 Workshop #3 Name: Lab Partner(s): Instructor: Time of Workshop: General Instructions Workshop exercises are to be carried out in groups of three. One report per group is due by

### Waves Physics Leaving Cert Quick Notes

Waves Physics Leaving Cert Quick Notes Waves A wave is a means of transferring energy from one point to another Waves can be classified as mechanical where the wave must have a medium to travel through,

### PS-7.2 Compare the nature and properties of transverse and longitudinal/compressional mechanical waves.

PS-7.1 Illustrate ways that the energy of waves is transferred by interaction with matter (including transverse and longitudinal /compressional waves). Understand that a wave is a repeating disturbance

### 4.4 WAVE CHARACTERISTICS 4.5 WAVE PROPERTIES HW/Study Packet

4.4 WAVE CHARACTERISTICS 4.5 WAVE PROPERTIES HW/Study Packet Required: READ Hamper pp 115-134 SL/HL Supplemental: Cutnell and Johnson, pp 473-477, 507-513 Tsokos, pp 216-242 REMEMBER TO. Work through all

### Physics 9e/Cutnell. correlated to the. College Board AP Physics 1 Course Objectives

Physics 9e/Cutnell correlated to the College Board AP Physics 1 Course Objectives Big Idea 1: Objects and systems have properties such as mass and charge. Systems may have internal structure. Enduring

### The Big Idea. Key Concepts

The Big Idea Objects in motion that return to the same position after a fixed period of time are said to be in harmonic motion. Objects in harmonic motion have the ability to transfer some of their energy

### Center of Mass/Momentum

Center of Mass/Momentum 1. 2. An L-shaped piece, represented by the shaded area on the figure, is cut from a metal plate of uniform thickness. The point that corresponds to the center of mass of the L-shaped

### Vibrations on a String and Resonance

Vibrations on a String and Resonance Umer Hassan and Muhammad Sabieh Anwar LUMS School of Science and Engineering September 7, 2010 How does our radio tune into different channels? Can a music maestro

### Chapter 30 Reflection and Refraction

Chapter 30 Reflection and Refraction Slide 30-1 Geometrical optics When light or other electromagnetic waves interact with systems much larger than the wavelength, it s a good approximation to Neglect

### Mathematical Physics

Mathematical Physics MP205 Vibrations and Waves Lecturer: Office: Lecture 19 Dr. Jiří Vala Room 1.9, Mathema

### Physics 2101 Section 3 Apr 14th Announcements: Quiz Friday Midterm #4, April Midterm #4,

Physics 2101 Section 3 Apr 14 th Announcements: Quiz Friday Midterm #4, April 28 th Final: May 11 th-7:30am Class Website: 6 pm Make up Final: May 15 th -7:30am http://www.phys.lsu.edu/classes/spring2010/phys2101

### Interference of Waves

Patterns and Predictions Activity 4 Interference of Waves GOALS In this activity you will: Generate waves to explore interference. Identify the characteristics of standing waves. Generate and identify

### CHAPTER 9 SOUND WAVES. - As a tuning fork vibrates a series of condensations and rarefactions moves

CHAPTER 9 SOUND WAVES 9.1 Producing a sound waes - As a tuning fork ibrates a series of condensations and rarefactions moes away outward, away from the fork. - Sound is a wae that propagate in solids,