College Physics Chapter 12 Lecture PDF

College Physics Chapter 12 Lecture Eleventh Edition Mechanical Waves and Sound 1) Mechanical Waves 2) Periodic Mechanical Waves 3) Wave Speeds 4) Mathematical Description of a Wave 5) Re...

College Physics Chapter 12 Lecture Eleventh Edition Mechanical Waves and Sound 1) Mechanical Waves 2) Periodic Mechanical Waves 3) Wave Speeds 4) Mathematical Description of a Wave 5) Reflections & Superposition 6) Standing Waves & Normal Modes 7) Longitudinal Standing Waves 8) Interference 9) Sound & Hearing 10) Sound Intensity 11) Beats 12) Doppler Effects Copyright © 2020, 2016, 2012 Pearson Education, Inc. All Rights Reserved Goals for Chapter 12 To describe mechanical waves. To study superposition, standing waves and sound. To present sound as a standing longitudinal wave. To see that waves will interfere (add constructively and destructively). To study sound intensity and beats. To solve for frequency shifts (the Doppler effect). To examine applications of acoustics and musical tones. Copyright © 2020, 2016, 2012 Pearson Education, Inc. All Rights Reserved 12.1 The Mechanical Wave Copyright © 2020, 2016, 2012 Pearson Education, Inc. All Rights Reserved  The Wave Model The wave model describes the basic properties of waves and emphasizes those aspects of wave behavior common to all waves. A traveling wave is an organized disturbance that travels with a well-defined wave speed. Copyright © 2020, 2016, 2012 Pearson Education, Inc. All Rights Reserved Mechanical Waves (1 of 2) Mechanical waves are waves that involve the motion of the substance through which they move. The substance is the medium. A disturbance is a wave that passes through a medium, displacing the atoms that make up the medium from their equilibrium position. Copyright © 2020, 2016, 2012 Pearson Education, Inc. All Rights Reserved Mechanical Waves (2 of 2) A wave disturbance is created by a source. Once created, the disturbance travels outward through the medium at the wave speed v. A wave does transfer energy, but the medium as a whole does not travel. A wave transfers energy, but it does not transfer any material or substance outward from the source. Copyright © 2020, 2016, 2012 Pearson Education, Inc. All Rights Reserved  Traveling Wave Due to Earthquake Wave speed = 940 Km/sec Wave height = 15 – 9.6 m In 1960, a magnitude of 9.5 scale In 1964, a magnitude of 9.2 scale earthquake occurred off the seabed earthquake occurred off the seabed in south-west Chile in Alaska. Copyright © 2020, 2016, 2012 Pearson Education, Inc. All Rights Reserved  EM Waves & Matter Waves EM Waves are waves of an electromagnetic field. They include visible light, radio waves, microwaves, and x rays. EM Waves require no material medium and can travel through a vacuum. Matter Waves describe the wave-like characteristics of material particles such as electrons and atoms at an atomic scale. Copyright © 2020, 2016, 2012 Pearson Education, Inc. All Rights Reserved Transverse & Longitudinal Waves (1/4) Most waves fall into two general classes: 1) Transverse waves and 2) Longitudinal waves. Transverse wave is a wave in which the particles in the medium move perpendicular to the direction in which the wave travels. Shaking the end of a stretched string up and down creates a wave that travels along the string in a horizontal direction while the particles that make up the string oscillate vertically. Copyright © 2020, 2016, 2012 Pearson Education, Inc. All Rights Reserved Transverse & Longitudinal Waves (2/4) Longitudinal wave: Particles in the medium move parallel to the direction in which the wave travels. Quickly moving the end of a spring back and forth sends a wave—in the form of a compressed region—down the spring. The particles that make up the spring oscillate horizontally as the wave passes. Copyright © 2020, 2016, 2012 Pearson Education, Inc. All Rights Reserved Transverse & Longitudinal Waves (3/4) The two most important types of earthquake waves are: 1) S waves (transverse) and 2) P waves (longitudinal). Copyright © 2020, 2016, 2012 Pearson Education, Inc. All Rights Reserved Transverse & Longitudinal Waves (4/4) The P waves are faster, but the S waves are more destructive. Copyright © 2020, 2016, 2012 Pearson Education, Inc. All Rights Reserved 12.2 Traveling Waves Copyright © 2020, 2016, 2012 Pearson Education, Inc. All Rights Reserved Traveling Waves When you drop a pebble in a pond, waves travel outward. How does a mechanical wave travel through a medium? To answer we must be careful to distinguish: – Motion of the wave – Motion of the medium A wave is not a particle, so we cannot use Newton’s laws on the wave itself. The medium is made of particles, so we can use Newton’s laws to examine how the medium responds to a disturbance. Copyright © 2020, 2016, 2012 Pearson Education, Inc. All Rights Reserved  Waves on a String (1 of 2) A transverse wave pulse traveling along a stretched string is shown below. The curvature of the string due to the wave leads to a net force that pulls a small segment of the string upward or downward. Copyright © 2020, 2016, 2012 Pearson Education, Inc. All Rights Reserved Waves on a String (2 of 2) Each point on the string moves perpendicular to the motion of the wave, so a wave on a string is a transverse wave. An external force created the pulse, but once started, the pulse continues to move because of the internal dynamics of the medium. Copyright © 2020, 2016, 2012 Pearson Education, Inc. All Rights Reserved  Types of Mechanical Waves – Figure 12.2 Transverse: the wave disturbance is perpendicular to the direction of propagation. Longitudinal: the wave disturbance is parallel to the direction of propagation. Water waves – a complex mixture of both. Copyright © 2020, 2016, 2012 Pearson Education, Inc. All Rights Reserved  Generating a Longitudinal Wave An object undergoing SHM can cause the disturbance and the medium can be a string, cord, or rope under tension. Copyright © 2020, 2016, 2012 Pearson Education, Inc. All Rights Reserved QuickCheck 1 A wave on a string is traveling to the right. At this instant, the motion of the piece of string marked with a dot is A. Up. B. Down. C. Right. D. Left. E. Zero, instantaneously at rest. Copyright © 2020, 2016, 2012 Pearson Education, Inc. All Rights Reserved QuickCheck 2 These two wave pulses travel along the same stretched string, one after the other. Which is true? A. vA > vB B. vB > vA C. vA = vB Wave speed depends on the properties D. Not enough of the medium, not on the amplitude of information the wave. to tell Copyright © 2020, 2016, 2012 Pearson Education, Inc. All Rights Reserved  Sound Waves When a loudspeaker cone moves forward, it compresses the air in front of it. The compression is the disturbance that travels through the air. A sound wave is a longitudinal wave. The motion of the sound wave is determined by the properties of the air. Copyright © 2020, 2016, 2012 Pearson Education, Inc. All Rights Reserved 12.3 Wave Speed Copyright © 2020, 2016, 2012 Pearson Education, Inc. All Rights Reserved Wave Speed Is a Property of the Medium (1 of 6) The wave speed does not depend on the size and shape of the pulse, how the pulse was generated or how far it has traveled—only the medium that carries the wave. Strings – properties that determine speed are string’s mass, length, and tension. The speed depends on the mass-to-length ratio, the linear density of the string: m = L Linear density characterizes the type of string we are using. Copyright © 2020, 2016, 2012 Pearson Education, Inc. All Rights Reserved Wave Speed Is a Property of the Medium (2 of 6) A string with a greater tension responds more rapidly, so the wave will move at a higher speed. Wave speed increases with increasing tension. A string with a greater linear density has more inertia. It will respond less rapidly, so the wave will move at a lower speed. Wave speed decreases with increasing linear density. Analysis of wave speed shows both of these trends: Copyright © 2020, 2016, 2012 Pearson Education, Inc. All Rights Reserved  Wave Speed Is a Property of the Medium (3 of 6) Sound speed is slightly less than the rms speed of the molecules of the gas medium, though it does have the same dependence on temperature and molecular mass: M is the molar mass,  is a constant that depends on the gas, kB is Boltzmann’s constant, and T is the absolute temperature in kelvin. Copyright © 2020, 2016, 2012 Pearson Education, Inc. All Rights Reserved Wave Speed Is a Property of the Medium (4 of 6) The speed of sound in air (and other gases) increases with temperature. For calculations in this chapter, you can use the speed of sound in air at 20°C, 343 m/s, unless otherwise specified. At a given temperature, the speed of sound increases as the molecular mass of the gas decreases. Thus the speed of sound in room-temperature helium is faster than that in room- temperature air. The speed of sound doesn’t depend on the pressure or the density of the gas. The speed of sound in liquids is faster than in gases, and faster in solids than in liquids. Copyright © 2020, 2016, 2012 Pearson Education, Inc. All Rights Reserved Wave Speed Is a Property of the Medium (5 of 6) Table 1 The speed of sound Medium Speed (m/s) Air (0°C) 331 Air (20°C) 343 Helium (0°C) 970 Ethyl alcohol 1170 Water 1480 Human tissue (ultrasound) 1540 Lead 1200 Aluminum 5100 Granite 6000 Diamond 12,000 Copyright © 2020, 2016, 2012 Pearson Education, Inc. All Rights Reserved Wave Speed Is a Property of the Medium (6 of 6) Electromagnetic waves, such as light, travel at much higher speeds than mechanical waves. The speed of light c is the speed that all electromagnetic waves travel in a vacuum. The value of the speed of light is v light = c = 3.00  10 m/s 8 Although light travels more slowly in air than in a vacuum, this value is still a good approximation for the speed of electromagnetic waves through air. At this speed, light could circle the earth 7.5 times in 1 s Copyright © 2020, 2016, 2012 Pearson Education, Inc. All Rights Reserved QuickCheck 3 For a wave pulse on a string to travel twice as fast, the string tension must be A. Increased by a factor of 4. B. Increased by a factor of 2. C. Decreased to one half its initial value. D. Decreased to one fourth its initial value. E. Not possible. The pulse speed is always the same. Copyright © 2020, 2016, 2012 Pearson Education, Inc. All Rights Reserved Example 12.1 When Does the Spider Sense His Lunch? BIO (1/2) All spiders are very sensitive to vibrations. An orb spider will sit at the center of its large, circular web and monitor radial threads for vibrations created when an insect lands. Assume that these threads are made of silk with a linear density of 1.0  10 −5 kg / m under a tension of 0.40 N, both typical numbers. If an insect lands in the web 30 cm from the spider, how long will it take for the spider to find out? STRATEGIZE When the insect hits the web, a wave pulse will be transmitted along the silk fibers. The speed of the wave depends on the properties of the silk. Copyright © 2020, 2016, 2012 Pearson Education, Inc. All Rights Reserved Example 12.1 When Does the Spider Sense His Lunch? BIO (2/2) PREPARE The speed of a wave on a string is given by Equation. SOLVE First, we determine the speed of the wave: Ts 0.40 N v= = = 200 m / s  −5 1.0  10 kg / m The time for the wave to travel a distance d = 30 cm to reach the spider is: d 0.30 m t = = = 1.5 ms v 200 m/s Copyright © 2020, 2016, 2012 Pearson Education, Inc. All Rights Reserved QuickCheck 4 A wave bounces back and forth on a guitar string; this is responsible for making the sound of the guitar. As the temperature of the string rises, the tension decreases. This Fill in the blank the speed of the wave on the string. A. Increases B. Does not change C. Decreases Copyright © 2020, 2016, 2012 Pearson Education, Inc. All Rights Reserved Example 12.3 How Far Away Was the Lightning? During a thunderstorm, you see a flash from a lightning strike. 8.0 seconds later, you hear the crack of the thunder. How far away did the lightning strike? d = v t = (343 m / s)(8.0 s) = 2.7  103 m = 2.7 km Copyright © 2020, 2016, 2012 Pearson Education, Inc. All Rights Reserved Wave Speed Is a Property of the Medium The wave speed of the strings: The wave speed of the sound: Speed of light c is the speed that all EM waves travel in a vacuum. Copyright © 2020, 2016, 2012 Pearson Education, Inc. All Rights Reserved 12.4 Graphical and Mathematical Descriptions of Waves Copyright © 2020, 2016, 2012 Pearson Education, Inc. All Rights Reserved Snapshot and History Graphs (1 of 4) A snapshot graph shows a wave’s displacement as a function of position at a single instant of time. Copyright © 2020, 2016, 2012 Pearson Education, Inc. All Rights Reserved Snapshot and History Graphs (1 of 4) Each snapshot shows a wave’s displacement as a function of x at an instant time. Copyright © 2020, 2016, 2012 Pearson Education, Inc. All Rights Reserved Mathematical Description of Sinusoidal Waves (1 of 7) A sinusoidal wave is the type of wave produced by a source that oscillates with simple harmonic motion (SH M). The amplitude A is the maximum value of displacement. The crests have displacement of A and the troughs have a displacement of −A. Copyright © 2020, 2016, 2012 Pearson Education, Inc. All Rights Reserved Mathematical Description of Sinusoidal Waves (2 of 7) The wave, like SHM, is repetitive. The wavelength  is the distance spanned in one cycle of the motion. At time t, the displacement as a function of distance is:  x y ( x ) = A cos  2    Copyright © 2020, 2016, 2012 Pearson Education, Inc. All Rights Reserved Mathematical Description of Sinusoidal Waves (3 of 7) A history graph of the motion of one point of the medium as a function of time is also sinusoidal. The graph looks the same but the meaning is different. Each point in the medium oscillates with simple harmonic motion as the wave passes. Copyright © 2020, 2016, 2012 Pearson Education, Inc. All Rights Reserved Mathematical Description of Sinusoidal Waves (4 of 7) The period T of the wave is the time interval to complete one cycle of motion. The wave frequency is related to the period T = 1/ f , exactly the same as in SHM. Therefore the motion of the point is  t  y (t ) = A cos  2   T Copyright © 2020, 2016, 2012 Pearson Education, Inc. All Rights Reserved Mathematical Description of Sinusoidal Waves (5 of 7) We combine the mathematical expressions for the displacement as a function of position at one time and the displacement as a function of time at one position: Copyright © 2020, 2016, 2012 Pearson Education, Inc. All Rights Reserved  Mathematical Description of Sinusoidal Waves (6 of 7) The notation y(x, t) indicates that the displacement of y is a function of two variables, x and t. In the figure, we have graphed the equation at five instants in time. As the time t increases, so does the position x of this point. One full period has elapsed and the wave has moved one full wavelength. Copyright © 2020, 2016, 2012 Pearson Education, Inc. All Rights Reserved  Mathematical Description of Sinusoidal Waves (7 of 7) For a wave travelling to the left, the equation is: Note that a wave moving to the right (the +x direction) has a − in the expression, while a wave moving to the left (the −x direction) has a + in the expression. Copyright © 2020, 2016, 2012 Pearson Education, Inc. All Rights Reserved QuickCheck 9 The period of this wave is A. 1 s B. 2 s C. 4 s D. Not enough information to tell Copyright © 2020, 2016, 2012 Pearson Education, Inc. All Rights Reserved QuickCheck 10 For this sinusoidal wave, what is the amplitude? A. 0.5 m B. 1 m C. 2 m D. 4 m Copyright © 2020, 2016, 2012 Pearson Education, Inc. All Rights Reserved QuickCheck 11 For this sinusoidal wave, what is the wavelength? A. 0.5 m B. 1 m C. 2 m D. 4 m Copyright © 2020, 2016, 2012 Pearson Education, Inc. All Rights Reserved Fundamental Relationship for Sinusoidal Waves During a time-interval of exactly one period T, each crest of a sinusoidal wave travels forward a distance of exactly one wavelength   distance  v= = time T In terms of frequency, the velocity of the wave is Copyright © 2020, 2016, 2012 Pearson Education, Inc. All Rights Reserved QuickCheck 12 For this sinusoidal wave, what is the frequency? A. 50 Hz B. 100 Hz C. 200 Hz D. 400 Hz Copyright © 2020, 2016, 2012 Pearson Education, Inc. All Rights Reserved QuickCheck 13 A speaker emits a 400-Hz tone. The air temperature increases. This Fill in the blank the wavelength of the sound. A. Increases B. Does not change C. Decreases Copyright © 2020, 2016, 2012 Pearson Education, Inc. All Rights Reserved QuickCheck 14 A snapshot and a history graph for a sinusoidal wave on a string appear as follows: What is the speed of the wave? A. 1.5 m/s B. 3.0 m/s C. 5.0 m/s D. 15 m/s Copyright © 2020, 2016, 2012 Pearson Education, Inc. All Rights Reserved QuickCheck 15 Which has a longer wavelength? A. A 400-Hz sound wave in air B. A 400-Hz sound wave in water Copyright © 2020, 2016, 2012 Pearson Education, Inc. All Rights Reserved Synthesis 1 Wave Motion (1 of 2) Wave speed is determined by the medium. Copyright © 2020, 2016, 2012 Pearson Education, Inc. All Rights Reserved Synthesis 1 Wave Motion (2 of 2) A sinusoidal wave moves one wavelength in one period, giving the fundamental relationship As a sinusoidal wave travels, each point in the medium moves with simple harmonic motion. Copyright © 2020, 2016, 2012 Pearson Education, Inc. All Rights Reserved “Time Lapse” Snapshot of a Traveling Wave If you follow the original set of markers (3 red dots at top of the figure), you can see the movement as time passes going down from top to bottom. Each fresh sketch as you go downward elapses 1/8 of the period. Recall that 8/8T (all the way from top to bottom) is one period, the time for one complete oscillation to pass. Copyright © 2020, 2016, 2012 Pearson Education, Inc. All Rights Reserved λf = vwave – Example 12.1 We know that for any wave, the wavelength (in meters) times the frequency (in 1/s or H z) will multiply to give the econd ert velocity of the wave (in m /s ).etre econds Sound in air, sound in water, sound in metal, light … this relationship will guide us. Refer to the worked example for sound in air at 20°C. elsius Copyright © 2020, 2016, 2012 Pearson Education, Inc. All Rights Reserved Longitudinal and Transverse Waves Figures 12.5 and 12.6 help us to see the sinusoidal waveform. Copyright © 2020, 2016, 2012 Pearson Education, Inc. All Rights Reserved Waves on a Long Rope Under Tension – Example 12.2 Refer to Figure 12.7. The velocity of the wave will depend on the type and size of rope as well as the tension we add with our geological sample. Follow the example on pages 358 and 359. Copyright © 2020, 2016, 2012 Pearson Education, Inc. All Rights Reserved We Can Solve Equation 12.5 as Needed – Figure 12.9 Follow the explanation on pages 360 and 361. We can express the wave in terms of trigonometric functions and observable data. Copyright © 2020, 2016, 2012 Pearson Education, Inc. All Rights Reserved 12.5 Reflections & Superposition Skip beyond! Copyright © 2020, 2016, 2012 Pearson Education, Inc. All Rights Reserved Waves Can Reflect – Figure 12.11 Copyright © 2020, 2016, 2012 Pearson Education, Inc. All Rights Reserved Waves Can Superimpose – Figure 12.12 Two waves come in from opposite directions. Each wave has amplitude inverted with respect to the other. During the superposition, there is nearly cancellation. After the collision, the outgoing waves resemble those that came in, with the sign of the amplitude inverted. The details are a complex function of time. Copyright © 2020, 2016, 2012 Pearson Education, Inc. All Rights Reserved Waves Become Coherent (Standing) When nodes and antinodes align, there is no destructive interference and a steady-state condition is established. Depending on the shape and size of the medium transmitting the wave, different standing wave patterns are established as a function of energy. Copyright © 2020, 2016, 2012 Pearson Education, Inc. All Rights Reserved Normal Modes for a Linear Resonator The resonator is fixed at both ends. Wave energy increases as you go down the y-axis below. Copyright © 2020, 2016, 2012 Pearson Education, Inc. All Rights Reserved  Fundamental Frequencies – Figure 12.17 The fundamental frequency depends on the properties of the resonant medium. If the resonator is a string, cord, or wire, the standing wave pattern is a function of tension, linear mass density, and length. Copyright © 2020, 2016, 2012 Pearson Education, Inc. All Rights Reserved Standing Waves on a String – Example 12.3 Refer to the worked example at the bottom of page 367. The bass viol follows the same logic as Quantitative Analysis 12.4. Copyright © 2020, 2016, 2012 Pearson Education, Inc. All Rights Reserved Longitudinal Standing Waves – Figure 12.20 May be experimentally demonstrated using a Kundt’s tube. A resonator closed at both ends must trap a wave with nodes at both ends (analogous to the transverse waves on a string). Copyright © 2020, 2016, 2012 Pearson Education, Inc. All Rights Reserved Speed of Sound in Hydrogen – Example 12.4 Refer to Example 12.4 on page 369. Copyright © 2020, 2016, 2012 Pearson Education, Inc. All Rights Reserved A New Resonator, the Organ Pipe – Figure 12.23 With a chamber closed at one end, the resonant waves must have nodes at the closed end and antinodes at the open end. Copyright © 2020, 2016, 2012 Pearson Education, Inc. All Rights Reserved A Resonator Open at Both Ends – Figure 12.25 This situation could arise from a pipe, a flute, or other such instruments in the orchestra. Since the resonant chamber is open at both ends, the waves therein must have antinodes at both ends. Refer to the worked examples on page 371. Copyright © 2020, 2016, 2012 Pearson Education, Inc. All Rights Reserved  Human Hearing – Figure 12.29 Refer to pages 373–377. 20–20,0000 H z is the approximate range of human ert hearing. Below that is infrasonic and above …. ultrasonic. Note, there are slight variations between animal species and effects on any hearing due to pressure changes. Copyright © 2020, 2016, 2012 Pearson Education, Inc. All Rights Reserved  Sound Intensity and the Decibel Scale – Figure 12.30 Use Table 12.2 to see logarithmic dB examples of common sounds. Refer to Examples 12.8 and 12.9 (see figure below). Copyright © 2020, 2016, 2012 Pearson Education, Inc. All Rights Reserved  Beats and the Beat Frequency – Figure 12.31 Two slightly different tuning forks will ring more loudly at the difference of the frequencies. Copyright © 2020, 2016, 2012 Pearson Education, Inc. All Rights Reserved The Doppler Effect – Figure 12.32 Shifts in observed frequency can be caused by motion of the source, the listener, or both. Refer to Examples 12.10– 12.13. Copyright © 2020, 2016, 2012 Pearson Education, Inc. All Rights Reserved Copyright This work is protected by United States copyright laws and is provided solely for the use of instructors in teaching their courses and assessing student learning. Dissemination or sale of any part of this work (including on the World Wide Web) will destroy the integrity of the work and is not permitted. The work and materials from it should never be made available to students except by instructors using the accompanying text in their classes. All recipients of this work are expected to abide by these restrictions and to honor the intended pedagogical purposes and the needs of other instructors who rely on these materials. Copyright © 2020, 2016, 2012 Pearson Education, Inc. All Rights Reserved