TECH PREP. Chapter 14 Chapter Organizer. Contents Text Features Teaching Aids Student Masters 326A. 6 class sessions. Transparency 21: Wave

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1 Chapter 14 Chapter Organizer 6 class sessions Contents Text Features Teaching Aids Student Masters 14.1 Wave Properties, pp (2 class sessions) Design Your Own Physics Lab: Waves on a Coiled Spring, p. 330 Help Wanted: Geologist, p. 332 Physics & Society: Predicting Earthquakes, p. 334 Earth Science Connection: p. 335 Transparency 21: Wave Properties L1 ELL Lesson Plans: p. 32 Study Guide: pp Transparency 21 Master and Worksheet: pp ELL L1 Physics Lab and Pocket Lab Worksheets: pp L1 L1 Reteaching: p. 19 L1 Enrichment: pp L1 Laboratory Manual: pp L Wave Behavior, pp (3 class sessions) Pocket Lab: Wave Reflections, p. 337 Pocket Lab: Wave Interaction, p. 339 Pocket Lab: Bent Out of Shape, p. 340 Lesson Plans: p. 33 Graphing Calculators in the Science Classroom L1 Problems and Solutions Manual: Chapter 14 L1 Study Guide: pp L1 Physics Lab and Pocket Lab Worksheets: pp L1 Critical Thinking: p. 20 L1 Laboratory Manual: pp L1 Chapter Review, pp (1 class session) Summary Key Terms Reviewing Concepts Applying Concepts Problems Critical Thinking Problems Going Further Chapter Assessment: pp L1 Supplemental Problems: Chapter 14 L2 Spanish Resources: Chapter 14 ELL Texas Lesson Plans TestCheck Software MindJogger Videoquizzes ELL Reviewing Physics: Mastering the TEKS L1 TECH PREP The following Glencoe resources provide opportunities for integrating science and technology. Student Edition: Help Wanted, p. 332; Physics & Society, p. 334 Teacher Wraparound Edition: Tech Prep, p. 342 KEY TO TEACHING STRATEGIES The following designations will help you decide which activities are appropriate for your students. L1 Level 1 activities should be within the ability range of all students including those with learning difficulties. L2 Level 2 activities should be within the ability range of the average to above-average student. L3 Level 3 activities are designed for the ability range of above-average students. ELL ELL activities should be within the ability range of English Language Learners. COOP LEARN Cooperative Learning activities are designed for small group work. P These strategies represent student products that can be placed into a best-work portfolio. These strategies are useful in a block scheduling format. 326A

2 Waves and Energy Transfer Objectives 14.1 Wave Properties 1. Identify how waves transfer energy without transferring matter. 2. Contrast transverse and longitudinal waves. 3. Relate wave speed, wavelength, and frequency Wave Behavior 4. Relate a wave s speed to the medium in which the wave travels. 5. Describe how waves are reflected and refracted at boundaries between media, and explain how waves diffract. 6. Apply the principle of superposition to the phenomenon of interference. National Science Content Standards UCP.1, UCP.2, UCP.3, A.1, A.2, B.6, E.1, F.5, F.6 UCP.2, A.1, A.2, B.6 State/Local Standards 1(A), 1(B), 2(A), 2(B), 2(D), 2(F), 3(B), 3(C), 3(D), 8(A), 8(B) 1(A), 2(A), 2(D), 3(B), 8(A), 8(B) Physics Lab Page 330 coiled spring toy meterstick stopwatch Activity and Demonstration Materials Pocket Lab Page 337 projection wave tank stopwatch Page 339 coiled spring toy Page 340 projection wave tank Demonstrations 14 1, Page 332 spring, long coiled 14 2, Page 338 coiled spring string (1 m) 14 3, Page 340 dowel rod projection wave tank straight boundary The following multimedia resources are available from Glencoe. Science and Technology Videodisc Series (STVS) Physics Seismic Simulator Underwater Seismograph Eliminating Potholes Earth and Space Artificial Waves Mapping With a Rifle Physics for the Computer Age CD-ROM WAVES: Wave Motion INTRODUCTION: Physics for the Computer Age The Mechanical Universe Videotape Quad 4: From Kepler to Einstein Introduction to Waves MindJogger Videoquizzes Chapter B

3 CHAPTER 14 Waves and Energy Transfer Chapter Overview This chapter introduces students to the concept of wave motion and the properties of waves. These properties are illustrated by waves in coiled springs and ripple tanks. Key Terms antinode constructive interference continuous wave crest destructive interference diffraction frequency incident wave interference law of reflection longitudinal wave node principle of superposition refraction reflected wave standing wave surface wave transverse wave trough wave wavelength wave pulse Surf s Up From where does the surfer s kinetic energy come? Trace the energy source back as far as you can. Look at the text on page 329 for the answer. PHYSICS Be sure to check the Glencoe Science Web site for links to chapter material: science.glencoe.com 326 Learning Styles LS Look for the following logo for strategies that emphasize different learning modalities. LS Kinesthetic Physics Lab, p. 330; Pocket Lab, pp. 337, 339, 340; Quick Demo, p. 342; Meeting Individual Needs, p. 342 Visual-Spatial Demonstration, p. 333; Check for Understanding, p. 335; Uncovering Misconceptions, p. 340; Assessment, p. 341 Interpersonal Uncovering Misconceptions, p. 337; Tech Prep, p. 342; Reteaching, p. 343 Intrapersonal Meeting Individual Needs, p. 329 Linguistic Quick Demo, p. 328; Physics Journal, pp. 329, 338 Logical-Mathematical Quick Demo, p. 327

4 CHAPTER 14 Waves and Energy Transfer H ave you ever been in a wave pool and caught a wave with your body, experiencing a push from the wave? Perhaps you ve splashed about in the tub, creating a miniwave and letting the water lift your body upward. Or maybe you have had the exhilarating experience of riding a surfboard near the ocean shore. As the wave pushes you toward the shore, you gain speed and stay just ahead of the breaking surf. As you surf, you may try to ride almost parallel to the wave at a very high speed, as this surfer does. Surfing, however, can be dangerous. Unless you are skilled, the energy carried by the wave can cause you to wipe out, throwing you into the ocean or up onto the sand. In each case, your body s kinetic energy increases. The question is, where does this extra energy come from, and how does it get from one place to another? In the wave pool, you can see the waves move from one end of the pool to the other. Even in the tub, you can see the miniwave move from your head to your toes. At the ocean shore, surfing a wave allows you to come rapidly toward the shore. In each case, you may think the water is moving from one location to another. However, that is not what occurs. In water waves, the wave carries energy from one location to another, while the water itself moves in circles. In the coming chapters, you will study the wave motions of light and sound. You will find out how light waves and sound waves are similar and how they are different. WHAT YOU LL LEARN You will determine how waves transfer energy. You will describe wave reflection and discuss its practical significance. WHY IT S IMPORTANT Waves enable the sun s energy to reach Earth and make possible all communication through sound. Because light waves can be reflected, you are able to see the world around you and even read these very words. Knowledge of the behavior of waves is essential to the designing of bridges and many other structures. PHYSICS To find out more about waves and energy transfer, visit the Glencoe Science Web site at science.glencoe.com Introducing the Chapter USING THE PHOTO Of all sports, surfing uses waves and their properties most directly. Obviously, both timing and balance play a big part in successful surfing. Have students comment on how physics principles are demonstrated in surfing. Ask them to compare and contrast the characteristics of the surfing wave with the properties of a slinky wave. QUICK DEMO Hang a long coiled spring from your classroom ceiling. To do this, tie a string on about every fifth individual coil. Then extend the spring and attach the other end of each string to the ceiling. In order to keep the spring extended, use a string to tie each end to the nearest wall. You can continually demonstrate wave properties on this spring to help students learn the concepts in this chapter. For an opening activity, have students measure the length of the spring and the time it takes a wave pulse to travel down its length. Then have students use this information to calculate the speed of the pulse. L1 LS Assessment Options PORTFOLIO ASSESSMENT Portfolio Assessment, TWE, p. 332 Activity, TWE, p. 332 PERFORMANCE ASSESSMENT Physics Lab, SE, p. 330 Pocket Labs, SE, pp. 337, 339, 340 Performance Assessment, TWE, p. 341 Demonstration, TWE, p KNOWLEDGE ASSESSMENT Section Review, SE, pp. 335, 343 Chapter Review, SE, pp Practice Problems, SE, pp. 335, 337 Demonstration, TWE, pp. 339, 341 Physics Lab, TWE, p. 330 SKILL ASSESSMENT Quick Demos, TWE, pp. 327, 328, 331 STUDENT EDITION Physics Lab: p. 330 Pocket Labs: pp. 337, 339, 340 TEACHER EDITION Demonstrations: pp. 332, 338, 340 Quick Demos: pp. 327, 328, 331, 336, 342 Activities: p. 332 LABORATORY MANUAL Labs 14.1,

5 SECTION 14.1 PREPARE Content Refresher Explain to students that when your eye follows the amber waves of grain in a field of wheat you see something moving across a field. However, it stands to reason that wheat plants are not moving across the field. What the eye is following is a moving disturbance. Continually evaluate students understanding of this concept. All waves have the property of a moving disturbance, but the material of the medium itself can only move a small distance around its normal position. Remind students that a wave may be a pulse, a series of pulses, or a series of pulses at regular intervals, such as in a periodic wave. The properties of waves include speed of propagation through medium, reflection, refraction, transportation of information and energy, superposition, and diffraction. Bridging This chapter begins a study of waves and wave properties. Emphasize the connections between particles and waves to help students generalize concepts such as speed. 1 FOCUS QUICK DEMO LS Linguistic If you have hung a coiled spring as described in the Quick Demo on the preceding page, use the spring to show the difference between a longitudinal wave and a transverse wave by shaking the end of the spring parallel, and then perpendicular, to its length. Have students verbalize the similarities and differences they observe between the two types of waves. L1 OBJECTIVES Identify how waves transfer energy without transferring matter. Contrast transverse and longitudinal waves. Relate wave speed, wavelength, and frequency. FIGURE 14 1 A quick shake of a rope sends out wave pulses in both directions. 328 Waves and Energy Transfer Program Resources Study Guide, pp L1 Transparency 21 and Master Laboratory Manual, pp L1 Reteaching, p. 19 L1 Enrichment, pp L1 Physics Lab and Pocket Lab Worksheets, pp L Wave Properties L1 Both particles and waves carry energy, but there is an important difference in how they do this. Think of a ball as a particle. If you toss the ball to a friend, the ball moves from you to your friend and carries energy. However, if you and your friend hold the ends of a rope and you give your end a quick shake, the rope remains in your hand, and even though no matter is transferred, the rope still carries energy. The waves carry energy through matter. Mechanical Waves You have learned how Newton s laws of motion and conservation of energy principles govern the behavior of particles. These laws also govern the motion of waves. There are many kinds of waves. All kinds of waves transmit energy, including the waves you cannot see, such as the sound waves you create when you speak and the light waves that reflect from the leaves on the trees. Transverse waves A wave is a rhythmic disturbance that carries energy through matter or space. Water waves, sound waves, and the waves that travel down a rope or spring are types of mechanical waves. Mechanical waves require a medium. Water, air, ropes, or springs are the materials that carry the energy of mechanical waves. Other kinds of waves, including electromagnetic waves and matter waves, will be described in later chapters. Because many of these waves cannot be directly observed, mechanical waves can serve as models for their study. The two disturbances that go down the rope shown in Figure 14 1 are called wave pulses. A wave pulse is a single bump or disturbance that travels through a medium. If the person continues to move the rope up and down, a continuous wave is generated. Notice that the rope is disturbed in the vertical direction, but the pulse travels horizontally. This wave motion is called a transverse wave. A transverse wave is a wave that vibrates perpendicular to the direction of wave motion. Longitudinal and surface waves In a coiled spring such as a Slinky toy, you can create a wave pulse in a different way. If you squeeze together several turns of the coiled spring and then suddenly release them, pulses of closely spaced turns will move away in both directions, as in Figure In this case, the disturbance is in the same direction as, or parallel to, the direction of wave motion. Such a wave is called a longitudinal wave. Sound waves are longitudinal waves. Fluids such as liquids and gases usually transmit only longitudinal waves. Although waves deep in a lake or ocean are longitudinal, at the surface of the water, the particles move in a direction that is both parallel ELL THE MECHANICAL UNIVERSE HIGH SCHOOL ADAPTATION Videotape Quad 4: From Kepler to Einstein Introduction to Waves 328

6 FIGURE 14 2 The squeeze and release of a coiled spring toy sends out wave pulses in both directions. 2 TEACH Physics Journal LS Linguistic Have students write a paragraph comparing and contrasting transverse and longitudinal waves. L1 and perpendicular to the direction of wave motion, as shown in Figure These are surface waves, which have characteristics of both transverse and longitudinal waves. The energy of water waves usually comes from storms far away. The energy of the storms initially came from the heating of Earth by solar energy. This energy, in turn, was carried to Earth by transverse electromagnetic waves. Measuring a Wave There are many ways to describe or measure a wave. Some methods depend on how the wave is produced, whereas others depend on the medium through which the wave travels. Surf s Up Answers question from page 326. Reinforcement Ask students to decide whether sound waves are most likely longitudinal or transverse, based on the properties of molecules in the air and the fact that air readily transmits sound. Because air molecules cannot pull one another, but can only push, they cannot support a transverse wave; thus, sound is most likely a longitudinal wave. L1 a b Crest Trough Wave motion Learning Disabled Pulses, traveling waves, and standing waves can be observed in many everyday occurrences. For example, waves occur in oceans, lakes, rivers, pools, and water glasses. Standing waves appear on telephone or power wires blown by the wind. A longitudinal wave pulse can be seen when a long line of automobile traffic begins to move as a traffic light turns green. Have learning disabled students collect descriptions of wave Meeting Individual Needs FIGURE 14 3 Surface waves have properties of both longitudinal and transverse waves (a). The paths of the particles are circular (b) Wave Properties 329 phenomena and indicate, where appropriate, those wave parameters, such as frequency, wavelength, speed, or amplitude, that can be identified or measured. L1 ELL LS Videodisc STVS: Earth and Space Disc 3, Side 2 Artificial Waves (Ch. 13)!8JÇ" Underwater Seismograph (Ch. 12)!8@Å" STVS: Physics Disc 1, Side 1 Seismic Simulator (Ch. 6)!7hÑ" Texas TEKS Pages : 8(A) 329

7 Process Skills LS Comparing and contrasting, recognizing cause and effect, formulating models, observing, interpreting data Uncovering Misconceptions Some students may think that the wave must slow down as the amplitude decreases. However, the results will demonstrate that the speed is constant. Possible Hypotheses Student hypotheses may state that wave pulses can be created on a coiled spring, and their properties can be observed and measured. Wave speed is dependent upon frequency. Possible Procedures Students could create wave pulses, time the pulses with a stopwatch, and measure the distances with the meterstick. Teams of students could develop their own data tables. Teaching Suggestions Suggest that students could place strips of masking tape on the floor for them to make any marks necessary for taking distance measurements. Have students within each team rotate roles so that they each may observe and measure wave properties. Analyze and Conclude 1. The amplitude (height) of the pulse decreases as it moves along the coiled spring. 2. No, the pulse takes equal amounts of time to move back and forth along the coiled spring, so the speed is constant. 3. The pulses stay the same distance apart. The wavelength does not change. 4. Allowing less time between the pulses makes the wavelength smaller. 330 Waves on a Coiled Spring Problem How can you model the properties of transverse waves? Hypothesis A coiled spring toy can be used to model transverse waves and to investigate wave properties such as speed, frequency, amplitude, and wavelength. Possible Materials a long coiled spring toy stopwatch meterstick Plan the Experiment 1. Work in pairs or groups, and clear a path of about 6 meters for this activity. 2. One member of the team should grip the Slinky firmly with one hand. Another member of the team should stretch the spring to the length suggested by your teacher. Team members should take turns holding the end of the spring. CAUTION: Coiled springs easily get out of control. Do not allow them to get tangled or overstretched. 3. The second team member should then make a quick sideways snap of the wrist to produce transverse wave pulses. Other team members can assist in measuring, timing, and recording data. It is easier to see the motion from one end of the Slinky, rather than from the side. 4. Design experiments to answer the questions under Analyze and Conclude. 5. Check the Plan Make sure your teacher has approved your final plan before you proceed with your experiments. 330 Waves and Energy Transfer 5. The pulses on the coiled spring travel through each other. (This may not be obvious to students unless they make different sizes or types of pulses.) Apply 1. Waves of all frequencies and wavelengths travel at the same speed (in non-dispersive media). 2. Instead of moving the spring with a sideways snap, the spring would need to be quickly pulled or pushed along its length. 3. Results should be similar. Each movement represents a wave moving through matter, so the principles remain the same. Analyze and Conclude 1. Interpreting Data What happens to the amplitude of the transverse wave as it travels? 2. Recognizing Cause and Effect Does the transverse wave s speed depend upon its amplitude? 3. Observing and Interpreting If you put two quick transverse wave pulses into the spring and consider the wavelength to be the distance between the pulses, does the wavelength change as the pulses move? 4. Applying How can you decrease the wavelength of a transverse wave? 5. Interpreting As transverse wave pulses travel back and forth on the spring, do they bounce off each other or pass through each other? Apply 1. How do the speeds of high frequency (short wavelength) transverse waves compare with the speeds of low frequency (long wavelength) transverse waves? 2. Suppose you designed the experiment using longitudinal waves. How would the procedure for longitudinal waves be different from the procedure for transverse waves? 3. Would you expect the results of an experiment with longitudinal waves to be similar to the results of the transverse wave experiment? Explain why or why not. Assessment KNOWLEDGE To further assess students understanding of wave interference, ask the following question. 1. What do you predict will happen to the wave s speed when you stretch the spring coil longer? Try it and describe your results. The speed increases. The pulse takes almost the same time, but it travels a greater distance.

8 Speed and amplitude How fast does a wave move? The speed of the pulse shown in Figure 14 4 can be found in the same way in which you would determine the speed of a moving car. First, you measure the displacement of the wave peak, d; then you divide this by the time interval, t, to find the speed, as shown by v v d/ t. The speed of a continuous wave, can be found the same way. For most mechanical waves, both transverse and longitudinal, the speed depends only on the medium through which the waves move. How does the pulse generated by gently shaking a rope differ from the pulse produced by a violent shake? The difference is similar to the difference between a ripple in a pond and a tidal wave. They have different amplitudes. The amplitude of a wave is its maximum displacement from its position of rest, or equilibrium. Two similar waves having different amplitudes are shown in Figure A wave s amplitude depends on how the wave is generated, but not on its speed. More work has to be done to generate a wave with a larger amplitude. For example, strong winds produce larger water waves than those formed by gentle breezes. Waves with larger amplitudes transfer more energy. Thus, although a small wave might move sand on a beach a few centimeters, a giant wave can uproot and move a tree. For waves that move at the same speed, the rate at which energy is transferred is proportional to the square of the Wave A Crest Amplitude FIGURE 14 4 These two photographs were taken 0.20 s apart. During that time, the crest moved 0.80 m. The velocity of the wave is 4.0 m/s. Uncovering Misconceptions Ask pairs of students whether they think a wave pulse will move with a greater speed down a coiled spring if the pulse has a greater amplitude. Have students discuss and then write a justifying explanation for their answer. Then do the following Quick Demo. L1 QUICK DEMO CAUTION: Wear goggles. Time a small amplitude and then a large amplitude pulse down a long stretched coiled spring. Have students discuss the observation that if the time is the same, then the speed is the same. Equal distance in equal time implies equal speeds. Ask: How does this relate to sound and light waves of varying amplitudes? If the speed of sound depended on the amplitude (i.e. loudness) of waves, we would hear loud sounds in concert before we would hear the soft sounds, which is clearly not the case. The same argument holds for bright and dim lights. Displacement Trough Wave B λ Distance FIGURE 14 5 The amplitude of wave A is larger than that of wave B Wave Properties 331 CD-ROM Physics for the Computer Age WAVES: Wave Motion Cultural Diversity Hertha Marks Ayrton was a British physicist who lived from 1854 to She invented a tool needed by architects that could divide a line segment into as many equal parts as desired. She studied the action of waves on a beach, and was the first woman to read a paper to the British Royal Society. She was later awarded the Hughes Medal for her original research. Connections To Architecture SEISMIC UPGRADING More than houses were damaged from the Loma Prieta quake that hit the San Francisco Bay area in Most of the damaged houses had no seismic upgrading, which can significantly help a house withstand an earthquake. Have students use the Internet to find information about earthquakes and seismic upgrading, and to identify areas where earthquake risk is high. L1 ELL Texas TEKS Pages : 1(A), 1(B), 2(A), 2(B), 2(D), 2(F), 3(B), 8(A) Pages : 3(B), 3(D), 8(B) 331

9 Enrichment Have students report to the class the information gathered from research into waves reported in an article Rogue Waves by Joseph Brown, Discover, April L1 FIGURE 14 6 One end of a string, with a piece of tape at point P, is attached to a vibrating blade. Note the change in position of point P over time. a Vibrating blade P b P Activity LS Kinesthetic This is a good time for a student experiment with the ripple tank. Students should get an opportunity to work with small water waves. Make waves with a small piece of cork in a ripple tank to show that the medium does not move in the direction of wave travel for transverse waves. The cork just bobs up and down as in a fishing bob. Or you can carefully put a drop of food coloring in the tank, then make some waves showing that the drop doesn t spread out along the direction of wave travel. Have students examine changes in wavelength to higher and lower frequencies in a ripple tank. L1 ELL Discussion Ask students to apply what they have learned about waves by describing experiences they have had at the beach or a lake. L1 ELL Assessment PORTFOLIO Students should collect reports of experiments they did with coiled springs and create a listing of wave properties they have demonstrated. L1 P Applying Physics HELP WANTED GEOLOGIST Major oil company seeks geologist or geophysicist to work on a team for a major exploration effort aimed at discovering new and better oil sources. The ideal candidate has a master s degree, with a specialty in areas relating to our industry, and a drive to succeed. He or she will persist when the average person says It can t be done. He or she must be able to think big, communicate well, and have the stamina and desire to do field work around the world. For information contact: American Geological Institute 4220 King Street Alexandria, VA Waves and Energy Transfer c P amplitude. Thus, doubling the amplitude of a wave increases the amount of energy it transfers each second by a factor of four. Wavelength Rather than focusing on one point on a wave, imagine taking a snapshot of a wave, so that you can see the whole wave at one instant in time. Figure 14 5 shows the low points, or troughs, and the high points, or crests, of a wave. The shortest distance between points where the wave pattern repeats itself is called the wavelength. Crests are spaced by one wavelength. Each trough is also one wavelength from the next. The Greek letter lambda,, represents wavelength. Period and frequency Although wave speed and amplitude can describe both pulses and continuous waves, period (T) and frequency (f) apply only to continuous waves. You learned in Chapter 6 that the period of a simple harmonic oscillator, such as a pendulum, is the time it takes for the motion of the oscillator to repeat itself. Such an oscillator is usually the source, or cause, of a continuous wave. The period of a wave is equal to the period of the source. In Figure 14 6, the period, T, equals 0.04 s, which is the time it takes the source to return to the same point in its oscillation. The same time is taken by point P, a point on the rope, to return to its initial position. The frequency of a wave, f, is the number of complete oscillations it makes each second. Frequency is measured in hertz. One hertz (Hz) is one oscillation per second. The frequency (f) and period (T) of a wave are related by the following equation. Frequency of a Wave f 1 T Both the period and the frequency of a wave depend only on its source. They do not depend on the wave s speed or the medium. Although you can measure a wavelength directly, the wavelength depends on both the frequency of the oscillator and the speed of the d P RADIO WAVES FM radio stations broadcast at a higher frequency than AM radio stations. Ask: What is the speed of radio waves? Same value as for the speed of light Then ask students to determine the wavelength of a local FM and AM radio station. A typical AM frequency is between 550 and 1600 khz, whereas the FM frequency range is 88 to 108 MHz. DEMONSTRATION 14-1 PURPOSE To illustrate properties of longitudinal waves MATERIALS Long, coiled spring PROCEDURE 1. Hang a coiled spring from the ceiling. Alternatively you can use a hallway or other place where you have a smooth floor area of about two by five meters and room around the edges to stand. 2. Stretch out the coiled spring to four or five meters. Let a student hold the other end. 3. Send a longitudinal pulse down the spring by pinching together several coils of the spring and then releasing them. Ask: What kind of pulse is this? longitudinal 4. Have students determine the time it takes a longitudinal pulse to travel down the spring. Change the amplitude of the pulse and again have students determine the travel 332

10 wave. In the time interval of one period, a wave moves one wavelength. Therefore, the speed of a wave is the wavelength divided by the period, v /T. Because the frequency is more easily found than the period, this equation is more often written as Example Problem Speed of a Wave Speed of a Wave v f. A sound wave has a frequency of 262 Hz and a wavelength measured at 1.29 m. a. What is the speed of the wave? b. How long will it take the wave to travel the length of a football field, 91.4 m? c. What is the period of the wave? Sketch the Problem Draw a model of one wavelength. Diagram a velocity vector. Calculate Your Answer Known: Unknown: f 262 Hz v? 1.29 m t? d 91.4 m T? Strategy: a. Find the speed of sound from the frequency and wavelength. b. Find the time required from speed and distance. c. Find the period from the frequency. Calculations: v f (1.29 m)(262 Hz) 338 m/s v d t, so t d v 91.4 m s 338 m/s T 1 f s 262 Hz Check Your Answer Hz has the units s 1 and so m Hz equals m/s, which is correct. Are the magnitudes realistic? A typical sound wave travels approximately 343 m/s. You can notice the delay in sound across a football field, so a few tenths of a second is reasonable. λ v F.Y.I. Because radio waves travel at m/s and sound waves are slower, m/s, a broadcast voice can be heard sooner miles away than it can be heard at the back of the room in which it originated Wave Properties 333 Concept Development In some materials the force that brings the particles displaced by the wave back to equilibrium is not proportional to the displacement that is, the medium is not linear. In these media, the wave speed will depend on the frequency. Such a medium is called dispersive. Examples are glass and diamond. Dispersion will be treated more fully in a later chapter. Explain to students that the basic equation v f will also be used when they study sound, light, and quantum theory. Point out that waves in an actual medium do not exhibit ideal wave behavior. In particular, waves die out, that is, they disappear after enough time has elapsed. The wave s energy gets used up in a frictional process, or its energy gets so spread out that it is no longer detectable. Convergent Question Ask: Why is the unit for frequency called a hertz? The unit hertz is named after Heinrich Hertz, who discovered radio waves in More about his scientific work will be found in Chapter 27. Enrichment Ask students why only longitudinal waves can travel through a gas. Because the molecules in a gas are not bonded to each other, there is no way for the medium to return to its original position when displaced transversely. Thus only longitudinal waves can travel through a gas. L2 time. Ask: How does changing the amplitude affect the speed of the wave? The amplitude does not affect the speed. 5. Alter the medium by stretching the spring to a different length, and have students determine the speed of a pulse in this new medium. Ask: How does altering the medium affect the speed of the wave? The speed increases when tension of the medium is increased. RESULTS A longitudinal wave is generated in step 1. Changing the amplitude in step 4 has no effect on the speed of the wave. In step 5, the speed increases when tension of the medium is increased. Assessment PERFORMANCE Have students follow up this demonstration with some chalkboard drawings, with labels to summarize the phenomena seen. This visual demonstration will be a great help in getting wave terminology across, and now ask students to supply words to describe what they observed. LS 333

11 Background Earthquakes produce four kinds of seismic waves. Primary waves, called P waves, and secondary waves, called S waves, travel outward from the quake s focus beneath Earth s surface. P waves travel three to four miles per second and cause rock to vibrate in the wave s direction of travel. S waves travel at about two miles per second. They create up and down and sideto-side movements at right angles to the direction of the wave. Earthquake energy that reaches the surface creates two types of surface waves: Love and Rayleigh waves. Love waves cause the ground to vibrate in a back-and-forth motion. Rayleigh waves create an undulating, elliptical motion that causes the ground to rise and fall. Surface waves are responsible for most of the structural damage produced by an earthquake. Teaching Strategies Ask a seismologist from a nearby university or office of the U.S. Geological Survey to make a class presentation, showing and explaining the graphs of seismic waves produced by an earthquake and displaying any photographs of resulting damage. Predicting Earthquakes Earthquakes are produced by the sudden motion of rock masses within Earth s crust. Although rocks can bend and twist to some extent, they break if they are exposed to forces that exceed their strength. The friction and crushing motions of breaking rock create seismic waves of energy that radiate outward. These seismic waves cause the shaking and trembling called an earthquake. The breaks in the rock are known as earthquake faults. The subsurface region where the rock ruptures is called the focus of an earthquake. The point on the surface directly above the focus is known as the epicenter. Several types of seismic waves travel outward from the focus. Waves that travel along the surface are called surface waves. They have characteristics of both transverse and longitudinal waves and cause most major earthquake damage to homes and cities. How much damage? Many earthquakes are quite small and are hardly felt. However, catastrophic earthquakes have been recorded in many regions of the world. One example is the deadly earthquake that hit the densely populated region of Izmir, Turkey, in Eighteen thousand people were killed, and damage estimates reached $40 billion. Can earthquakes be predicted? Most geologists agree that regions along portions of California s famous San Andreas Fault will experience a major earthquake before the middle of the 21st century. The broad time frame of a prediction such as this doesn t enable people to evacuate an area in anticipation of a quake on any particular date. Efforts are under way to develop more precise earthquake predictions. Scientists constantly use seismographs to monitor major faults such as the San Andreas Fault for the smallest Earth tremors. A seismograph records the magnitude of seismic waves by suspending a pen on a pendulum over a paper-covered drum. The stronger the motion, the larger the arc of the pen s motion on the drum. Lasers and creep meters measure differences in land movement on the two sides of a fault. A creep meter consists of wires stretched across a fault, and a laser beam is timed as it returns to its source. Scientists monitor radon and hydrogen concentrations in groundwater to determine how they change prior to an earthquake. Antennae monitor changes in electromagnetic waves coming from deep beneath Earth s surface. Investigating the Issue 1. Acquiring Information Use your library skills to find out more about the Parkfield experiment near the San Andreas Fault in California. What kinds of instruments are being used by seismologists to monitor the fault? Have any earthquakes predicted for Parkfield actually occurred? 2. Debating the Issue Evaluate the impact of earthquake research on society and the environment. How can studying wave properties and behaviors impact the building industry? What is the responsibility of scientists, government, and citizens with respect to earthquake-resistant structures? PHYSICS To find out more about earthquakes, visit the Glencoe Science Web site at science.glencoe.com Investigating the Issue 1. In 1985, U.S. Geological Survey seismologists made the first official earthquake forecast. They predicted a moderate earthquake would take place on the San Andreas fault at Parkfield by 1993, but their forecast did not come true. The prediction was 334 Texas TEKS Pages : 3(B), 3(C), 8(A) 334 Waves and Energy Transfer based on the history of Parkfield quakes. Since 1857, Parkfield had experienced a moderate earthquake approximately every 22 years. 2. Earthquake research provides a better understanding of the environment that we live in so predictions are more accurate, saving lives. By studying wave properties and behaviors, we can build better buildings that can withstand earthquakes. Newer steel and reinforced concrete buildings experienced much less damage. Earthquake-resistant highway supports are made of vertical steel rods wrapped with reinforcing rods and enclosed in concrete. Rubber and steel foundation moorings used in construction of new high-rise buildings can absorb much of the wave energy of an earthquake. Teacher Resources Monastersky, Richard. The Overdue Quake: Unusual activity along the San Andreas hints at a long-expected tremor. Science News, July 5, 1997, pages 8 9. Ritchie, David. The Encyclopedia of Earthquakes & Volcanoes. Facts on File, New York, 1994.

12 Practice Problems 1. A sound wave produced by a clock chime is heard 515 m away 1.50 s later. a. What is the speed of sound of the clock s chime in air? b. The sound wave has a frequency of 436 Hz. What is its period? c. What is its wavelength? 2. A hiker shouts toward a vertical cliff 685 m away. The echo is heard 4.00 s later. a. What is the speed of sound of the hiker s voice in air? b. The wavelength of the sound is m. What is its frequency? c. What is the period of the wave? 3. If you want to increase the wavelength of waves in a rope, should you shake it at a higher or lower frequency? 4. What is the speed of a periodic wave disturbance that has a frequency of 2.50 Hz and a wavelength of m? 5. The speed of a transverse wave in a string is 15.0 m/s. If a source produces a disturbance that has a frequency of 5.00 Hz, what is its wavelength? 6. Five pulses are generated every s in a tank of water. What is the speed of propagation of the wave if the wavelength of the surface wave is 1.20 cm? 7. A periodic longitudinal wave that has a frequency of 20.0 Hz travels along a coil spring. If the distance between successive compressions is m, what is the speed of the wave? 14.1 Section Review 1. Suppose you and your lab partner are asked to measure the speed of a transverse wave in a giant, coiled spring toy. How could you do it? List the equipment you would need. 2. Describe longitudinal waves. What types of media transmit longitudinal waves? 3. You are creating transverse waves in a rope by shaking your hand from side to side. Without changing the distance your hand moves, you begin to shake it faster and faster. What happens to the amplitude, frequency, period, and velocity of the wave? EARTH SCIENCE CONNECTION Earth s Core An earthquake produces both transverse and longitudinal waves that travel through Earth. Geologists studying these waves with seismographs found that only the longitudinal waves could pass through Earth s core. Only longitudinal waves can move through a liquid or a gas. From this observation, what can be deduced about the nature of Earth s core? 4. If you pull on one end of a coiled spring toy, does the pulse reach the other end instantaneously? What if you pull on a rope? What if you hit the end of a metal rod? Compare the responses of these three materials. 5. Critical Thinking If a raindrop falls into a pool, small-amplitude waves result. If a swimmer jumps into a pool, a largeamplitude wave is produced. Why doesn t the heavy rain in a thunderstorm produce large waves? 14.1 Wave Properties 335 Practice Problems Have students refer to Appendix C for complete solutions to Practice Problems. 1. a. 343 m/s b ms c m 2. a. 343 m/s b. 457 Hz c ms 3. at a lower frequency, because wavelength varies inversely with frequency m/s m m/s m/s 3 ASSESS Checking for Understanding LS Visual-Spatial Ask students to draw and label the parts of a transverse wave, and indicate several places where wavelength can be measured. Make sure students understand that wavelength does not have to be measured from crest to crest or trough to trough. L1 ELL Reteaching Review basic wave terminology, then choose a type of wave, such as small water waves, as an example. Ask: If you are generating waves, which wave properties are under your control? Frequency, wavelength, amplitude, and speed if you change the depth of the water. Then ask students to describe how they could change a water wave s amplitude and its frequency, and how to measure the wave s speed Section Review 1. You would need something to measure distance and a stopwatch timer. Extend the coiled spring toy to a measured length. One of you starts a wave pulse at one end. The other person starts the timer, stopping it when the pulse reaches the other end. Divide distance by time. 2. Longitudinal waves are waves in which the disturbance is in the same direction as the direction of wave motion. They can travel in fluids as well as solids. 3. Amplitude and velocity don t change. Frequency increases, period decreases. 4. No, the disturbance moves faster in the rope and metal rod, but does take some time. 5. The waves are not large because small waves are formed at random times. For example, a drop might fall on the peak of one wave, reducing its amplitude. Extension For students who have mastered the lesson, assign problems from the Supplemental Problems booklet. L2 4 CLOSE Convergent Question Ask students to describe how an orchestra would sound if different frequencies and/or amplitude waves traveled at different speeds. L1 335

13 SECTION 14.2 PREPARE Content Refresher Waves can undergo partial reflection and refraction. In addition, two waves can be in the same place at the same time, and thus waves can pass through each other. Bridging Help students understand what occurs when a wave stays in its original medium, as opposed to when it enters a new medium. Point out that wave speed changes only when it enters a new medium. 1 FOCUS QUICK DEMO CAUTION: Wear goggles. Send a pulse down the suspended spring while someone holds the far end rigid. Explain to students what to look for at the point where the pulse reflects. Help students observe that upon reflection from a fixed end, an inverted wave returns on the opposite side of the coiled spring OBJECTIVES Relate a wave s speed to the medium in which the wave travels. Describe how waves are reflected and refracted at boundaries between media, and explain how waves diffract. Apply the principle of superposition to the phenomenon of interference. FIGURE 14 7 The junction of the two springs is a boundary between two media. A pulse reaching the boundary (a) is partially reflected and partially transmitted (b). Wave Behavior When a wave encounters the boundary of the medium in which it is traveling, it sometimes reflects back into the medium. In other instances, some or all of the wave passes through the boundary into another medium, often changing direction at the boundary. In addition, many properties of wave behavior result from the fact that two or more waves can exist in the same medium at the same time quite unlike particles, which consist of matter and take up space. Waves at Boundaries Recall that the speed of a mechanical wave depends only on the properties of the medium it passes through, not on the wave s amplitude or frequency. For water waves, the depth of the water affects wave speed. For sound waves in air, the temperature affects wave speed. For waves on a spring, the speed depends upon the spring s rigidity and its mass per unit length. Examine what happens when a wave moves across a boundary from one medium into another, as in two springs of different thicknesses joined end to end. Figure 14 7 shows a wave pulse moving from a large spring into a smaller one. The wave that strikes the boundary is called the incident wave. One pulse from the larger spring continues in the smaller spring, at the speed of waves on the smaller spring. Note that this transmitted wave pulse remains upward. Some of the energy of the incident wave s pulse is reflected backward in the larger spring. This returning wave is called the reflected wave. Whether or not the reflected wave is upward (erect) or downward (inverted) depends on the comparative thicknesses of the two springs. If waves in the smaller spring have a higher speed because the spring is heavier or stiffer, then the reflected wave will be inverted. a 336 Waves and Energy Transfer b Videodisc STVS: Physics Disc 1, Side 1 Eliminating Potholes (Ch. 5)!7^É" STVS: Earth and Space Disc 3, Side 2 Mapping with a Rifle (Ch. 20)!9,Ä" Program Resources Study Guide, pp L1 Laboratory Manual, pp L1 Critical Thinking, p. 20 L1 Physics Lab and Pocket Lab Worksheets, pp L1 336

14 a What happens if the boundary is a wall rather than another spring? When a wave pulse is sent down a spring connected to a rigid wall, the energy transmitted is reflected back from the wall, as shown in Figure The wall is the boundary of a new medium through which the wave attempts to pass. The pulse is reflected from the wall with almost exactly the same amplitude as the pulse of the incident wave. Thus, almost all the wave s energy is reflected back. Very little energy is transmitted into the wall. Note also that the pulse is inverted. Practice Problems 8. A pulse is sent along a spring. The spring is attached to a lightweight thread that is tied to a wall, as shown in Figure a. What happens when the pulse reaches point A? b. Is the pulse reflected from point A erect or inverted? c. What happens when the transmitted pulse reaches point B? d. Is the pulse reflected from point B erect or inverted? FIGURE 14 9 b A B FIGURE 14 8 A pulse approaches a rigid wall (a) and is reflected back (b). Note that the amplitude of the reflected pulse is nearly equal to the amplitude of the incident pulse, but it is inverted and appears as a downward curve. Pocket Lab Wave Reflections Practice Problems Have students refer to Appendix C for complete solutions to Practice Problems. 8a. The pulse is partially reflected and partially transmitted. b. erect, because reflection is from a less dense medium c. It is almost totally reflected from the wall. d. inverted, because reflection is from a more dense medium 9. pulse inversion means rigid boundary; attached to wall 10 a. The pulse is partially reflected, partially transmitted; it is almost totally reflected from the wall. b. inverted, because reflection is from a more dense medium; inverted, because reflection is from a more dense medium 9. A long spring runs across the floor of a room and out the door. A pulse is sent along the spring. After a few seconds, an inverted pulse returns. Is the spring attached to the wall in the next room or is it lying loose on the floor? 10. A pulse is sent along a thin rope that is attached to a thick rope, which is tied to a wall, as shown in Figure a. What happens when the pulse reaches point A? Point B? b. Is the pulse reflected from point A displaced in the same direction as the incident pulse, or is it inverted? What about the pulse reflected from point B? FIGURE Meeting Individual Needs Learning Disabled Produce a periodic wave by shaking a spring back and forth at a uniform rate. Have students determine the frequency of the waves and make an approximate measurement of the wavelength. Repeat the procedure using a higher and then a lower frequency. Ask: How is the wavelength of a wave in a given medium related to its frequency? The frequency is related inversely to the wavelength. L1 ELL A B Waves lose amplitude and transfer energy when they reflect from a barrier. What happens to the speed of the waves? Use a wave tank with a projection system. Half-fill the tank with water. Dip your finger into the water near one end of the tank and notice how fast the wave that you make moves to the other end. Analyze Does the wave slow down as it travels? Use a stopwatch to measure the time for a wave to cover two lengths, then four lengths, of the wave tank Wave Behavior 337 Physics Journal LS Linguistic Have students describe an antinode and a node. Ask them to explain what a node and an antinode would sound like with sound waves. Then, have them explain what a node and an antinode would look like with light waves. A sound node is quiet, a light node is dark, a sound antinode is loud, and a light antinode is bright. L1 Wave Reflections Purpose To refute the common misconception that the speed of a wave decreases as it travels from its source Materials Wave tank with projection system, stopwatch Outcome Students will be surprised to find that the wave s speed does not decrease as it travels. This implies that the wave s speed does not decrease as the amplitude decreases. Analyze No, the time for the wave to travel four lengths is about twice the time for two lengths. LS Texas TEKS Pages : 1(A), 2(A), 2(D), 8(A) 337

15 2 TEACH Uncovering Misconceptions LS Interpersonal Have students work in pairs using a coiled spring to observe reflection of a wave and answer the question: Does the speed of a wave change when the wave reflects off a boundary? CAUTION: Wear goggles. Have students report on their observations. NOTE: The speed does not change. L1 COOP LEARN QUICK DEMO Use a video of wave motion that shows the superposition of two waves producing nodes and antinodes. Analyze the video frame by frame to help students understand the conditions needed for constructive and destructive interference. FIGURE When two equal pulses meet there is a point, called the node, (N), where the medium remains undisturbed (a). Constructive interference results in maximum displacement at the antinode, (A), (b). If the opposite pulses have unequal amplitudes, cancellation is incomplete (c). Superposition of Waves Suppose a pulse traveling down a spring meets a reflected pulse coming back. In this case, two waves exist in the same place in the medium at the same time. Each wave affects the medium independently. The displacement of a medium caused by two or more waves is the algebraic sum of the displacements caused by the individual waves. This is called the principle of superposition. In other words, two or more waves can combine to form a new wave. If the waves are in opposite directions, they can cancel or form a new wave of less or greater amplitude. The result of the superposition of two or more waves is called interference. Wave interference Wave interference can be either constructive or destructive. When two pulses with equal but opposite amplitudes meet, the displacement of the medium at each point in the overlap region is reduced. The superposition of waves with equal but opposite amplitudes causes destructive interference, as shown in Figure 14 11a. When the pulses meet and are in the same location, the displacement is zero. Point N, which doesn t move at all, is called a node. The pulses continue to move and eventually resume their original form. As in constructive interference, the waves pass through each other unchanged. Constructive interference occurs when the wave displacements are in the same direction. The result is a wave that has an amplitude larger than any of the individual waves. Figure 14 11b shows the constructive interference of two equal pulses. A larger pulse appears at point A when the two waves meet. Point A has the largest displacement and is called the antinode. The two pulses pass through each other without 1 A Critical Thinking Have students image a wave pulse approaching a fixed boundary. Ask: What would happen if the leading half of this pulse hit a rigid boundary and reflected upright into the oncoming pulse? Ask: Why is this not possible? If the reflected front half of the wave were not inverted, the front and back of the wave would undergo constructive superposition. This would mean that the wave medium would move up, and this is a contradiction to the condition that the end of the wave medium is fixed. 1 N 2 N 3 N 4 N 5 N a 338 Waves and Energy Transfer b A A A A c N N N N DEMONSTRATION 14-2 PURPOSE To demonstrate reflection of waves in a medium with a non-fixed end MATERIALS Coiled spring, string PROCEDURE Set up a spring as described in the Quick Demo on page 327, then follow these steps: Tie a piece of string about one meter long to one end of the spring. Hold the spring, and have the student extend the string. Send a transverse pulse down the spring toward the student. Ask students to observe the phases of the original and reflected pulses. Have students observe and record the behavior at the spring and string at the point where they are joined. 2. Remove the string from the spring and have a student hold the end securely. Pass a transverse pulse down the spring. Ask students to observe the phases of the original and reflected pulses. RESULTS Most of the wave energy is reflected from the free end of the spring, and the reflected wave is erect. When the end of

16 changing their shapes or sizes. If the pulses have opposite and unequal amplitudes, the resultant pulse at the overlap is the algebraic sum of the two pulses, as shown in Figure 14 11c. Continuous waves You have read how wave pulses move through each other and are reflected from boundaries. What happens when continuous waves meet a boundary? Figure 14 12a shows a continuous wave moving from a region with higher speed to a region with lower speed. On the left-hand side of the boundary, the amplitude of the reflected wave has been added to that of the incident wave because some of the wave energy has been reflected. Recall that velocity of a wave is the product of wavelength and frequency, v f. Thus, the transmitted wave on the other side of the boundary has a shorter wavelength because of its slower speed. The transmitted wave also has a smaller amplitude because less wave energy is available. Notice in Figure 14 12b how the relative amplitudes and wavelengths change when a continuous wave moves from a region with lower speed to one with higher speed. Pocket Lab Wave Interaction What happens to the waves coming from different directions when they meet? Do they slow down, bounce off each other, or go through each other? Design an Experiment Use a coiled spring toy to test these questions. Record your procedures and observations. Concept Development Inverted, reflected waves can be shown by rigidly attaching one end of a coiled spring and making waves at the other end. Erect reflected waves can be shown by attaching a short length of rubber hose or other flexible material to a coiled spring, and then making waves from the non-spring end. Standing waves You can use the concept of superimposed waves to control the frequency and formation of waves. If you attach one end of a rope or coiled spring to a fixed point such as a doorknob, and then start to vibrate the other end, the wave leaves your hand, is reflected at the fixed end, is inverted, and returns to your hand. When it reaches your hand, it is inverted and reflected again. Thus, when the wave leaves your hand the second time, its displacement is in the same direction it was when it left your hand the first time. But what if you want to magnify the amplitude of the wave you create? Suppose you adjust the motion of your hand so that the period of the rope s vibration equals the time needed for the wave to make one round-trip from your hand to the door and back. Then, the displacement Displacement Incident + Reflected wave v 1 v 1 v 2 Transmitted wave Incident + Reflected wave v 1 v 1 v 2 FIGURE In each of the two examples below, continuous waves pass from the medium on the left to the medium on the right. Wave speed depends upon the medium. For example, light waves travel faster in air than they do in water. Transmitted wave Wave Interaction Purpose To investigate transverse wave interaction on a coiled spring Materials Coiled spring Outcome Students will find it almost impossible to decide what happened unless they try different sizes, types, or orientations of waves. Design an Experiment Students can observe that waves go through each other if: (a) they send different amplitude waves from different directions; (b) one student sends a pressure wave while another student sends a transverse wave; or (c) one student sends a transverse pulse in a horizontal plane as the other student makes a similar pulse in a vertical plane. LS a Higher speed Longer wavelength Boundary Lower speed Shorter wavelength b Lower speed Shorter wavelength Boundary Higher speed Longer wavelength 14.2 Wave Behavior 339 the spring is fixed, most of the wave energy is reflected, but the reflected wave is inverted. Assessment KNOWLEDGE 1. What happens when the pulse arrives at the boundary between the two media of spring and string? Most of the pulse is reflected. Part of the pulse is transmitted. The reflected pulse is erect; that is it undergoes no phase change. 2. What happens to the wave when it strikes the boundary between the string and slinky? Pulses reflected from a rigid barrier are inverted, thus undergoing a 180 degrees phase change. Those reflected from a nonrigid barrier undergo no phase change. Texas TEKS Pages : 1(A), 2(A), 2(D), 8(A) 339

17 Reinforcement Call students attention to the fact that light is reflected from mirrors and other shiny surfaces. Sound is reflected from hard surfaces to produce echoes. Have students give examples of light and sound reflecting, and relate the examples to reflection of waves. L1 FIGURE Interference produces standing waves in a rope. As the frequency of vibration is increased, as shown from top to bottom, the numbers of nodes and antinodes increase. Uncovering Misconceptions LS Visual-Spatial Ask students to draw a straight wave as it reflects from a straight barrier at some angle other than 45 degrees. Ask them if the wavelength is the same after reflection, and ask them to explain why? Yes, because neither the speed nor frequency of the waves change, the wavelength must also remain the same. L1 Bent Out of Shape Purpose Reinforce the fact that a wave s speed depends on the properties of the medium. In this case, the speed of water waves depends on the depth of the water. Materials Wave tank with a projection system Outcome The waves will travel slower in the shallow water and faster in the deeper water. Therefore, the wave circle will be lengthened in the direction of the deeper water and shortened in the shallow end. Pocket Lab Bent Out of Shape What happens to a water wave s speed when the depth of the water changes? How does a change in speed affect the shape of the waves? Try this activity to find out. Use a wave tank with a projection system. Adjust the tank so that the water is shallow on one side and deep on the opposite side. Dip your finger or pencil eraser into the middle of the tank, and gently tap the water to make a circular wave. Watch closely. Do the waves hit the sides of the tank at the same time? What happens to the wavelength in different directions? Modeling Make a sketch of the shape of the waves. Label the deep and shallow ends on your drawing. Describe the relationship between the depth of the water and the wave s speed (inverse or direct). What did you notice about the wavelength in different directions? 340 Waves and Energy Transfer Modeling The wavelength is greater in the deeper water. LS DEMONSTRATION 14-3 given by your hand to the rope each time will add to the displacement of the reflected wave. As a result, the oscillation of the rope in one segment will be much larger than the motion of your hand, as expected from your knowledge of constructive interference. This large-amplitude oscillation is an example of mechanical resonance. The nodes are at the ends of the rope and an antinode is in the middle, as shown in Figure top. Thus, the wave appears to be standing still and is called a standing wave. If you double the frequency of vibration, you can produce one more node and one more antinode in the rope. Now it appears to vibrate in two segments, as in Figure center. Further increases in frequency produce even more nodes and antinodes, as shown in Figure bottom. Waves in Two Dimensions You have studied waves on a rope or spring reflecting from a rigid support, where the amplitude of the wave is forced to be zero by destructive interference. These mechanical waves move in only one dimension. However, waves on the surface of water move in two dimensions, and sound waves and electromagnetic waves will later be shown to move in three dimensions. How can two-dimensional waves be demonstrated? Reflection of waves in two dimensions A ripple tank can be used to show the properties of two-dimensional waves. A ripple tank contains a thin layer of water. Vibrating boards produce wave pulses or, in this case, traveling waves of water with constant frequency. A lamp above the tank produces shadows below the tank that show the locations of the crests of the waves. Figure 14 14a shows a wave pulse traveling toward a rigid barrier that reflects the wave. The incident wave moves upward. The reflected wave moves to the right. PURPOSE To illustrate reflection of two dimensional waves from a straight boundary MATERIALS Ripple tank or ripple tank for overhead projector, straight boundary, dowel to produce waves PROCEDURE 1. Produce an incident wave by rolling the dowel in water at an angle of 30 degrees from the normal to the barrier. 2. Have students observe the incident and reflected wave fronts and compare the angles of incidence and reflection. RESULTS The angle of incidence is equal to the angle of reflection. 340

18 a Barrier Incident ray The direction of waves moving in two dimensions can be modeled by ray diagrams. Ray diagrams model the movement of waves. A ray is a line drawn at a right angles to the crests of the waves. Figure 14 14b shows the ray diagram for the wave in the ripple tank. The ray representing the incident ray is the arrow pointing upward. The ray representing the reflected ray points to the right. The direction of the barrier is also shown by a line, which is drawn at a right angle to the barrier. This line is called the normal. The angle between the incident ray and the normal is called the angle of incidence. The angle between the normal and the reflected ray is called the angle of reflection. The law of reflection states that the angle of incidence is equal to the angle of reflection. Refraction of waves in two dimensions A ripple tank also can be used to model the behavior of waves as they move from one medium into another. Figure 14 15a shows a glass plate placed in a ripple tank. The water above the plate is shallower than the water in the rest of the tank, and the water there acts like a different medium. As the waves move from deep to shallow water, their wavelength decreases, and the direction of the waves changes. Because the waves in the shallow water are generated by the waves in deep water, their frequency is not changed. Based on the equation v f, the decrease in the wavelength of the waves means that the velocity is lower in the shallower water. This is similar to what happens to a sound wave in the air that collides with and then travels through another medium such as a wall. This same phenomenon can be seen at the coast when the land gently slopes down into the sea. In Figure 14 15b, the waves approach the shore. The ray direction is not parallel to the normal. Not only does the wavelength decrease over the shallower bottom, but also the direction of the waves changes. The change in the direction of waves at the boundary between two different media is known as refraction. b θ i θr Normal Reflected ray FIGURE A wave pulse in a ripple tank is reflected by a barrier (a). The ray diagram models the wave in time sequence as it approaches the barrier and then is reflected to the right (b) Wave Behavior 341 Concept Development Refraction of water waves can be shown by placing a glass plate on the bottom of a ripple tank so that its edge is at an angle to the oncoming wave front. Hint: Keep the depth of the water in the shallow region as low as possible. Because refraction of waves is difficult to see in a ripple tank, it is also good to use video clips to show refraction of waves. L1 Wave machines made of rods mounted on a flexible spine are available. If you have one, it will demonstrate wave behaviors at boundaries between media. To build your own wave machine, refer to the book by R. D. Edge, String and Sticky Tape Experiments. Assessment PERFORMANCE Have students draw a diagram showing two different pulses approaching each other from opposite sides of a coiled spring or string. Have students draw a second diagram that shows the superposition of these two pulses as they pass through each other. Students should then draw a third diagram showing the waves after they have passed through each other. L1 ELL LS Concept Development A wave machine, coiled spring, or a rope can be used to show standing waves with nodes and antinodes. Standing waves are formed in most musical instruments. They were also produced during the collapse of the Tacoma Narrows Bridge. Assessment KNOWLEDGE 1. What is the value of the angle of incidence? 30 degrees. Remind students to measure the incident ray between the wave front and the normal to the barrier. 2. How does the angle of incidence compare to the angle of reflection. They are numerically equal. CD-ROM Physics for the Computer Age INTRODUCTION: Physics for the Computer Age Texas TEKS Pages : 1(A), 2(A), 2(D), 8(A) 341

19 QUICK DEMO CAUTION: Wear goggles. Have two students send simultaneous pulses from opposite ends of a spring. Have students experiment with pulses of the same and different sizes and pulses in phase and out of phase, with particular attention to pulses that are 180 degrees out of phase. Ask: What happens to the pulses when they meet? The amplitudes of the pulses are additive. What happens to the pulses after they have passed through one another? The pulses continue unchanged. L1 ELL LS Applying Physics THE TACOMA NARROWS BRIDGE Show the film loop or video of the collapse of the Tacoma Narrows Bridge. The following comments about the Tacoma Narrows Bridge collapse are summarized from the book by Jearl Walker, The Flying Circus of Physics. The bridge oscillated even as it was being built. It often made the workmen seasick. After the bridge opened, motorists would come from miles away to be on the bridge when it was in motion. One day the bridge went into a torsional oscillation that destroyed it in about an hour. The question is why should a moderately strong steady wind cause such strong oscillations? One explanation is that the large vertical plates on the bridge were probably responsible for the oscillations. Wind flowing around the plates caused pressure differences that ultimately made the bridge oscillate. Have interested students research and report on the causes of the collapse. L1 a FIGURE As the water waves move over a shallower region of the ripple tank where a triangular glass plate is placed, they slow down and their wavelength decreases (a). When waves approach the shore, they are refracted by the change in depth of the water (b). FIGURE Waves that bend around the edges of barriers demonstrate diffraction. 342 Waves and Energy Transfer Meeting Individual Needs Learning Disabled Standing waves can clearly be shown by using a string vibrator. Students will find it easy to identify the nodes and antinodes. You can vary the tension in the string, producing different numbers of nodes and antinodes and therefore a different number of wavelengths. ELL LS b Diffraction and Interference of Waves If particles are thrown at a barrier with holes in it, the particles will either reflect off the barrier or pass straight through the holes. When waves encounter a small hole in a barrier, however, they do not pass straight through. Rather, they bend around the edges of the barrier, forming circular waves that radiate out, as shown in Figure The spreading of waves around the edge of a barrier, such as a small barrier coral reef, is called diffraction. Diffraction also occurs when waves meet a small obstacle. They can bend around the obstacle, producing waves behind it. The smaller the wavelength in comparison to the size of the obstacle, the less the diffraction. If a barrier has two closely spaced holes, the waves are diffracted by each hole and form circular waves, as shown in Figure 14 17a. These two sets of circular waves interfere with each other. There are regions of constructive interference where the resulting waves are large, and bands of destructive interference where the water remains almost undisturbed. Constructive interference occurs where two crests or two troughs of the circular waves meet. The antinodes formed lie on antinodal lines that TECHPREP BROADCAST FREQUENCIES LS Interpersonal Have teams of students survey local radio stations to determine their broadcast frequencies and band widths. Students should explain what these terms mean in the broadcasting industry and explain by using the principle of superposition how FCC regulations prevent interference of radio signals. L1 COOP LEARN 342

20 Visual Learning Use the photograph in Figure to draw what happens when a wave enters a medium in which the speed changes. Check that students understand that the wavelength is shorter in the medium in which the wave travels at a slower speed. a FIGURE Waves are diffracted at two openings in the barrier. At each opening, circular waves are formed that interfere with each other. Points of constructive interference appear as bright spots in the photograph (a). Lines of constructive interference, called antinodal lines, occur where crest meets crest (b) radiate outward from the barrier, Figure 14 17b. Between these antinodal lines are areas where a crest of one wave meets a trough from another wave. Destructive interference produces nodes where the water is undisturbed. The lines of nodes, or nodal lines, lie between adjacent antinodal lines. Thus, it is interference of the water waves that produces the series of light and dark lines observed in Figure 14 17a. Section Review 1. Which of the following wave characteristics remain unchanged when a wave crosses a boundary into a different medium: frequency, amplitude, wavelength, velocity, or direction? 2. A rope vibrates with the two waves shown in Figure Sketch the resulting wave. FIGURE Section Review 1. frequency 2. b 3. Describe diffraction. How can diffraction lead to interference? 4. Would you expect high-frequency or low-frequency sound waves to be more diffracted when they pass through an open door? Explain. 5. Critical Thinking As another way to understand wave reflection, cover the right-hand side of each drawing in Figure 14 11a with a piece of paper. The edge of the paper should be at point N, the node. Now, concentrate on the resultant wave, shown in blue. Note that it acts like a wave reflected from a boundary. Is the boundary a rigid wall or open ended? Repeat this exercise for Figure 14 11b Wave Behavior Diffraction is the bending of waves around obstacles. When a wave encounters more than one obstacle, the waves are diffracted by the obstacles and interfere with each other. 4. Low frequency (long wavelength), because the smaller the wavelength, the less the diffraction. 5. For Figure 14 11a, the boundary is a rigid wall; For Figure 14 11b, the boundary is open-ended. 3 ASSESS Checking for Understanding Ask: What quantities change when a wave undergoes refraction? Frequency does not change; however, both speed and wavelength do change. Reteaching LS Interpersonal Have students work in their lab groups to determine why an AM radio signal could be heard behind a hill but an FM signal could not. Ask them to compare the signals. The AM signal undergoes diffraction around the hill and the FM signal does not. Because less diffraction occurs when the wavelength is smaller in comparison to an obstacle, the AM signal must have a longer wavelength than the FM signal. L1 COOP LEARN Extension For students who have mastered the lesson, assign problems from the Supplemental Problems booklet. L2 4 CLOSE Give students a copy of the photo in Figure 14 17a or similar twopoint interference pattern. Ask student to make a few points on the diagram, and then exchange with another student. Students should determine if the marked points are nodes or antinodes and the difference in the distance of the points from each of the sources. L1 343

21 14 CHAPTER REVIEW Review Summary statements and Key Terms with your students. Reviewing Concepts Section Two. Energy is transferred by particle transfer and by waves. There are many examples that can be given of each, a baseball and a bullet for particle transfer; sound waves and light waves. 2. The primary difference is that mechanical waves require a medium to travel through and electromagnetic waves do not need a medium. 3. A transverse wave causes the particles of the medium to vibrate in a direction that is perpendicular to the direction in which the wave is moving. A longitudinal wave causes the particles of the medium to vibrate in a direction parallel with the direction of the wave. Surface waves have characteristics of both. 4. Once the pulse has passed, the point is exactly as it was prior to the advent of the pulse. 5. A pulse is a single disturbance in a medium, whereas a wave consists of several adjacent disturbances. 6. Frequency is the number of vibrations per second of a part of the medium. Velocity describes the motion of the wave through the medium. CHAPTER 14 REVIEW Key Terms 14.1 wave wave pulse continuous wave transverse wave longitudinal wave surface wave trough crest wavelength frequency 14.2 incident wave reflected wave principle of superposition interference destructive interference node constructive interference antinode standing wave law of reflection refraction diffraction Summary 344 Waves and Energy Transfer 14.1 Wave Properties Waves transfer energy without transferring matter. Mechanical waves require a medium. A continuous wave is a regularly repeating sequence of wave pulses. In transverse waves, the displacement of the medium is perpendicular to the direction of wave motion. In longitudinal waves, the displacement is parallel to the wave direction. In surface waves, matter is displaced in both directions. The wave source determines the frequency of the wave, f, which is the number of vibrations per second. The wavelength of a wave,, is the shortest distance between points where the wave pattern repeats itself. The medium determines wave speed, which can be calculated for continuous waves using the equation v f Wave Behavior When a wave crosses a boundary between two media, it is partially transmitted and partially reflected, depending on how much the wave velocities in the two media differ. When a wave moves to a medium with higher wave speed, the reflected wave is inverted. When moving to a medium with lower wave speed, the displacement of the reflected wave is in the same direction as the incident wave. Reviewing Concepts Section How many general methods of energy transfer are there? Give two examples of each. 2. What is the primary difference between a mechanical wave and an electromagnetic wave? The principle of superposition states that the displacement of a medium resulting from two or more waves is the algebraic sum of the displacements of the individual waves. Interference occurs when two or more waves move through a medium at the same time. Destructive interference results in decreased wave displacement with its least amplitude at the node. Constructive interference results in increased wave displacement with its greatest amplitude at the antinode. A standing wave has stationary nodes and antinodes. When two-dimensional waves are reflected from boundaries, the angles of incidence and reflection are equal. The change in direction of waves at the boundary between two different media is called refraction. The spreading of waves around a barrier is called diffraction. Key Equations 14.1 f 1 T v f 3. What are the differences among transverse, longitudinal, and surface waves? 4. Suppose you send a pulse along a rope. How does the position of a point on the rope before the pulse arrives compare to the point s position after the pulse has passed? Texas TEKS Pages : 8(A) Pages : 3(B), 8(A), 8(B) Videotape MindJogger Videoquizzes Chapter 14: Waves and Energy Transfer Have students work in groups as they play the videoquiz game to review key chapter concepts. 344