Introduction to Waves

Transcription

1 Introduction to Waves Building to the Performance Expectations The learning experiences in this lesson prepare students for mastery of MS-PS4-1 Use mathematical representations to describe a simple model for waves that includes how the amplitude of a wave is related to the energy in a wave. Trace Tool to the NGSS Go online to view the complete coverage of standards across lessons, units, and modules. SEP Science & Engineering Practices DCI DCI Disciplinary Core Core Ideas CCC CCC Crosscutting Concepts Using Mathematics and Computational Thinking Use mathematical representations to describe and/or support scientific conclusions and design solutions. (MS-PS4-1) VIDEO Using Data, Mathematical Thinking, and Computational Thinking Scientific Knowledge is Based on Empirical Evidence Science knowledge is based upon logical and conceptual connections between evidence and explanations. (MS-PS4-1) PS4.A-1 Wave Properties A simple wave has a repeating pattern with a specific wavelength, frequency, and amplitude. (MS-PS4-1) Patterns Graphs and charts can be used to identify patterns in data. (MS-PS4-1) CONNECTION TO MATH MP.2 Reason abstractly and quantitatively. MP.4 Model with mathematics. 6.RP.A.1 Understand the concept of a ratio and use ratio language to describe a ratio relationship between two quantities. 7.RP.A.2 Recognize and represent proportional relationships between quantities. 8.F.A.3 Interpret the equation y = mx + b as defining a linear function, whose graph is a straight line; give examples of functions that are not linear. Use ratios and proportional relationships and functions. CONNECTION TO ENGLISH LANGUAGE ARTS SL.8.5 Integrate multimedia and visual displays into presentations to clarify information, strengthen claims and evidence, and add interest. 4A Unit 1 Waves

2 Supporting All Students, All Standards Integrating the Three Dimensions of Learning In this lesson, students will recognize that waves are disturbances that transfer energy in a repeating pattern with a specific wavelength, frequency, and amplitude (DCI PS4.A-1 Wave Properties). They will observe that waves can be represented using graphs and charts that make it possible to identify patterns (CCC Patterns) and compare wave properties (DCI PS4.A-1 Wave Properties). Students will observe and make models to represent different types of waves and relate energy to amplitude. Students will use mathematical and computational thinking (SEP Using Mathematics and Computational Thinking) to describe wave speed and the relationship between changes in energy and amplitude. Preassessment Have students complete the unit pre-test online or see the Assessment Guide. Build on Prior Knowledge Students should already know and be prepared to build on the following concepts: SEP Construct an explanation that includes qualitative or quantitative relationships between variables that describe phenomena. (Mod D, Unit 2, Lessons 2, and 3) DCI Waves of the same type can differ in amplitude (height of the wave) and wavelength (spacing between wave peaks). (Grade 4) CCC Matter is conserved because atoms are conserved in physical and chemical processes. (Mod J, Unit 3, Lesson 2) CCC The transfer of energy can be tracked as energy flows through a designed or natural system. (Mod J, Unit 3, Lesson 3) Have a brief discussion to differentiate between matter and energy. Review these topics with students to prepare them to understand that energy can travel through matter through the vibration of particles. Professional Development Content Background Energy is anything that can do work or cause change. Energy can be transferred through a medium by causing the particles of the medium to vibrate back and forth. When the first particles become energized, they vibrate. As they do, the particles transfer energy to the particles next to them, causing those particles to vibrate. As particles lose energy, they slow down and return to their resting states. In this way, energy is transferred from one part of a medium to another. When this process is regular and repeating, the energy is transferred as a wave. Waves can transfer energy in different ways, which determine whether the wave is transverse or longitudinal. In a transverse wave, the particles of the medium vibrate perpendicular to the direction of energy transfer. In a longitudinal Differentiate Instruction Lesson Vocabulary wave amplitude wavelength frequency wave speed Reinforcing Vocabulary Ask students to create a description wheel for each of the vocabulary terms. Students should write the word, its definition, and several details related to it. Go online to view Professional Development videos with strategies to integrate CCCs and SEPs, including the ones used in this lesson. wave, the particles of the medium vibrate parallel to the direction of energy transfer. Both transverse and longitudinal waves are described by several properties, including wavelength, amplitude, frequency, and wave speed. It is helpful to graph waves in order to identify patterns in their properties. One characteristic that becomes obvious on a graph is amplitude. The amplitude of a wave is related to the amount of energy being transferred. As energy increases, the amplitude increases as well. ELL Multiple Meaning Words Remind students that some words in English have more than one meaning. For example, a common meaning of wave is to use a hand gesture to say hello or goodbye. Explain that in science, the word wave means a repeating disturbance that transfers energy. Ask students to describe any prior experiences with waves. Lesson 1 Introduction to Waves 4B

3 ENGAGE: Lesson Phenomenon Lesson Objective Students investigate and model the relationship between properties of waves and wave behavior. Throughout the lesson, students will use what they learn about waves to determine if a falling row of dominoes constitutes a wave. Introduction to Waves SEP Asking Questions and Defining Problems Alternative Engage Strategy Do The Wave Whole class 10 minutes Ask students if they have ever seen or participated in the wave at an event. Explain it to any students who may not be familiar with it. Then have students stand up in a circle around the classroom. When you point to a student, ask that student to start the wave. Have students observe as the wave moves back to the student who started it. As students become comfortable with the motion, challenge them to move the wave around the circle several times at different speeds. Once students return to their seats, discuss the characteristics of the wave they made. Lead students to include terms, such as energy, pattern, repetition, and speed in their discussion. Supporting the Unit Project As students work through this lesson, encourage them to think about what types of waves they interact with in daily life. Students should think about what properties of those waves might affect their interactions with the wave. Ocean waves can be described by the same properties as some other kinds of waves. By the end of this lesson... you will be able to model and discuss similarities and differences between waves you encounter every day. Houghton Mifflin Harcourt Image Credits: Willyam Bradberry/Shutterstock 4 Unit 1 Waves 4 Unit 1 Waves Propose Your Own Path Throughout the lesson, encourage students to ask questions about concepts they do not understand. Students may use the Research Proposal Worksheet online in the Elaborate section to explore questions further.

4 CAN YOU EXPLAIN IT? Do falling dominoes form a wave? Go online to view the digital version of the Hands-On Lab for this lesson and to download additional lab resources. Can You Explain It? Students are asked to decide if falling dominoes form a wave. Students will collect evidence related to this phenomenon throughout the lesson and revisit the question at the end of the lesson to use what they have learned to explain if the falling dominoes exhibit characteristics of waves. The person in the picture transfers energy from himself to the first domino, which causes the rest of the dominoes to fall. 1. How does the energy from the person's hand get to the last domino? Collaboration Group Activity Provide groups of students with dominoes. Have them set the dominoes up in a row. Allow them to be creative in their setups. Have them tip the first domino over and observe what happens to the others. Allow students to experiment with placing the dominoes closer together and farther apart to determine how it affects the falling motion. Houghton Mifflin Harcourt Image Credits: JGI/Blend Images/Getty Images EVIDENCE NOTEBOOK As you explore the lesson, gather evidence to help explain whether the domino example is similar to a wave. 1. should describe how the first domino transfers energy to the next domino. Sample answer: When the person pushes the first domino, it falls into the second domino. When the first domino falls into the second domino, it transfers energy to the second domino. This continues until all of the dominoes have fallen. EVIDENCE NOTEBOOK Encourage students to use a graphic organizer, such as a main idea and supporting details organizer, to set up their notebook to record evidence related to the lesson phenomenon. Find more strategies in the online ELA Handbook. Lesson 1 Introduction to Waves 5 Lesson 1 Introduction to Waves 5

5 EXPLORATION 1 Exploring Waves 3D Learning Objective Students relate energy transfer to waves and recognize that a simple wave has a repeating pattern. They will analyze models to identify patterns in waves. Differentiate Instruction DCI Explore ONLINE! PS4.A Wave Properties Students observe the properties of a wave to relate wave motion to the movement of energy. EXPLORATION 1 Exploring Waves Water crashing onshore, the spotlight on center stage, a siren blaring. These things may seem unrelated, but they have one thing in common waves. The world is full of waves, including water, light, and sound waves. A wave is a repeating disturbance that transfers energy from one place to another. When a swimmer jumps into the pool, it doesn t just make a big splash. It also causes waves to spread through the pool. RTI/Extra Support Have students share an experience they may have had in a tube, on a raft, or in a boat as waves passed. Then have students relate their experiences to that of the bug in the animation. On Level Ask students to review the diagram of the bug on water. Ask several questions to confirm that students understand the content. Ask about the directions in which the bug, wave, and water move. Relate this to the direction in which energy travels. Connection to English Language Arts To introduce the topic of waves, challenge students to create a storyboard for a video that describes a wave. Students can present the video as a series of frames, each of which should be shown on the storyboard. Allow students to present their storyboards and explain how they define a wave. Hold a class discussion about how showing the wave in this format helps viewers learn more about what is being shown. SL Think about the energy that was needed to form the wave in the pool. Where did the energy come from? Waves Transfer Energy A wave transfers energy in the direction that the wave travels. In the picture of the bug, the wave travels to the right, so energy is being transferred to the right. How much energy is transferred? That depends on the size of the disturbance. The greater the disturbance, the more energy is transferred. However, a wave does not transfer matter. The matter, or medium, in which a wave travels does not move along with it. Waves are quite varied and can be complex, but we can learn a lot from a simple wave. The rope wave on the next page shows energy being transferred in the direction the wave is traveling. Waves on a pond move toward the shore, but the bug only bobs up and down due to a small disturbance. Explore ONLINE! Houghton Mifflin Harcourt Image Credits: Victoria Snowber/The Image Bank/Alamy 2. should include that the energy came from the person who jumped into the pool. 6 Unit 1 Waves 6 Unit 1 Waves Find more support in the online ELA Handbook.

6 Houghton Mifflin Harcourt Image Credits: (bl) Denis Trofimov/Shutterstock; (br) Nicholas Diehm/Image Bank Film/Getty Images 3. Look at the wave that is traveling through the rope. The left end of the rope is being shaken, so the wave is traveling to the right / left. The energy of the wave travels to the right / left along the rope. As the wave goes by, each piece of the rope moves up and down / along with the wave. Waves Can Be a Pulse or a Repeating Movement As a wave travels, energy is transferred. If the wave s energy is transferred only one time, then a wave pulse is formed. You can see the single pulse disturbance as it moves through the medium. If the disturbance transfers energy in a repeating pattern, then a wave is formed. You can see the wave moving continuously. pulse A finger plucks a guitar string one time, creating a wave pulse. A wave forms when energy is transferred in a repeating pattern. 4. Discuss Together with a partner, look at the two photos and compare your observations. What wave patterns do you observe? Think about how they are similar and how they are different. Summarize your conclusions. repeating The points on the rope vibrate perpendicularly, or up and down, to the direction that the wave moves. Differentiate Instruction CCC Explore ONLINE! Patterns ELL Encourage students to watch the animation of the wave in the rope. Review the terms parallel and perpendicular. Hold up two rulers in each position and ask students to use the terms to describe how the rulers are arranged. Then direct students to the diagram or video of the wave along the rope. Ask students how they would add arrows representing the movement of energy perpendicular to the rope. RTI/Extra Support Ask students to give examples of events that occur once and events that repeat. Have students draw examples to represent pulse patterns and repeating patterns. Explore ONLINE! Collaboration Small Groups Encourage students to watch videos of traveling waves. In small groups, have students hold a plastic ruler off the edge of a desk and observe its movement after they strike it. Have students pluck it repeatedly and continue to observe. Encourage students to discuss what happened to the ruler in each case. Lead them to recognize that striking the ruler once resulted in vibrations like a pulse wave, while plucking it repeatedly created a repeating wave movement. Lesson 1 Introduction to Waves 7 3. right, right, up and down; The left end of the rope is shaken, so the wave travels away from it, toward the right end of the rope. 4. Sample answer: The guitar string is plucked once; the vibrating string is the result of a single wave. The heart monitor shows waves resulting from the repeating pattern of a beating heart. Lesson 1 Introduction to Waves 7

7 EXPLORATION 1 Exploring Waves, continued DO NOT EDIT--Changes must be made through File info LONumber=6P1_0910; CorrectionKey=NL-B EVIDENCE NOTEBOOK 5. should include that dominoes transfer energy in the direction that they move and exhibit the property of a pulse, not of a repeating series. Connection to Earth Science CCC Cause and Effect To help students understand the diagram, remind them that Earth s crust is broken into large regions called tectonic plates. When plates slide in opposite directions, a great amount of force is generated. This force causes the plates to slip and release energy as an earthquake. EVIDENCE NOTEBOOK 5. Do the dominoes from the beginning of the lesson exhibit any of the properties of waves discussed so far? List each of the properties. For each property, indicate whether the dominoes exhibit that property and record the evidence to support your statement. Compare a Tsunami to Smaller Water Waves Waves can be different sizes and shapes, and they can transfer different amounts of energy. A tsunami is a large ocean wave caused by a disturbance in or around the sea. It takes a great amount of energy to generate such a large wave. A tsunami can cause a lot of destruction once it reaches land. The Formation of a Tsunami 3 2 FORMATIVE ASSESSMENT DCI Wave Properties 4 Students compare the properties of two different kinds of waves a tsunami and a wave in a swimming pool. 1 Ask: How is a wave formed in water? Sample answer: Some water particles are pushed and collide with the particles near them. Ask: When you are in a pool or at the beach, how does the energy transferred to you from the waves relate to the frequency of the waves? Sample answer: The energy increases when the frequency increases. 6. should include the wave motion of a tsunami to a wave formed in a swimming pool. Sample answer: The person jumping into the pool is like the fault movement that causes the tsunami wave. The waves in the pool and the waves of the tsunami move outward from the disturbance. The greater the disturbance, the more energy that is transferred, thus the larger the resulting wave An underwater fault in the ocean floor releases a massive amount of energy and displaces the water above it. Waves are formed as energy moves outward from the fault. The waves build quickly and move as fast as 800 km/h. In deep water, the waves only rise cm above sea level, but the wave may be hundreds of miles long. 3 4 The waves approach the shallower coastline and undergo a change. As the bottom of a wave hits the beach floor, the wave slows down, increases in height, and decreases in wavelength. At the coast, the waves are at their largest. These giant waves crash onto the shore and can cause massive damage. 6. What does a tsunami wave have in common with the wave generated by a person jumping into a pool? Unit 1 Waves Houghton Mifflin Harcourt 6L_CNLESE861053_U01L01EXP1.indd 8 5/16/2017 2:31:18 AM 8 Unit 1 Waves

8 EXPLORATION 2 Comparing Longitudinal and Transverse Waves EXPLORATION 2 Comparing Longitudinal and Transverse Waves As a wave travels through a medium, the particles of the medium move, or vibrate. Think back to the wave in the rope. If the wave is traveling to the right, which way are the pieces of rope moving? Up and down. The parts of rope are the particles of the medium. In this case, the particles vibrate perpendicularly (up and down) to the direction the wave travels (to the right). This is an example of a transverse wave. In another type of wave, the particles vibrate parallel to the direction the wave travels. This is called a longitudinal wave. During an earthquake, both types of waves occur. 3D Learning Objective Students recognize that all waves have a repeating pattern. Students understand that in transverse waves, the energy flow perpendicular to the direction of vibration of the medium and in longitudinal waves, the energy flows parallel to the direction of vibration of the medium. Students record observations in charts to compare transverse and longitudinal waves, and they use mathematical and computational thinking to model the two types of waves. DCI PS4.A Wave Properties Students analyze earthquake damage to observe the up and down motion of a wave pattern. Houghton Mifflin Harcourt Image Credits: SDubi/Shutterstock During an earthquake, the ground can move in dramatic ways. Powerful waves both longitudinal and transverse waves travel through Earth s crust. 7. Language SmArts Study the photo. What type of movement do you think is responsible for the damage shown? How could you relate the ground movement during an earthquake to wave type? Create a visual model to clarify how the waves cause damage. Language SmArts SL.8.5 Integrate multimedia and visual displays into presentations to clarify information, strengthen claims and evidence, and add interest. Make sure students use specific evidence from the photo of the roadway when answering which wave type they think caused the damage shown. Students may have an easier time drawing how the roadway moved with the wave and labeling it than explaining their thought process verbally. 7. should include that the road looks like it cracked because the ground moved up and down. A transverse wave could have caused the damage because transverse waves move up and down. The road also looks like it cracked because the ground was pushed together and then stretched. A longitudinal wave could have caused some of the damage because longitudinal waves move back and forth. Lesson 1 Introduction to Waves 9 Find more support in the online ELA Handbook. Lesson 1 Introduction to Waves 9

9 EXPLORATION 2 Comparing Longitudinal and Transverse Waves, continued Hands-On Lab Partners 15 minutes Model Two Types of Waves SEP Developing and Using Models Students construct models to represent longitudinal and transverse waves. Students compare their models to observe the repeating patterns of the two types of waves. Safety Information Remind students to review all safety cautions and icons before beginning this lab. Ensure they wear goggles to prevent the coiled springs from hitting their eyes. Remind students that they can get cut if they handle the coils improperly. Putting This Lab in Context Encourage students to consider this activity in a larger context. What do all waves have in common? What are some ways waves can differ from one another? What are some examples of waves in the real world? Hands-On Lab Model Two Types of Waves You will use a coiled spring toy to model two types of waves: a longitudinal wave and a transverse wave. Procedure STEP 1 Hold a coiled spring toy on the floor between you and a lab partner so that the spring is straight. This is the rest position of the spring. You and your lab partner should be facing each other. Another lab partner will document each step. STEP 2 Move one end of the spring left and right at a constant rate. Record your observations for Wave 1. Based on your observations, identify the type of wave you generated in this step. Wave Wave 1 Observations and Wave Types MATERIALS coiled spring toy STEP 2 Observations should indicate a transverse wave. Sample answer: The wave was curvy and alternated between high points (crests) and low points (troughs). It was a transverse wave. Wave 2 STEP 4 Observations should indicate a longitudinal wave. Sample answer: The wave stayed in line, but there were alternating areas of coils close together (compressions) and coils spread out (rarefactions). It was a longitudinal wave. STEP 3 Allow the spring to return to its rest position. Be sure you and the lab partner holding the other end of the spring are facing each other. STEP 4 Push the spring toward your partner and then pull the spring backward repeatedly at a constant rate. Record your observations for Wave 2. Based on your observations, identify the type of wave you generated in this step. Houghton Mifflin Harcourt 10 Unit 1 Waves Student Lab Worksheet available online 10 Unit 1 Waves

10 Analysis STEP 5 Discuss Together with your partner, compare the waves you made. How are they alike? How are they different? What patterns did you observe? Include examples from your investigation. STEP 5 Sample answer: For both waves, energy was transferred in the direction of travel. Energy was transferred from me to my lab partner holding the other end of the spring. In the first wave, the spring was curvy. We formed alternating areas of high points (crests) and low points (troughs). In the second wave, the spring stayed in a straight line, but there were areas where the coils were close together (compressions) and other areas where the coils were spread out (rarefactions). Longitudinal and Transverse Waves Both longitudinal waves and transverse waves transfer energy in the direction they travel. However, they differ in the way the disturbances move in relation to the direction of wave motion. In a longitudinal wave, the coils move parallel to the direction the wave travels. An area where the coils are close together is called a compression. An area where the coils are spread out is called a rarefaction. In a transverse wave, the coils move perpendicularly to the direction the wave travels. The highest point of the wave is called a crest, and the lowest point is called a trough. There are other types of waves in the world. In fact, there is another kind of wave that is a combination of longitudinal waves and transverse waves. This is referred to as a surface wave. A ripple on a pond is an example of this combined wave type. 8. Label the type and parts of the waves shown here. Hands-On Lab Scoring Rubric Points Criteria Follows lab procedures carefully and fully Uses safety equipment consistently and appropriately, displays knowledge of safety procedures and hazards Supports conclusions and explanations with valid and reliable evidence longitudinal wave WORD BANK longitudinal wave transverse wave compression rarefaction crest trough CCC Patterns Records observations clearly and completely Students use visual representations of wave models to compare the characteristics of two types of waves. Houghton Mifflin Harcourt Differentiate Instruction ELL Confirm student understanding of the words crest and trough. List synonyms for crest, such as top, tip, and crown. Help students relate these words to the highest point on a wave diagram. Then have students list synonyms for trough and relate these words to the lowest point on a wave diagram. Lesson 1 Introduction to Waves From left to right: compression, rarefaction, transverse wave, crest, trough Lesson 1 Introduction to Waves 11

11 EXPLORATION 2 Comparing Longitudinal and Transverse Waves, continued EVIDENCE NOTEBOOK 9. should include similarities between falling dominoes and longitudinal waves. Sample answer: The dominoes move parallel to the direction in which energy is transferred. The movement of the dominoes is like the back and forth motion of particles in a longitudinal wave. However, the dominoes do not move back and forth. They only move in one direction. DCI PS4.A Wave Properties Students relate their understanding of waves to models of earthquake waves in the real world. Misconception Alert Particle Motion As students continue to observe diagrams of waves, they may not realize that the particles of the medium are not being transported with the wave. After the disturbance passes, the particles return to their resting positions. Students may incorrectly envision moving water in a stream. Use these diagrams and student observations from the lab to point out that the particles in the medium stop vibrating over time and do not travel with the energy. EVIDENCE NOTEBOOK 9. Remember the dominoes from the beginning of the lesson? Describe the movement of the dominoes as energy is transferred through them and then compare the movement of longitudinal waves to the movement of the dominoes. Record your evidence. Analyze the Types of Waves in Earthquakes Earthquakes produce both longitudinal waves and transverse waves. Both are types of mechanical waves, waves that transfer energy through a medium. Earthquake waves travel through Earth s crust. Longitudinal waves and transverse waves often travel at different speeds in a medium. During earthquakes, longitudinal waves are faster. They arrive first during an earthquake. Seconds later, the transverse waves arrive. These waves are slower but usually more destructive. 10. Based on what you learned in the modeling activity, label the two images below as an example of either a longitudinal wave or a transverse wave. FORMATIVE ASSESSMENT Have students use what they know about waves to decide why longitudinal waves are faster than transverse waves. Students should consider how matter is affected by each type of wave. 10. transverse, longitudinal; The first wave is transverse because the ground moves back and forth, but the energy moves toward the right. The second wave is longitudinal because the ground moves in the same direction as energy is transferred. 11. longitudinal, transverse, energy; Earthquakes cause destructive seismic waves that travel through the ground During an earthquake, if you see the ground moving forward and backward, then you are probably experiencing a longitudinal / transverse wave. If you see the ground moving up and down, then it s likely a longitudinal / transverse wave. In both cases, matter / energy is being transferred. Unit 1 Waves Houghton Mifflin Harcourt 12 Unit 1 Waves

12 EXPLORATION 3 Identifying the Properties of Waves Houghton Mifflin Harcourt Image Credits: EuroStyle Graphics/Alamy rest position Identifying the Properties of Waves Picture it: It s a calm day on a quiet street. Nobody is around. A car pulls up to the curb and parks. The driver gets out of the car, pulls down his hat to hide his face, and hurries away. Suddenly, the car explodes! This is part of an exciting scene from a movie. The explosion created a blast wave. A high-pressure wave radiated out with great energy from the center of the explosion. Special effects experts carefully design and carry out these types of controlled explosions. They also set up situations that look like what would happen after an explosion without actually putting people and property in the path of the blast wave. 12. A film crew is setting up a scene to show the effects of a blast wave on nearby cars. Why do you think the crew has suspended the cars by cables? wavelength amplitude trough EXPLORATION 3 Properties of Waves Can Be Graphed An explosion is a high-energy event that happens very quickly. A big part of a special effects team s job is ensuring the safety of people and the environment. Waves are described by their properties. A measure of how far a particle in the medium moves away from its normal rest position is the amplitude. Amplitude is half of the difference between the crest and the trough. The distance from any point on a wave to an identical point on the next wave pulse is the wavelength. Wavelength measures the length of one cycle, or repetition, of a wave. Waves can be represented on a graph. crest amplitude wavelength 13. Discuss In a small group, discuss the wave characteristics shown in the image above. Explain why the wavelength can be measured as the distance between consecutive peaks or consecutive troughs. Find more support in the online Math Handbook. Lesson 1 Introduction to Waves 13 3D Learning Objective Students are introduced to measurable properties of waves and see that each wave has a specific wavelength, frequency, and amplitude. They learn how graphs and charts can be used to identify patterns in data. Students use mathematical and computational thinking to analyze wave measurements and relate energy to amplitude. Exploring Visuals CCC Patterns When a transverse wave is graphed, it appears similar to the physical wave it represents. However, a longitudinal wave appears different than the physical wave when graphed. To graph a longitudinal wave, the wave s compression and rarefaction at a certain location over time are graphed. When graphed, the longitudinal wave will look similar to a transverse wave. The peaks of the graph correspond to the compression of the longitudinal wave. The dips of the graph correspond to the rarefaction of the longitudinal wave. Connection to Math As students observe the graph, remind them about linear functions. Have students describe the shape of a graph of a linear function. Ask: Can the graph of a wave be described by an equation in the form y = mx + b? Why or why not? Sample answer: No, because waves are repeating patterns. Their graphs do not form straight lines. 8.F.A should include an understanding of how special effects crews make it look like blast waves are affecting cars. Sample answer: The cables make it look like the wave blasted the cars into the air. 13. should include that a wave moves from the rest position in a regular pattern. The distance between any two consecutive corresponding points is the same. So wavelength can be measured from peak-to-peak or trough-to-trough. Lesson 1 Introduction to Waves 13

13 EXPLORATION 3 Identifying the Properties of Waves, continued Hands-On Lab Small groups 20 minutes Investigate Waves SEP Using Mathematics and Computational Thinking Students investigate the relationship between wave energy and mediums in which the waves travel. Safety Information Ensure students wear goggles and follow safety procedures for spills to prevent slipping and falling. Putting This Lab in Context Encourage students to consider this activity in a larger context. What happens to a boat when a wave passes it? What effect does the amount of energy in a wave have on the boat? STEP 3 Sketches and descriptions should show that the cork remains in the same place as it bobs up and down. Hands-On Lab Investigate Waves You will investigate how mechanical waves in a water-filled tray affect the medium they pass through. Procedure and Analysis STEP 1 Fill the tray about halfway with water. Place a cork in the water near the center of the tray. STEP 2 Choose one group member to move the block up and down in the water at one end of the tray to create waves. STEP 3 Observe the motion of the cork and the water. Sketch and describe your observations. MATERIALS block, rectangular wood cooking trays, aluminum, deep cork water STEP 4 Sample answer: The frequency of the wave is related to how often the block is moved up and down. The more often the block is moved, the more energy is transferred to the wave, and the higher frequency of the wave. STEP 5 Sample answer: I could tap the water with the end of my pencil and record observations about wave size and the path they take. I could repeat this using two pencils at once. In comparing my observations, I can determine differences in wave height. Hands-On Lab Scoring Rubric Points Criteria Follows lab procedures carefully and fully Identifies relationships Develops claim based on evidence STEP 4 What is the relationship between the energy of the wave you created in Step 2 and the wave s frequency? STEP 5 How could you test the following question: Do waves made by a large disturbance carry more energy than waves made by a small disturbance? 14. Collaborate With a partner, create an informational pamphlet that teaches a student how to graph the properties of a wave. You may use any wave source in your examples. Houghton Mifflin Harcourt 14. Students should choose a wave source and explain how to show amplitude, wavelength, and wave period on a graph. 14 Unit 1 Waves 14 Unit 1 Waves Student Lab Worksheet available online

14 Frequency and Speed in a Wave Think about the water waves you made. The number of waves that you could make in five seconds depended on how quickly you moved the block. The number of waves produced in a set amount of time is the frequency of the wave. Frequency is usually expressed in hertz (Hz). For waves, one hertz equals one wave per second (1 Hz = 1/s). The rate at which a wave travels is wave speed. It can be calculated by multiplying wavelength and frequency. 15. Do the Math The equation for wave speed (v) can be calculated using wavelength (λ) and frequency (f): v = λ f. For example, to determine the wave speed of a wave that has a wavelength of 5 m and a frequency of 4 Hz, replace the λ and f with the values given and solve: v = 5 m 4 Hz = 20 m/s. What is the speed of a wave that has a wavelength of 2 m and a frequency of 6 Hz? Do the Math 7.EE.B.4 Use variables to represent quantities in a real-world or mathematical problem, and construct simple equations and inequalities to solve problems by reasoning about the quantities. Students use the formula for wave speed to calculate the speed of a wave given its wavelength and frequency m/s; 2 m x 6 Hz = 12 m/s Houghton Mifflin Harcourt Image Credits: (t) Rita Melo/EyeEm/Getty Images; (b) Greg Ewing/Getty Images Energy and Amplitude in a Wave The amplitude of a wave is dependent on energy. For example, when using a string to make waves, you have to work harder to create a wave with a large amplitude than to create one with a small amplitude. It takes more energy to move the string farther from its rest position. When comparing waves of the same frequency in the same medium, the energy of a wave is proportional to the amplitude of the wave squared. A wave with a large amplitude carries more energy than a wave with a small amplitude does. Energy Is Proportional to Amplitude Amplitude most energy least energy most energy Time 16. Engineer It An engineer has been asked to give advice about a wave pool at a local water park. The wave pool is generating waves that move too fast for the safety of park guests. Explain why the engineer suggested reducing the frequency of the wave generator. Lower amplitude waves are perfect for a fun day at the beach. Surfers need higher amplitude waves to catch an exciting ride. CCC Patterns Students analyze a graph to compare the properties of different wave patterns. Collaboration Claims, Evidence, Reasoning Distribute a short string or shoelace to small groups of students. Have them tie one end to the back of a chair while a student moves the other end of the string up and down. Ask students to observe the string. Encourage students to change the amplitude of the wave by moving their hands farther. Invite students to state a claim about the relationship between their hand movement and the amplitude of the wave. Ask them to use their observations as evidence and explain their reasoning for the relationship. Engineer It Identify Solutions Students identify why an engineer proposed a solution for the safety of a wave pool. Students must relate their understanding of the relationship among energy, frequency, and amplitude to this engineering problem. Find more support in the online Math Handbook. Lesson 1 Introduction to Waves need to relate the solution to the problem. Sample answer: Wave speed is a product of frequency and wave length. If the wave generator is set to a lower frequency, the wave length will be the same, but the wave speed will be lower. Lesson 1 Introduction to Waves 15

15 EXPLORATION 3 Identifying the Properties of Waves, continued Do the Math 7.RP.A.2 Recognize and represent proportional relationships between quantities. Students relate the energy of a wave to its amplitude. 17. If energy increases by a factor of 25, then amplitude increased by a factor of 5 because energy is proportional to the square of the amplitude. Differentiate Instruction SEP Using Mathematics and Computational Thinking RTI/Extra Support When two quantities are proportional, the ratio of the quantities is constant. Energy is proportional to the square of a wave s amplitude. So if energy changes by a factor of 36, the square of the wave s amplitude changes by a factor of 36. The change in amplitude would be 6, which is the square root of 36. FORMATIVE ASSESSMENT Language SmArts Apply Your Wave Knowledge of Wave Energy and Amplitude WHST Write informative/explanatory texts to examine a topic and convey ideas, concepts, and information through the selection, organization, and analysis of relevant content. Ask students to identify information from the text relevant to the situation of the special effects team. Calculate Amplitude The relationship between amplitude and wave energy is that energy is proportional to amplitude squared. For example, if the amplitude of the waves at one beach is three times the amplitude of the waves at another beach, you might think that the higher waves had three times as much energy as the smaller. However, it turns out that the higher waves would actually have nine times as much energy (because nine is three squared)! But what if we started by knowing energy instead? If your lab partner told you the energy of a wave had increased by a factor of 16, then how must the amplitude have changed? The amplitude must have quadrupled (because 4 is the square root of 16). If you know one variable, you can use the relationship between amplitude and energy to find the other variable. 17. Do the Math Suppose the energy of a wave increased by a factor of 25. By what factor did the amplitude of the wave increase? Language SmArts Apply Your Knowledge of Wave Energy and Amplitude Think back to the movie scene where the car explodes. Special effects experts have to know how to keep people on the set safe during such dangerous scenes. An explosion produces a blast wave that radiates out with a lot of energy. Special effects experts apply their knowledge of wave energy and amplitude when designing a safe controlled explosion. 18. Special effects experts want the largest explosion that is safe for the people on set. Knowing that the energy of a wave is proportional to its amplitude squared helps them mathematically model the energy of the explosion and the amplitude of the blast wave. How does this knowledge help them determine where to place the actors and crew? The special effects team is working hard to modify a vehicle for a special effect that will only last a few seconds. Houghton Mifflin Harcourt Image Credits: Rick Doyle/Corbis 18. Sample answer: Special effects experts know that more explosives will make a bigger wave. They know that they need to place the actor farther away for explosions with more energy because the blast wave will be bigger. 16 Unit 1 Waves Find more support in the online Math Handbook. Find more support in the online ELA Handbook. 16 Unit 1 Waves

16 TAKE IT FURTHER Continue Your Exploration Houghton Mifflin Harcourt Image Credits: (t) Volker Steger/Photo Researchers, Inc. (b) Gib Martinez/Alamy Name: People in Science TAKE IT FURTHER Continue Your Exploration Hands-On Labs Earthquakes and Waves Propose Your Own Path James West, Research Scientist Date: Check out the path below or go online to choose one of the other paths shown. James West s parents wanted him to be a medical doctor, but he wanted to study physics. His father was sure he d never find a job that way. But West wanted to study what he loved. He did study physics, and he did find a job. He worked for Bell Laboratories and developed a microphone called the electret microphone. Today, West s microphone is in almost all telephones, cell phones, and other equipment that records sound. West s interest in the microphone started with a question about hearing. A group of scientists wanted to know how close together two sounds could be before the ear would not be able to tell them apart. They needed a very sensitive microphone to produce the sounds for their tests. At the time, there was no microphone sensitive enough. West and fellow scientist Dr. Gerhard Sessler found that they could make a more sensitive microphone by using materials called electrets. The new microphones were cheaper, more reliable, smaller, and lighter than any microphone before. Go online to choose one of these other paths. James West s research into sound waves and hearing has helped make microphones smaller. Explore ONLINE! Collaboration You may choose to assign this path or direct students online to the Interactive Online Student Edition where they can explore and choose from all four paths. These activities can be assigned individually, to pairs, or to small groups. People in Science Students explore the contributions of research scientist James West. Special emphasis is placed on his development of a smaller microphone using his understanding of waves and how they can be detected and transmitted. (Outside research is not required.) DCI PS4.A-1 Wave Properties, CCC Patterns Differentiate Instruction RTI/Extra Support Confirm that students understand the properties behind a microphone. Explain that a microphone is a device that changes sound waves into electrical signals that can be transmitted to other devices, made louder, or recorded. Extension Have students work in small groups to discuss other devices that have been made smaller, such as cellular telephones and cameras. Ask them to think about the advantages of reducing the sizes of certain technology. Have students choose one example and discuss pros and cons of reducing its size. Propose Your Own Path Research Proposal Worksheet available online Lesson 1 Introduction to Waves 17 Remind students that they can pursue any questions they developed as they worked through the lesson as part of the Propose Your Own Path. Students can present their findings in a variety of formats, including a class presentation, a debate, or a research paper. Lesson 1 Introduction to Waves 17

17 TAKE IT FURTHER, continued 1. Sample answer: Research science can develop new technologies, which in turn can lead to other new discoveries. Mobile phones needed other technologies to be developed, but had the electret microphone not existed, cell phone development could have been further delayed as researchers had to develop a similar technology. 2. Sample answer: A research scientist studies how things work. Curiosity will make it more likely for a research scientist to continue studying a phenomenon until it can be understood. 3. Sample answer: If I were a research scientist I would be interested in studying biology, specifically how genetic diseases are inherited. I would study this because it is interesting how some people inherit these diseases when their siblings do not. 4. should include an explanation of the recent discovery and an idea for further research that this discovery will enable. DO NOT EDIT--Changes must be made through File info LONumber=6P1_0910; CorrectionKey=NL-B TAKE IT FURTHER Continue Your Exploration Microphones convert sound waves into electrical signals. The original design West and his colleagues were researching used a battery to power a dieletric material. An accident converted the dieletric material to an electret material. West and his colleagues began to study this new material and found it was not only more sensitive but did not require a battery to maintain its charge. Based on this evidence, the researchers reasoned that this material could be used in more sensitive microphones. At the time, they could not have foreseen the use of this technology in mobile phones, so the application was initially purely for research. 1. How does this example show that there is value in research science, even if a practical application for the science does not currently exist? 2. James West has always been interested in how things work. When he was younger, he enjoyed taking apart small appliances to see what was inside. Why would curiosity about how things work be useful to a research scientist? Explore ONLINE! The following are brief descriptions of the paths available online. Hands-On Labs Go online to view the digital version of the Hands-On Lab for this lesson and to download additional lab resources. Earthquakes and Waves Students relate the properties of waves to earthquakes. (This path requires additional research.) Propose Your Own Path Students develop a research proposal to explore a topic of their choice. Remind students that they can choose a question to explore that they developed over the course of the lesson. (This path requires additional research.) Research scientists work in all scientific disciplines. James West studied physics and focused his research around sound waves. If you were a research scientist, what discipline would you be most interested in studying and what specific topics would you be interested in focusing your research around? Explain why. 4. Collaborate Work with a group to find a recent discovery in wave research. As a group imagine how this discovery may lead to other applications. Share your ideas with the class. Unit 1 Waves Houghton Mifflin Harcourt 6L_CNLESE861053_U01L01TF.indd 18 5/16/2017 3:23:02 AM 18 Unit 1 Waves

18 LESSON SELF-CHECK Name: SELF-CHECK Can You Explain It? Date: Do falling dominoes form a wave? Can You Explain It? EVIDENCE NOTEBOOK Students should have gathered the following evidence to explain whether falling dominoes form a wave: Dominoes fall when energy is transferred to them. The energy is transferred in the direction they move. (Exploration 1) Dominoes do not exhibit a repeating pattern. (Exploration 2) Houghton Mifflin Harcourt Image Credits: JGI/Blend Images/Getty Images EVIDENCE NOTEBOOK Refer to the notes in your Evidence Notebook to help you determine whether falling dominoes are a wave. 1. State your claim. Make sure your claim fully explains whether falling dominoes form a wave. 2. Summarize the evidence you have gathered to support your claim and explain your reasoning. Lesson 1 Introduction to Waves Students may make one of two claims: Collapsing dominoes do form a wave, or collapsing dominoes do not form a wave. 2. Scoring Guidelines: should include the following: A description of a wave as a disturbance that transfers energy through a medium. An understanding of how the dominoes are the medium through which energy is transferred because energy is transferred from the finger to the last domino. A description of how each domino falls onto the next domino and stops. Once the dominoes fall down, they stay down. It is not possible to send a repeating pulse through the dominoes without setting them up again. In real waves, the particles eventually return to their original positions. Collaboration Cultivating New Questions After discussing the evidence, ask students to identify other questions. If needed, prompt a discussion. Ask: What are some other examples of wave-like phenomena you can think of? Are they really waves, or do they share some, but not all, properties of waves? This question could lead to a discussion of phenomena such as the way grasses ripple in the wind, or when people do the wave in a stadium. Consider revisiting this example when discussing Lesson 2 The Behavior of Mechanical Waves. Formal Assessment Lesson Quiz and other assessments available online Lesson 1 Introduction to Waves 19

19 SELF-CHECK, continued Checkpoints SUMMATIVE ASSESSMENT Using Representations to Assess Proficiency In Exploration 1, students learned that a wave is a repeating disturbance that transfers energy. As students analyze the diagrams, help them recall what properties all waves have in common. Make sure they recognize that the wave is traveling through the water and the ball is floating on the water. Using Vocabulary to Assess Proficiency In Exploration 3, students learned that waves can be described by properties including wavelength, amplitude, frequency, and wave speed. As students compare the waves, ask them to define each of the terms provided. Then have them describe what information they can learn by looking at the image and comparing the waves. SELF-CHECK Checkpoints Answer the following questions to check your understanding of the lesson. Use the image to answer Questions The upper wave shown in the image has more / less energy than the bottom wave, because the amplitude / wavelength / frequency of the upper wave is greater than the bottom wave. 4. Look at the bottom waveform. How many wavelengths are shown? A. 2.5 B. 4 C. 8 D. 16 Use the diagram to answer Question more; amplitude; Energy of a wave is related to the amplitude of the wave. A wave with a greater amplitude has more energy than a wave with a lower amplitude. 4. C; The waveform begins at a crest. Counting crest to crest shows a total of 8 wavelengths. 5. B and C; The particles of the medium, water, vibrate up and down so the ball moves along with the water. A wave is a disturbance that transfers energy. 6. B; The wave is traveling through the water. 5. Which statements are true about the diagram? Choose all that apply. A. The ball moves along with the wave as the wave moves. B. The ball moves up and down as the wave passes by. C. The wave transfers energy as it moves. D. The ball transfers energy to the wave. 6. Through which medium is the wave in the diagram traveling? A. Air B. Water C. Plastic D. Vacuum Explore ONLINE! Houghton Mifflin Harcourt Image Credits: Clive Streeter/Dorling Kindersley/Getty Images 20 Unit 1 Waves Explore ONLINE! Encourage students to go online to view the animation of a beach ball riding water waves. 20 Unit 1 Waves

20 Houghton Mifflin Harcourt Image Credits: (t) Victoria Snowber/The Image Bank/Alamy; (b) Greg Ewing/Getty Images SELF-CHECK Interactive Review Complete this section to review the main concepts of the lesson. A wave is a disturbance that transfers energy from one place to another. A wave transfers energy in the direction that it travels. Waves can travel as a single pulse or as a repeating series. A. Explain how a wave transfers energy from one place to another. Waves can be classified by comparing the direction of the disturbance and the direction the wave travels. B. Explain the difference between longitudinal and longitudinal wave transverse waves in terms of particle vibration. transverse wave Graphs can be used to represent waves. The key properties of waves include amplitude, wavelength, frequency, and wave speed. C. Use a model to explain how frequency and wavelength relate to wave speed. Interactive Review A. should include that particles in a wave vibrate and transfer energy in the direction of the wave. Sample answer: Particles in a wave vibrate in a repeating pattern. As the particles vibrate, the vibrations are transferred to nearby particles in a repeating fashion. In this way energy is transferred from one location to another. B. should include that when a longitudinal wave passes through matter, the matter moves back and forth parallel to the direction the wave is traveling. When a transverse wave passes through matter, the matter also moves back and forth. However, it moves perpendicular to the direction the wave is traveling. C. should include a model explaining the relationships among frequency, wavelength, and wave speed. Sample answer: The speed of a wave depends on the wavelength and frequency of the wave. Each time a cycle is completed, the wave will travel the distance of the wavelength. The frequency is how often a wavelength is completed, so the speed of the wave is the product of the frequency and wavelength. Explore ONLINE! Make Your Own Study Guide EVIDENCE NOTEBOOK Lesson 1 Introduction to Waves 21 Have students go online for strategies on how to make their own study guides in their Evidence Notebooks. Strategies include asking students to provide evidence to support Study Guide Statements specific to the lesson and collaborating with other students to study the lesson as a group. Lesson 1 Introduction to Waves 21