Chapter Waves. What is an oscillator? How can you describe the speed of a wave? How are sound waves and water waves similar and different?

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1 Chapter Waves The word waves might cause you to think of many things. Does going to a beach pop into your head? At the beach, you can enjoy the warm sunshine and swimming in water waves. Water waves come at regular intervals and seem to move up and down even as they move toward the shore. In this chapter, you will learn about water waves. You will also learn that you are surrounded by waves! Light and sound are waves. Our electronic devices depend on the transmission of waves. Whether a wave is occurring in water or in the air, it follows certain rules that you will learn about in this chapter. For example, wave-like motion is a type of harmonic, or repetitive, motion. A swing, a rocking chair, and all waves exhibit this kind of motion. Harmonic motion also includes motion that goes go around and around, such as a ferris wheel turning or Earth orbiting the Sun. In this sense, anywhere you go it s possible to catch a wave! What is an oscillator? How can you describe the speed of a wave? How are sound waves and water waves similar and different? 23

2 Chapter 23 WAVES 23.1 Harmonic Motion When you travel from one place to another, either on foot or by bicycle or car, you use linear motion. Linear motion goes from one place to another without repeating (Figure 23.1A). This chapter is about another kind of motion. Harmonic motion is motion that repeats over and over (Figure 23.1B). For example, our four seasons are caused by Earth s harmonic motion. Other types of harmonic motion cause your heartbeat and create sounds. Motion in cycles What is a cycle? Looking at one cycle To describe harmonic motion we need to learn how to describe a repeating action or motion. A cycle is one unit of harmonic motion. This motion can be back-and-forth or a full revolution or rotation. One full swing of a child on a swing is one cycle. As the child continues to swing, the back-and-forth motion or cycle repeats over and over again. A pendulum is a device that swings back and forth. We can use a pendulum to better understand a cycle. Each box in the diagram below is a snapshot of the motion at a different time in one cycle. VOCABULARY linear motion - motion that goes from one place to another without repeating. harmonic motion - motion that repeats in cycles. cycle - a unit of motion that repeats. pendulum - a device that swings back and forth due to the force of gravity. The cycle of a pendulum The cycle starts with (1) the swing from left to center. Next, the cycle continues with (2) center to right, and (3) back from right to center. The cycle ends when the pendulum moves (4) from center to left because this brings the pendulum back to the beginning of the next cycle. Once a cycle is completed, the next cycle begins without any interruption in the motion. Figure 23.1: (A) A sprinter is a good example of linear motion. (B) A person on a swing is a good example of harmonic motion. 554 UNIT 8 WAVES, SOUND, AND LIGHT

3 WAVES Chapter 23 Oscillators What is an oscillator? Equilibrium Restoring forces Inertia causes an oscillator to go past equilibrium An oscillator is a physical system that has repeating cycles (harmonic motion). A child on a swing is an oscillator, as is a vibrating guitar string. A wagon rolling down a hill is not an oscillator. Which properties determine whether a system will oscillate or not? Systems that oscillate move back and forth around a center or equilibrium position. You can think of equilibrium as the system at rest, undisturbed, with zero net force. A wagon rolling down a hill is not in equilibrium because the force of gravity that causes it to accelerate is not balanced by another force. A child sitting motionless on a swing is in equilibrium because the force of gravity is balanced by the tension in the ropes. A restoring force is any force that always acts to pull a system back toward equilibrium. Restoring force is related to the force of gravity or weight and the lift force (or tension) of the string of a pendulum (Figure 23.2). If a pendulum is pulled forward or backward, gravity creates a restoring force that pulls it toward equilibrium. Systems with restoring forces become oscillators. The motion of an oscillator is the result of the interaction between a restoring force and inertia. For example, the restoring force pulls a pendulum toward equilibrium. But, because of Newton s first law, the pendulum does not just stop at equilibrium. According to the first law, an object in motion tends to stay in motion. The pendulum has inertia that keeps it moving forward so it overshoots its equilibrium position every time. VOCABULARY oscillator - a physical system that has repeating cycles. restoring force - any force that always acts to pull a system back toward equilibrium. Figure 23.2: Restoring force keeps a pendulum swinging. Restoring force is related to weight and the lift force (or tension) of the string of a pendulum HARMONIC MOTION 555

4 Chapter 23 WAVES Frequency and period A period is the time to complete one cycle Frequency is the number of cycles per second Frequency is the inverse of period Harmonic motion can be fast or slow, but we don t use speed to tell the difference. This is because the speed of a pendulum constantly changes during its cycle. We use the terms period and frequency to describe how quickly cycles repeat themselves. The time it takes for one cycle to occur is called a period. A clock pendulum with a period of one second will complete one full back and forth swing each second. The frequency is the number of complete cycles per second. The unit of one cycle per second is called a hertz (Hz). Something that completes ten cycles each second has a frequency of 10 Hz. A guitar string playing the note A vibrates back and forth at a frequency of 220 Hz (Figure 23.3). Your heartbeat has a frequency between one-half and two cycles per second (0.5 Hz 2 Hz). Frequency and period are inversely related. The period is the number of seconds per cycle. The frequency is the number of cycles per second. For example, if the period of a pendulum is 2 seconds, its frequency is 0.5 cycles per second (0.5 Hz). VOCABULARY period - the time it takes for each complete cycle. frequency - how often something repeats, expressed in hertz. hertz (Hz) - the unit of frequency. One hertz is one cycle per second. When to use period or frequency PERIOD AND FREQUENCY T = Period (seconds) Frequency (hertz) 1 f Frequency (hertz) f = 1 T Period (seconds) While both period and frequency tell us the same information, we usually use period when cycles are slower than a few per second. A simple pendulum has a period between 0.9 and 2 seconds. We use frequency when cycles repeat faster. For example, the vibrations that make sound in musical instruments have frequencies between 20 and 20,000 Hz. Figure 23.3: All musical instruments use harmonic motion to create sound. 556 UNIT 8 WAVES, SOUND, AND LIGHT

5 WAVES Chapter 23 Solving Problems: Frequency and Period The period of an oscillator is 2 minutes. What is the frequency of this oscillator in hertz? 1. Looking for: You are asked for the frequency in hertz. 2. Given: You are given the period in minutes. 3. Relationships: Convert minutes to seconds using the conversion factor 60 seconds/1 minute; Use the formula: f = 1 / T. 4. Solution: 2 minutes 60 seconds/1 minute = 120 seconds The period (T) is 120 seconds. f = 1/120 s = Hz Figure 23.4: The parts of a pendulum clock. Your turn... a. Every 5 seconds, a pendulum completes one cycle. What are the period and frequency of this pendulum? b. The period of an oscillator is 1 minute. What is the frequency of this oscillator in hertz? c. How often would you push someone on a swing to create a frequency of 0.4 hertz? d. Figure 23.4 shows the parts of a pendulum clock. The minute hand moves 1/60 of a turn after 30 cycles. What is the period and frequency of this pendulum? e. A ferris wheel spins 5 times in 10 minutes. Calculate the period and frequency of the ferris wheel. a. The period is 5 seconds and the frequency is 0.2 Hz. b. The frequency is 0.02 Hz. c. You would need to push once every 2.5 seconds. d. There are 30 cycles/second so the frequency is 30 Hz. The period is 0.03 second. e. The frequency is Hz. The period is 120 seconds or 2 minutes HARMONIC MOTION 557

6 Chapter 23 WAVES Amplitude Amplitude describes the size of a cycle How do you measure amplitude? Damping and friction The size of a cycle is called amplitude. Figure 23.5 shows a pendulum with a small amplitude and one with a large amplitude. With a moving object like a pendulum, the amplitude is often a distance or angle. With other kinds of oscillators, the amplitude might be voltage or pressure. The amplitude of an oscillator is measured in units appropriate to the kind of harmonic motion being described. The amplitude is measured as the maximum distance the oscillator moves away from its equilibrium position. For the pendulum in Figure 23.6, the amplitude is 20 degrees because the pendulum moves 20 degrees away from the equilibrium position in either direction. The amplitude can also be found by measuring the distance between the farthest points the motion reaches. The amplitude is half this distance. The amplitude of a water wave is often found this way. Look at the illustration below. Friction slows a pendulum down, just as it slows all motion. That means the amplitude gets reduced until the pendulum is hanging straight down, motionless. We use the word damping to describe the gradual loss of amplitude. If you wanted to make a clock with a pendulum, you would have to find a way to keep adding energy to counteract the damping of friction so the clock s pendulum would work continuously. VOCABULARY amplitude - the amount that a cycle moves away from equilibrium. Figure 23.5: Small amplitude versus large amplitude. Figure 23.6: A pendulum with an amplitude of 20 degrees swings 20 degrees away from the center in either direction. 558 UNIT 8 WAVES, SOUND, AND LIGHT

7 WAVES Chapter 23 Graphs of harmonic motion Graphing harmonic motion It is easy to recognize cycles on a graph of harmonic motion. Figure 23.7 illustrates the difference between a graph of linear motion and a graph of harmonic motion. The most common type of harmonic motion graph places time on the horizontal (x) axis and position on the vertical (y) axis. The graph below shows how the position of a pendulum changes over time. The repeating wave on the graph represents the repeating cycles of motion of the pendulum. Finding the period Using positive and negative positions Showing amplitude on a graph In the graph above, the pattern repeats every 1.5 seconds. This repeating pattern represents the period of the pendulum, which is 1.5 seconds. If you were to cut out any piece of the graph and slide it left or right 1.5 seconds it would line up exactly. Harmonic motion graphs often use positive and negative values to represent motion on either side of a center (equilibrium) position. Zero usually represents the equilibrium point. Notice that zero is placed halfway up the y-axis so there is room for both positive and negative values. This graph is in centimeters, but the motion of the pendulum could also have been graphed using the angle measured relative to the center (straight down) position. The amplitude of harmonic motion can also be seen on a graph. The graph above shows that the pendulum swings back and forth from +20 centimeters to 20 centimeters. The equilibrium position is represented as the zero line. Therefore, the amplitude of the pendulum is 20 centimeters. Figure 23.7: A harmonic motion graph shows repeating cycles. SOLVE IT! Measuring Amplitude Use a protractor to find the amplitude (in degrees) of the pendulum in the graphic below HARMONIC MOTION 559

8 Chapter 23 WAVES Natural frequency and resonance Natural frequency Changing natural frequency How mass affects oscillators Periodic force and resonance An oscillator will have the same period and frequency each time you set it moving. This phenomenon is called natural frequency, the frequency at which a system naturally oscillates. Musical instruments use natural frequency. For example, guitar strings are tuned by adjusting their natural frequency to match musical notes (Figure 23.8). The natural frequency of an oscillator changes according to its length. In the case of a vibrating guitar string, you can shorten the string to increase the force pulling the string back toward equilibrium. Higher force means higher acceleration so the natural frequency is higher and the period is shorter. Lengthening an oscillator results in a lower frequency and a longer period. For oscillators with side-to-side movement, increasing the mass means the oscillator moves slower and the period gets longer. This is because of Newton s second law of motion as mass increases, the acceleration decreases proportionally. However, for a pendulum, changing the mass does NOT affect its period (also because of Newton s second law). The restoring force on a pendulum is created by gravity. Like in free fall, if you add mass to a pendulum, the added inertia is exactly equal to the added force from gravity. The acceleration is the same and therefore the period stays the same. A force that is repeated over and over is called a periodic force. A periodic force supplies energy to an oscillator and has a cycle with an amplitude, frequency and period. Resonance happens when a periodic force has the same frequency as the natural frequency. For example, small pushes (a periodic force) to someone on a swing add together if they are applied at the right time (once each cycle). In time, the amplitude of the motion grows and can become very large compared to the strength of the force! VOCABULARY natural frequency - the frequency at which a system oscillates when disturbed. periodic force - a repetitive force. resonance - an exceptionally large amplitude that develops when a periodic force is applied at the natural frequency. Figure 23.8: This guitarist is tuning his guitar by adjusting the natural frequency of the strings to match particular musical notes. 560 UNIT 8 WAVES, SOUND, AND LIGHT

9 WAVES Chapter Section Review 1. Which is the best example of a cycle: a turn of a wheel or a slide down a ski slope? 2. Describe one example of an oscillating system you would find at an amusement park. 3. What is the relationship between period and frequency? 4. Every 10 seconds a pendulum completes 2 cycles. What are the period and frequency of this pendulum? 5. What is the difference between a graph of linear motion and a graph of harmonic motion? 6. A graph of the motion of a pendulum shows that it swings from +5 centimeters to 5 centimeters for each cycle. What is the amplitude of the pendulum? Figure 23.9: Question What is the period of the oscillation shown in the diagram above? 8. Figure 23.9 shows a sliding mass on a spring. Assume there is no friction. Will this system oscillate? Explain why or why not. 9. Which pendulum in Figure will have the longer period? Justify your answer. 10. Why does mass NOT affect the period of a pendulum? 11. Resonance happens when: a. a periodic force is applied at the natural frequency. b. an oscillator has more than one natural frequency. c. a force is periodic and not constant. d. the amplitude of an oscillator grows large over time. Figure 23.10: Question HARMONIC MOTION 561

10 Chapter 23 WAVES 23.2 Properties of Waves A wave is an oscillation that travels from one place to another. A musician s instrument creates waves of sound that move through air to your ears. When you throw a stone into a pond, the energy of the falling stone creates waves in the water that carry energy to the edge of the pond. You are familiar with waves, but what are they exactly? What is a wave? Defining a wave If you poke a floating ball, it oscillates up and down. But something also happens to the water as the ball oscillates. The surface of the water oscillates in response and the oscillation spreads outward from where it started. An oscillation that travels is a wave. VOCABULARY wave - a traveling oscillation that has properties of frequency, wavelength, and amplitude. Why do waves travel? When you drop a ball into water, some of the water is pushed aside and up by the ball (A). The higher water pushes the water next to it (B). The water that has been pushed then pushes on the water next to it, and so on. The waves spread or propagate through the connection between each drop of water and the water next to it (C). Energy and information Waves are a traveling form of energy because they can cause changes in the objects they encounter. Waves also carry information, such as sound, pictures, or even numbers. Waves are used in many technologies because they quickly carry information over great distances. All the information you receive in your eyes and ears comes from waves. Figure illustrates the many types of waves in our environment. Figure 23.11: There are many types of waves in our environment. 562 UNIT 8 WAVES, SOUND, AND LIGHT

11 WAVES Chapter 23 Frequency, amplitude, and wavelength Waves are oscillators Wavelength Like all oscillators, waves have cycles, frequency, and amplitude. The frequency of a wave is a measure of how often it goes up and down at any one place (Figure 23.12). The frequency of one point on the wave is the frequency of the whole wave. Distant points on the wave oscillate up and down with the same frequency. A wave carries its frequency to every place it reaches. Like other frequencies, the frequency of a wave is measured in hertz (Hz). A wave with a frequency of one hertz (1 Hz) causes everything it touches to oscillate at one cycle per second. You can think of a wave as a moving series of high points and low points. A crest is the high point of the wave, a trough is the low point. Wavelength is the distance from any point on a wave to the same point on the next cycle of the wave (Figure 23.13). The distance between one crest and the next crest is a wavelength. So is the distance between one trough and the next trough. We use the Greek letter lambda for wavelength. A lambda (λ) looks like an upside down y. VOCABULARY wavelength - the distance from any point on a wave to the same point on the next cycle of the wave. Figure 23.12: The frequency of a wave is the rate at which every point on the wave moves up and down. Amplitude You have learned that the amplitude of an oscillator such as a wave is measured as the maximum distance it moves away from its equilibrium position. For a wave, equilibrium is the average, or resting, position. You can measure amplitude as one-half the distance between the crest and the trough of a wave. Figure 23.13: The wavelength can be measured from crest to crest. This is the same as the distance from one point on a wave to the same point on the next cycle of the wave PROPERTIES OF WAVES 563

12 Chapter 23 WAVES The speed of waves Waves spread Measuring wave speed Wave motion is due to the spreading of the wave from where it begins. For a water wave, the water itself stays in the same average place. Therefore, to gauge the speed of a wave you measure how fast the wave spreads, not how fast the water surface moves up and down. The graphic below shows what happens in water when you begin a wave in one location. You can measure the speed of this spreading wave by timing how long it takes the wave to affect a place some distance away. The speed of a typical water wave is about 1 m/s. Light waves are extremely fast 300,000 km/s (or 186,000 mi/s). Sound waves travel at about 1,000 km/hr (or 660 mph). Speed is frequency times wavelength In one complete cycle, a wave moves one wavelength (Figure 23.14). The speed is the distance traveled (one wavelength) divided by the time it takes (one period). We can also calculate the speed of a wave by multiplying wavelength and frequency. This is mathematically the same because multiplying by frequency is the same as dividing by period. These formulas work for all kinds of waves, including water waves, sound waves, light waves, and even earthquake waves! Figure 23.14: A wave moves one wavelength in each cycle. WAVE SPEED Speed (m/s) Frequency (hertz or 1 ) T v = f Wavelength (m) Period (s) Remember these relationships... period = T frequency = 1 / T Speed = wavelength period Speed = frequency wavelength 564 UNIT 8 WAVES, SOUND, AND LIGHT

13 WAVES Chapter 23 Solving Problems: Wave Speed The wavelength of a wave on a string is 1 meter and its speed is 5 m/s. Calculate the frequency and the period of the wave. 1. Looking for: You are asked to find the frequency (f) and period (T) of a wave. 2. Given: You know the wavelength of the wave is 1 meter and its speed is 5 m/s. 3. Relationships: The formulas you know include: speed = frequency wavelength f = 1 / T and T = 1 / f 4. Solution: Solve for frequency. frequency = speed wavelength frequency = 5 m/s 1 m = 5 Hz Then solve for period. period = 1 / f = 1 / 5 Hz = 0.20 s The frequency of the wave is 5 Hz and the period is 0.20 second. Your turn... a. The wavelength of a wave is 0.5 meter and its period is 2 seconds. What is the speed of this wave? b. The wavelength of a wave is 100 meters and its frequency is 25 hertz. What is the speed of this wave? What is its period? c. If the period of a wave is 15 seconds, how many wavelengths pass a certain point in 2 minutes? SOLVE IT! Making Waves Make a harmonic motion graph of a wave. Place time on the x-axis and position on the y-axis. The period is 2 seconds and the amplitude is 5 centimeters. On your graph, label a crest, trough, and the wavelength. a. The speed is 1 m/s. b. The speed is 2,500 m/s. The period is 0.04 second. c. two minutes = 120 seconds 120 s 15 s/cycle or wavelengths = 8 cycles or wavelengths pass the point 23.2 PROPERTIES OF WAVES 565

14 Chapter 23 WAVES 23.2 Section Review 1. A wave and a pendulum are both oscillators. Why isn t a pendulum a wave? 2. Make a list of three types of waves that you encountered today. 3. The distance from the crest of a wave to the next crest is 10 centimeters. The distance from a crest of this wave to a trough is 4 centimeters. a. What is the amplitude of this wave? b. What is the wavelength of this wave? 4. The wavelength of the wave shown in this harmonic motion graph is about: a. 1.2 meters b. 2.5 meters c. 5.0 meters 5. Which is the fastest way to send information, using sound waves, light waves, or water waves? 6. Is a wave that travels slower than 50 m/s most likely to be a sound wave, a light wave, or a water wave? 7. How far does a wave travel in three cycles? 8. How is the formula for finding the speed of a wave like the formula for finding the speed of a person running a race? 9. You are given the speed of a wave and its period. What kind of information can you also find out about this wave? Justify your answer. 10. You are watching a water wave in a long tank. Describe how you could determine the speed of the wave. 11. What is the speed of a wave that has a wavelength of 0.4 meter and a frequency of 10 hertz? 12. What is the period of a wave that has a wavelength of 1 meter and a speed of 20 m/s? SCIENCE FACT Waves and Earthquakes The outer layer of Earth is broken up into huge slabs called plates. Sometimes a sudden slip happens between two plates and an earthquake occurs. The quake releases powerful seismic waves that travel along the surface and through Earth. Because these waves travel through the planet, they are used to investigate Earth s internal structure. For example, the way that seismic waves refract and reflect within Earth provided scientists with the clues they needed to prove that Earth has a liquid core. Investigate! (1) Find out more about seismic waves by doing research in your local library or the Internet. Write up your findings in one or two paragraphs. (2) Is your city or town ever affected by seismic waves? If so, how do you know? 566 UNIT 8 WAVES, SOUND, AND LIGHT

15 WAVES Chapter Wave Motion Sometimes your car radio fades out. Why? It s because the radio waves are affected by objects. For example, if you drive into a tunnel, some or all of the radio waves get blocked. In this section, you will learn how waves move and discover what happens when they encounter objects or collide with other waves. When a wave encounters objects Wave fronts The direction a wave moves The four wave interactions A wave front is the leading edge of a moving wave and is often considered to be a wave crest rather than a trough. You can make waves in all shapes but plane waves and circular waves are easiest to create and study (Figure 23.15). The crests of a plane wave look like parallel lines. The crests of a circular wave are circles. A plane wave can be started by disturbing water in a line. A circular wave can be started by disturbing water at a single point. The shape of the wave front determines the direction the wave moves. Circular waves have circular wave fronts that move outward from the center. Plane waves have straight wave fronts that move in a line perpendicular to the wave fronts. Both circular and plane waves eventually hit surfaces. Four interactions are possible when a wave encounters a surface reflection, refraction, diffraction, or absorption. VOCABULARY wave front - the leading edge of a moving wave. plane wave - moving waves that have crests in parallel straight lines. circular wave - moving waves that have crests that form circles around a single point where the wave began. Figure 23.15: Plane waves move perpendicular to the wave fronts. Circular waves radiate outward from a single point WAVE MOTION 567

16 Chapter 23 WAVES Wave interactions Boundaries Reflection Refraction Diffraction Absorption A boundary is an edge or surface where one material meets a different material. The surface of a glass window is a boundary. A wave traveling in the air experiences a sudden change when it encounters the boundary between the air and the glass of a window. Reflection, refraction, and diffraction usually occur at boundaries. Absorption also occurs at a boundary, but happens to a greater extent within the body of a material. When a wave bounces off an object we call it reflection. A reflected wave is like the original wave but moving in a new direction. The wavelength and frequency are usually unchanged. An echo is an example of a sound wave reflecting from a distant object or wall. People who design concert halls pay careful attention to the reflection of sound from the walls and ceiling. Refraction occurs when a wave bends as it crosses a boundary. We say the wave is refracted as it passes through the boundary. The process of refraction of light through eyeglasses helps people see better. The lenses in a pair of glasses bend incoming light waves so that an image is correctly focused within the eye. The process of a wave bending around a corner or passing through an opening is called diffraction. We say a wave is diffracted when it is changed by passing through a hole or around an edge. Diffraction usually changes the direction and shape of the wave. When a plane wave passes through a small hole, diffraction turns it into a circular wave (Figure 23.16). Diffraction explains why you can hear sound through a partially closed door. Diffraction causes the sound wave to spread out from any small opening. Absorption is what happens when the amplitude of a wave gets smaller and smaller as it passes through a material. The wave energy is transferred to the absorbing material. A sponge can absorb a water wave while letting the water pass. Theaters often use heavy curtains to absorb sound waves so the audience cannot hear backstage noise. The tinted glass or plastic in the lenses of your sunglasses absorbs some of the energy in light waves. Cutting down the energy of light makes your vision more comfortable on a bright, sunny day so you don t have to squint! VOCABULARY reflection - the process of a wave bouncing off an object. refraction - the process of a wave bending as it crosses a boundary between two materials. diffraction - the process of a wave bending around a corner or passing through an opening. absorption - what happens when the amplitude of a wave gets smaller and smaller as it passes through a material. Figure 23.16: An illustration of diffraction. 568 UNIT 8 WAVES, SOUND, AND LIGHT

17 WAVES Chapter 23 Transverse and longitudinal waves Wave pulses Transverse waves A wave pulse is a short burst of a traveling wave. A pulse can be produced with a single up-down movement. The illustrations below show wave pulses in springs. You can see the difference between the two basic kinds of waves transverse and longitudinal by observing the motion of a wave pulse. The oscillations of a transverse wave are not in the direction the wave moves. For example, the wave pulse in the illustration below moves from left to right. The oscillation (caused by the boy s hand) is up and down. Water waves are an example of a transverse wave (Figure top). p VOCABULARY transverse wave - a wave is transverse if its oscillations are not in the direction it moves. longitudinal wave - a wave is longitudinal if its oscillations are in the direction it moves. Longitudinal waves The oscillations of a longitudinal wave are in the same direction that the wave moves (Figure bottom). A sharp push-pull on the end of the spring makes a traveling wave pulse as portions of the spring compress then relax. The direction of the compressions are in the same direction that the wave moves. Sound waves are longitudinal waves. Figure 23.17: Transverse and longitudinal waves WAVE MOTION 569

18 Chapter 23 WAVES Constructive and destructive interference Wave pulses If you have a long elastic string attached to a wall, you can make a wave pulse. First you place the free end of the string over the back of a chair. The string should be straight so that each part of it is in a neutral position. To make the pulse, you pull down a short length of the string behind the chair and let go. The pulse then races away from the chair all the way to the wall. You can see the wave pulse move on the string. Each section of string experiences the pulse and returns to the neutral position after the wave pulse has moved past it. VOCABULARY constructive interference - when waves add up to make a larger amplitude. destructive interference - when waves add up to make a smaller, or zero, amplitude. Constructive interference Destructive interference Suppose you make two wave pulses on a stretched string. One comes from the left and the other comes from the right. When the waves meet, they combine to make a single large pulse. Constructive interference happens when waves combine to make a larger amplitude (Figure 23.18). There is another way to add two pulses. Sometimes one pulse is on top of the string and the other is on the bottom. When these pulses meet in the middle, they cancel each other out (Figure 23.19). One pulse pulls the string up and the other pulls it down. The result is that the string flattens and both pulses vanish for a moment. In destructive interference, waves add up to make a wave with smaller or zero amplitude. After interfering, both wave pulses separate again and travel on their own. This is surprising if you think about it. For a moment, the middle of the cord is flat, but a moment later, two wave pulses come out of the flat part and race away from each other. Waves still store energy, even during destructive interference. Noise cancelling headphones are based on technology that uses destructive interference. Figure 23.18: This is an example of constructive interference. Figure 23.19: This is an example of destructive interference. 570 UNIT 8 WAVES, SOUND, AND LIGHT

19 WAVES Chapter Section Review 1. How does the motion of a plane wave differ from the motion of a circular wave? 2. For each of the examples below, identify whether reflection, refraction, diffraction, or absorption is happening. a. During a total solar eclipse, the Moon is in front of the Sun but you can still see some sunlight around the edges of the Moon. b. The black surface of a parking lot gets hot in the summer when exposed to sunlight. c. The image at the right of a straw in a glass looks funny. d. When you look in a mirror, you can see yourself. e. Sound seems muffled when it is occurring on the other side of a wall. f. Light waves bend when they move from water to air. g. A ball bounces back when you throw it at a wall. 3. When a wave is being absorbed, what happens to the amplitude of the wave? Use the term energy in your explanation. 4. Compare and contrast transverse waves and longitudinal waves. 5. Two waves combine to make a wave that is larger than either wave by itself. Is this constructive or destructive interference? 6. When constructive interference happens between two sound waves, the sound will get louder. What does this tell you about the relationship between amplitude and volume of sound? 7. One wave on a string is moving toward the right and another is moving toward the left. When, they meet in the middle, half of the cycle of the wave from the right overlaps with half of the cycle of the wave from the left. The result is that the string gets flat when the two waves meet. What happened? What will happen after the waves meet? TECHNOLOGY Noise-Cancelling Headphones The graphic below illustrates how noise-cancelling headphones work. Study the graphic and write a description that explains why noisecancelling technology is a good way to reduce noise. Verify your description by doing some research about these special headphones WAVE MOTION 571

20 Technology 8CONNECTION Chapter 23 Cell Phones: How They Work See if you can solve this puzzle: You dial a friend s number, and she answers on her cell phone. Name a three-word question that you can ask her only because she is on a cell phone. Thirty years ago, people never called someone and asked this question. Why? They already knew the answer! Give up? The question is: Where are you? Using Electromagnetic Waves By now you know that waves of all kinds exist around us and that they are the result of the harmonic motion of an oscillator. You should also be familiar with the kinds of waves make up the electromagnetic spectrum. Cell phones use electromagnetic waves in the low end of the microwave range of frequencies to send and receive signals. This does not mean that your cell phone can cook your food! The frequencies used by cell phones are lower in frequency and at a much lower power than the electromagnetic waves produced by microwave ovens. The process that allows a cell phone to communicate is the same as for a radio or walkie-talkie. All of these devices use electromagnetic waves of within a specific frequency range to send information. Walkie-talkies commonly use frequencies of MHz (megahertz, or million hertz). FM radios use frequencies of MHz, and cell phones are between 800 and 1900 MHz. Transmitting and Receiving Sound is translated into an electromagnetic wave at the desired frequency by a transmitter through a process called encoding. The electromagnetic wave is created by a rapidly changing electric current in a wire. Any device that creates a changing current creates electromagnetic waves. In theory, you can create radio waves by making a simple circuit with a battery, switch, and wire. Quickly flipping the switch would cause the current to flow and then stop in the wire. This process would create very low energy electromagnetic waves that would sound like crackles of static if you could detect them on a radio! When a cell phone, radio tower, or walkie-talkie sends out a signal, it travels at the speed of light (300,000 km/s) to the recipient. An antenna detects the wave because it causes electrons to move in the antenna. A tuner sorts through the thousands of electromagnetic waves coming into the antenna to find the correct one. Once the correct signal is detected, the information is taken from the signal, called decoding. An electric current is then sent to the speaker, where it is translated back into a sound wave. A radio is only able to receive signals, while walkie-talkies and cell phones can both transmit and receive. A walkie-talkie uses only one frequency, so a transmitting and receiving must take place individually. You can t talk and listen at the same time. Cell phones use a more sophisticated type of technology called full-duplex radio. This process uses two separate frequencies at the same time, so a person can transmit on one frequency and receive on a different frequency simultaneously. 572 Ch a p t e r 23 Wav e s

21 Technology 8CONNECTION The solution to this problem was to divide regions into small areas called cells. The name cell phone comes from this idea. Each cell contains its own tower that sends and receives signals from the phones located within that cell. Attached to each cell tower is a base station that connects the tower to the telephone system. The size of each cell depends on the population density. In a city, cell towers may be as close as one half mile apart, while in rural areas with flat terrain, towers can be separated by up to 50 miles. Chapter 23 Catching the Wave The distance the electromagnetic wave can travel depends on the power of the signal, which is measured in watts. When taking a long trip in a car, you may have noticed that you can listen to your favorite radio station for an hour or so, and then the signal gradually fades out. A city in another state can use the same frequency as the radio station in your hometown without interference, as long as the cities are farther apart than the reach of their signals. Many people can receive the same radio broadcast, so all of the radio stations in one city can transmit within a narrow range of frequencies and not interfere with each other. This is not true of cell phones, because each caller needs two frequencies to make his or her call one to transmit and one to receive. When cell phones began to get popular, people quickly realized that there are not enough cell phone frequencies available for thousands of people in a city to be talking at the same time. Dividing a city into small cells means that the same frequency can be reused in different locations, similar to the way a radio station frequency can be reused in a different state. Each cell phone company has a set of hundreds of frequencies used for their customers. The company divides their frequencies into several different groups. Each cell uses frequencies in only one of these groups. The diagram at left shows the arrangement of cells that use four groups of frequencies. A person in the top green cell can be using the same frequency as a person in the bottom green cell without the signals interfering. But what happens if you make a call and then move from one cell to another? As you travel, your signal is handed off from one cell phone tower to the next. The frequencies your cell phone transmits and receives on can change many times changes without you ever noticing. Questions: 1. How are cell phones, walkie-talkies, and radios similar? How are they different? 2. How are electromagnetic waves created? 3. Why are cities divided into regions called cells? Unit 8 Waves, Sound, and Light 573

22 Chapter 23 WAVES Chapter 23 Assessment Vocabulary Select the correct term to complete the sentences. wave cycle diffraction period reflection absorption refraction pendulum linear motion frequency constructive interference harmonic motion oscillator amplitude hertz resonance wavelength wave front circular wave restoring force plane wave transverse wave longitudinal wave natural frequency periodic force destructive interference Section This kind of force pulls a system back to equilibrium:. 2. The harmonic motion of a boy on a swing is like the motion of a(n). 3. A pendulum is a kind of in that it has repeating cycles of motion. 4. The note A in the musical scale has a(n) of 220 Hz. 5. One unit of harmonic motion is called a(n). 6. The motion of a girl running is called and the motion of a girl riding a ferris wheel is called. 7. The formula for is the inverse of the formula for frequency. 8. One equals one cycle per second. 9. When the periodic force matches the natural frequency of an object, the object experiences. 10. To have a high on a swing, your friend needs to push you with a large. 11. When I hit a drum, it will vibrate at its. Section A(n) is a travelling oscillation. 13. The distance from one crest to the next is a wave s. Section The process of a wave bouncing off a surface is called. 15. is the process of the amplitude of a wave diminishing as it enters another material. 16. The of a plane wave is perpendicular to the direction of motion of this wave. 17. The crests of (s) look like parallel lines. 18. is when waves bend when they enter another material and is when waves bend around an object or outward after exiting a hole. 19. If you disturb water in a single point, (s) will be created. 20. The amplitude of two waves will cancel when occurs. 21. The amplitude of two waves gets larger when occurs. 22. Sound waves are an example of this kind of wave:. 23. Water waves are an example of this kind of wave:. Concepts Section State whether the following are linear or harmonic motions. a. skiing downhill c. riding on a merry-go-round b. hiking uphill d. jumping on a trampoline 574 UNIT 8 WAVES, SOUND, AND LIGHT

23 WAVES Chapter How is the force of gravity involved in the motion of a pendulum? Use the words equilibrium and restoring force in your answer. 3. The motion of an oscillator is related to the interaction of what two factors? Describe each of these. 4. If the frequency of a heartbeat is 1 hertz, what is the period of this heartbeat? 5. Describe how you find the amplitude of a pendulum and of a water wave. 6. What information can you learn about the harmonic motion of an object by looking at a graph of its motion? 7. What will happen to the period of a pendulum if you: a. increase its mass? b. increase its length? c. Challenge: increase the amplitude? Section Identify how each of the following situations involves waves. Explain each of your answers. a. A person is talking to someone on a cell phone. b. An earthquake causes the floor of a house to shake. c. A person listens to her favorite radio station on the car stereo. d. A doctor makes an X-ray to check for broken bones. e. You turn on a lamp when you come home in the evening. 9. Arrange the equation relating wave speed, frequency, and wavelength for each of the following scenarios. Let v =wave speed, f = frequency, and l = wavelength. a. You know frequency and wavelength. Solve for v. b. You know frequency and wave speed. Solve for l. c. You know wave speed and wavelength. Solve for f. 10. Write a formula relating the speed of a wave to its period and wavelength. 11. How many wavelengths of a wave pass a point if the frequency of the wave is 4 hertz? 12. For the wave in the diagram, which measurement shows the amplitude? Which measurement shows the wavelength? Section Describe the shape of the light waves that would be created from a single, uncovered light bulb. 14. At the beach, describe where or when you would see wave fronts. How are wave fronts useful to surfers? 15. Below are diagrams representing interactions between waves and boundaries. Identify each interaction by name. 16. Read the descriptions below and indicate which of the four types of wave interactions (absorption, reflection, refraction, or diffraction) has occurred for each. a. The distortion of your partially submerged arm makes it look broken when viewed from the air. b. You hear the music even though you are seated behind an obstruction at a concert. c. You see yourself when you look at a highly polished car hood. d. Water ripples passing through a sponge become smaller. e. Heavy curtains are used to help keep a room quiet. 17. Can two waves interfere with each other so that the new wave formed by their combination has NO amplitude? Explain your answer. CHAPTER 23 ASSESSMENT 575

24 Chapter 23 WAVES Problems Section The frequency of an oscillator is 20 hertz. What is its period? How long does it take this oscillator to complete one cycle? 2. A bicycle wheel spins 25 times in 5 seconds. Calculate the period and frequency of the wheel. 3. The piston in a gasoline engine goes up and down 3,000 times per minute. For this engine, calculate the frequency and period of the piston. 4. What is the period and frequency of the second hand on a clock? (Hint: How long does it take for the second hand to go around?) 5. The frequencies of musical instruments range between 20 and 20,000 Hz. Give this range in units of seconds per cycle. 6. Make a harmonic motion graph for a pendulum. Place time in seconds on the x-axis and position on the y-axis. The period of the pendulum is 0.5 second and the amplitude is 2 centimeters. a. What is the frequency of this pendulum? b. If you shortened the string of this pendulum, would the period get shorter or longer? Section A wave has a frequency of 10 hertz and a wavelength of 2 meters. What is the speed of the wave? 8. A sound wave has a speed of 400 m/s and a frequency of 200 Hz. What is its wavelength? 9. If the frequency of a wave is 30 hertz, how many wavelengths pass a certain point in 30 seconds? 10. Draw two cycles of a transverse wave with an amplitude of 4 cm and a wavelength of 8 cm. If the frequency of this wave is 10 Hz, what is its speed? Section A wave with a period of 1 second comes from the left. At the same time, a wave with a period of 2 seconds comes from the right. The amplitude of each wave is 5 centimeters. Draw a harmonic motion graph for each of these waves with time on the x-axis and position on the y-axis. Overlay two wavelengths of the 1-second wave on one wavelength of the 2-second wave. How do these two waves interfere by constructive interference, destructive interference, or both? Applying Your Knowledge Section Explain how Newton s laws of motion are helpful in understanding harmonic motion. 2. Does friction affect the amplitude of a pendulum as it is swinging? Does it affect the frequency? You may want to experiment to figure this out. 3. How might the period and frequency of the two rubber band oscillators at the right be different? Justify your answer. Section When you watch fireworks, sometimes you see the explosion and then hear the sound. Why do you think this is? Section One of the four wave interactions is very important to how plants use light to grow. Guess which interaction this is, and write a couple of sentences justifying your answer. 576 UNIT 8 WAVES, SOUND, AND LIGHT