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Waves in Different Media What happens when waves move from one medium to another? Introduction
Vocabulary
Small waves nudge you back and forth as you paddle on a surfboard away from the beach. When you see a wave swell, you jump up on your board and take off. You time it perfectly to catch the wave just as it begins to slow down and grow larger. The wave breaks and white froth foams around you as the wave carries you toward the beach. You hear your friends’ cheers echo off of the nearby cliffs. Why do waves near the beach slow down and foam, making them perfect for surfing? And how are those changes related to the echoing of your friends’ voices off of the cliffs? Waves behave in predictable ways when they meet a new medium, such as shallow water or the rocky walls of the cliff. How can you use your understanding of how the properties of different materials affect waves to make predictions? For example, what information will you need to predict where the best surf waves will be? What materials and design will work best for building a concert hall? In this lesson, you will extend your model of waves to explore how waves interact with the media they travel through. You will learn what happens to a wave when it moves from one medium to another and when the properties of its medium change. Finally, you will learn how engineers use their knowledge of the interactions between sound waves and matter to build models that help them test the designs of concert halls.
ray a straight arrow in a diagram used to represent the direction a wave travels in reflection when a wave reaches a boundary between two media and bounces back transmission when a wave passes through the boundary between two media refraction when a wave bends as it is transmitted from one medium into another medium absorption when a wave transfers energy to the medium it is passing through scale model a representation of an system or object that is larger or smaller than the object, but all parts of the object are the same relative size
Next Generation Science Standards Performance Expectations MS-PS4-2. Develop and use a model to describe that waves are reflected, absorbed, or transmitted through various materials. MS-ETS1-4. Develop a model to generate data for iterative testing and modification of a proposed object, tool, or process such that an optimal design can be achieved. Science and Engineering Practices Developing and Using Models • Develop and use a model to describe phenomena. • Develop a model to generate data to test ideas about designed systems, including those representing inputs and outputs.
Crosscutting Concepts Structure and Function Structures can be designed to serve particular functions by taking into account properties of different materials, and how materials can be shaped and used. Cause and Effect Cause and effect relationships may be used to predict phenomena in natural or designed systems. Patterns Graphs and charts can be used to identify patterns in data.
Disciplinary Core Ideas PS4.A. A sound wave needs a medium through which it is transmitted. ETS1.B. • A solution needs to be tested, and then modified on the basis of the test results, in order to improve it. • Models of all kinds are important for testing solutions. ETS1.C. The iterative process of testing the most promising solutions and modifying what is proposed on the basis of the test results leads to greater refinement and ultimately to an optimal solution.
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Waves Reflecting off the Boundary Between Media
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Figure 4.1A The rays, or arrows, in this model show how reflected sound waves bounce back when they hit the surface of a new medium.
1. Reflection and Transmission Suppose you are looking out a window and see some friends walking by. You yell to get their attention. Even though your voice sounds loud to you, your friends on the other side of the glass may only hear a muffled sound. Why does the sound seem so much quieter outside the window than inside? In order to answer this question, scientists need a model to help them understand how waves move through matter, such as the air and the window. A common way to model the motion of waves is using rays. A ray is a straight arrow in a diagram that is used to represent the direction that a wave travels. By using a ray model, you can describe how a wave behaves as it travels from one medium to another. Two different things happen when waves, such as sound waves, meet a boundary between two media: reflection and transmission. Reflection  Waves travel outward from their source in straight lines when they are in a medium. But a wave may change direction when it meets a boundary between two media, such as sound waves moving from air to the glass of a window. The sound waves in Figure 4.1A, for example, meet a boundary at walls as they travel through the air in a building. Instead of stopping at a boundary, the waves bounce off. Reflection happens when a wave reaches a boundary between two media and bounces back. When a wave changes direction, the ray representing that wave points in the new direction.
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Transmissions and Reflections in Two Kinds of String Original wave pulse
Thick rope
Thin string
Reflected wave pulse
Transmitted wave pulse
Thick rope
Thin string
Transmission Waves are not only reflected when they meet a new medium; they are also transmitted. This is why your friends hear you when you shout at them through the closed classroom window. They are hearing sound waves that were transmitted through the window. Transmission happens when a wave passes from one medium into and through a new medium. When a wave hits the surface of a new medium, such as a classroom wall, the particles in the new medium vibrate. As these particles push and pull on nearby particles, the wave passes into the new medium, such as the glass of the window. Transmission allows you to hear sounds in the classroom from outside. Transmission also works in waves that move along strings and ropes. Think about tying a thick rope and thin string together, such as in Figure 4.1B. When you shake the rope once, you make a wave pulse. The wave pulse travels down the thick rope to the thin string, and it does not stop when it meets the string. Some of the wave pulse’s energy is reflected and travels back toward you and some of the wave pulse’s energy is transmitted and travels through the thin string. When a wave is transmitted into a new medium, many of its properties may change. For instance, the wave pulse that is transmitted to the thin string travels faster than it did in the thick rope. Sound waves also change speed when they are transmitted through a wall. They speed up as they travel through the solid parts of the wall, and they slow down on the other side of the wall when they transmit back into air. Figure 4.1C shows how the speed of the wave depends on the medium. Being transmitted into a new medium may also change a wave’s amplitude and wavelength. How much of a wave is reflected or transmitted when it meets a new medium depends on the media’s properties. Hard walls reflect more sound waves than carpeted floors. These reflected waves continue to transfer energy through the same medium (the air). The transmitted waves carry energy through the new medium, which is why your friends only hear sound waves that are transmitted through the window.
Figure 4.1B When a wave pulse in a thick rope meets a string, part of the wave is reflected and part is transmitted. The reflected part travels back along the rope, while the transmitted part continues to travel along the string.
Figure 4.1C Sound waves tend to travel fastest in solids, slower in liquids, and slowest in gases. So, the speed of a sound wave changes when it is transmitted into a new medium. What patterns do you see? Speed of Sound Waves in Different Media Material
v (m/s)
Diamond
12000
Iron
4480
Gold
3240
Rubber
1600
Water (25°C)
1493
Lead
1210
Air (20°C)
343
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2. Refraction You watch distant waves as they approach the beach. When they are far away, you watch them travel in observable directions. But as they approach the shore, their direction changes. They seem to bend toward the shore. What makes ocean waves bend toward the beach?
Figure 4.2A The angle of a line of bikers changes when the they reach sand because they slow down at different times. Similarly, waves refract when they meet a new medium because they change speed. Different parts of the wave slow down at different times.
Reasons Waves Refract  Ocean waves changing direction and bending toward the beach is an example of refraction. Refraction is the bending of a wave when it changes speed. This usually happens when it travels from one medium to another. It also happens when the properties of a medium change, causing waves in the medium to change speed. When a wave approaches shore, it moves from deep to shallow water. Water waves move slower in shallow water than in deep water, so the waves bend when they move from deep to shallow water. You can see why a wave speeding up or slowing down causes it to change direction by picturing a line of bikers like the ones in Figure 4.2A. aSuppose you and your friends are biking on the pavement in a straight line. The sidewalk ends at an angle where it meets sand, and you are the first person in the line to reach the sand. You have to slow down, but your friends can keep biking fast until they reach the sand. By the time the last person in the line reaches the sand, the angle of your line of bikers has changed. A similar change happens with water waves. Water waves slow down when they move from deep to shallow water. The part of the wave that meets the shallow water first slows down first. The other parts of the wave travel farther before they meet the boundary and slow down. As a result, the wave refracts. After the wave bends, it continues traveling in a straight line until its medium changes again.
Changes in Wave Speed Cause Refraction Pavement Fast biking
Sand Slow biking
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Shallow Water Slow Waves
Shoreline
Direction of Refraction in Waves
85°
90°
Some refraction 80°
45°
Most refraction
Deep water Fast Waves
90°
70°
Amount of Refraction The direction a wave bends and how much it bends vary. A wave does not bend at all if its direction is perpendicular to the boundary between the media. When it is perpendicular, it meets the new medium straight on. The ray showing the wave’s direction forms a 90° angle with the boundary between media. All of the parts at the front of the wave meet the boundary and change speed at the same time, so the wave passes straight into the medium without changing direction. Figure 4.2B shows that when a water wave moves from deep to shallow water at a 90° angle it passes straight into shallow water and does not refract. Refraction only happens when a wave meets the new medium at an angle other than 90°. How much the wave refracts depends on how different the angle is from 90° and how much the wave changes speed. As shown by Figure 4.2B, the further the wave is from being 90° to the boundary, the more it bends, or refracts. Whether a wave speeds up or slows down affects the direction in which the wave bends. Notice in Figure 4.2B that the waves traveling from deep water to shallow water bend so that the angle between the waves and the boundary is closer to 90°. The opposite happens when the waves travel from shallow water to deep water—the waves bend so that they the angle between the waves and the boundary is farther from 90°. When waves slow down, they refract so that they are closer to forming a 90° angle with the boundary. When they speed up, they refract to be farther from forming a 90° angle with the boundary.
Figure 4.2B Water waves refract, or bend, when they move from deep to shallow water because they travel slower in shallow water than in deep water. The further the waves are from being perpendicular to the boundary between the shallow and deep water, the more they bend.
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Absorption of Sound Waves
Figure 4.3 When a wave meets a new medium, some of its energy may be absorbed by that medium. When a sound wave traveling through air meets a concrete wall, the thick concrete will absorb the sound wave. The wave disappears as its energy is transferred into the new medium.
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3. Absorption When you walk through the hallway on your way to your next class, you are surrounded by all kinds of sounds. However, when you enter the music classroom and close the door, the noise disappears. Why does the sound not follow you into this classroom? A wave may pass into the surface of a new medium but not travel all the way through the medium. Absorption happens when a wave transfers its energy into the medium it is passing through. When sound waves meet a concrete wall, they are partly reflected. Some of the waves also pass into the wall and are absorbed by the wall. You do not hear sound waves that are absorbed. As you can see by the direction of the narrow red arrows in Figure 4.3, the energy of the absorbed waves is transferred to the wall. The energy may heat the wall, causing the particles in the wall to vibrate faster. As the sound wave’s energy is absorbed by the wall, the sound wave’s amplitude gets smaller, and the sound gets quieter. The amount of energy that is absorbed by a wave’s medium depends on the medium. Some media, such as air, hardly absorb any energy at all as waves pass through them. Waves can travel long distances through these media without losing too much energy. Other media, such as a foam wall, absorb most of the energy of waves passing through them. Even a thin foam wall will absorb most of the energy of sound waves that are transmitted through it. The amount of energy absorbed by a medium can also depend on the properties of the wave. For example, some media will absorb high frequency waves, but have little effect on low frequency waves.
Key Science Concept
Reflection, Transmission, Refraction, and Absorption When waves meet the boundary between different media, they will do a combination of two things. The waves are partly reflected off the boundary, and they are partly transmitted through to the new medium. As a wave is transmitted to a new medium, if the wave speed in the new medium is different than the old medium, the wave will also refract. Additionally, as waves travel, some of their energy is absorbed by the medium they are travelling in.
The sound waves are partially reflected off of the wall and partially transmitted through the wall.
Sound waves leaving the wall slow down. They refract in the opposite direction, moving parallel to the original sound waves.
Sound waves entering the wall speed up. They refract to be farther from forming a 90° angle with the wall.
As the sound waves pass through the wall, some of the energy they carry is absorbed by the medium, heating it up.
The sound waves of the man’s voice are transmitted through the air toward a wall.
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Engineering Design
4. Engineering Concert Halls Your family might prefer that you practice playing your musical instrument in a carpeted room with the door closed to absorb some of the sound. When you play a concert in an auditorium, the music needs to reach every member of the audience. How do engineers design concert halls to provide the best sound quality for the audience? Acoustic engineers apply what they know about how sound interacts with matter to design rooms, such as concert halls. They must consider how sound waves are reflected, absorbed, and transmitted by the materials in the concert hall. Concert hall walls should not transmit sound from outside or absorb too much sound inside the hall. Engineers need to design the ceilings and walls to reflect just the right amount of sound waves to make the music sound full and rich without producing echoes. They need to choose a shape for the room so that sound waves are reflected in certain directions for the best sound quality. Once they finish their design, engineers do not begin building a concert hall right away. A mistake would be very expensive and difficult to fix. Instead, they use different kinds of models to test and optimize their design. Tests with Scale Models  One kind of model that acoustic engineers use is a model that is built to scale. A scale model is a representation of an object that is larger or smaller than the object, but all parts of the object are the same relative size. For example, the size of a scale model may be 1/20th the size of the real hall, but will have the same proportions. The model chairs, model doors, and model stage will all be 1/20th the size of their real counterparts. Engineers use scale models to test how sound waves travel through the hall. One test involves engineers making a loud noise in the scale model. Then, they use several microphones to record the sound at different parts of the concert hall model.
Acoustic engineers use scale models to design concert halls. Using their knowledge of how sound waves interact with matter, engineers consider how sound waves are reflected, transmitted, and absorbed by different media to choose the best materials to build the concert hall.
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To get the most reliable results from the tests with scale models, engineers must select materials carefully. They test the materials used to build the model. And they make sure that the model materials absorb and reflect sound in the same way that the actual materials will. Engineers even include models of people, who also reflect and absorb sound, to test the sound quality when the concert hall is full. Tests with Computer Models Acoustic engineers also use computer models of the concert hall to test how sound will be reflected and absorbed. The image shows one kind of computer model. It models sound waves as rays to predict their path through the room. Engineers can use the computer models to simulate how music might sound in the concert. But the results are not always accurate. So, they are improving their computer models. Engineers use the results of the tests with the computer model and scale model to adjust their design. They apply design changes, such as a change in shape or materials, to their model. Then, they repeat the tests to see if their changes improved the sound quality. The process of testing the models and adjusting the design is repeated until the design meets the sound quality requirements. Then, the actual concert hall can be built. Acoustic engineers may not be able to use computer and scale models to predict whether or not you will enjoy the music in the concert hall. But they can design a concert hall so that you have the best possible listening experience.
A three-dimensional computer model is used to predict how sound waves will travel through the room. The path of the sound waves is shown as a straight line in the model.
LESSON SUMMARY
Waves in Different Media Reflection and Transmission Reflection happens when a wave bounces back from the surface of a new medium. Transmission happens when a wave passes through the boundary between media and then passes through the new medium. Refraction Refraction happens when a wave bends as its speed changes when it enters a new medium or when the properties of its medium changes. The amount that a wave refracts depends on how much its speed changes and on how close the wave’s direction of travel is to being perpendicular to the boundary. Absorption Absorption happens when a wave transfers some or all of its energy to its medium. Absorbed waves do not pass through a medium. Engineering Concert Halls Acoustic engineers use scale and computer models to test and improve their designs of concert halls. The optimized design should produce the best possible sound quality in the concert hall.
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READING FURTHER
The Doomed Bridge Called Galloping Gertie The Tacoma Narrows Bridge opened in the summer of 1940. By autumn of the same year, it fell apart and crashed into the water beneath it. What role do you think the energy of wind and the transmission of waves played in this engineering disaster? Puget Sound is a body of water in the northwestern corner of the United States in Washington. Traveling from one side of the Sound to the other was not convenient in the early 1900s. Travelers going between the Olympic Peninsula and the cities of Seattle and Tacoma had to take a long drive around the Sound or a costly ferry ride across it. People suggested building a bridge across a part of the Sound called Tacoma Narrows. Here the distance across the Sound
The Tacoma Narrows Bridge was built to provide a quick route across the Puget Sound. Excited travelers lined up to cross the bridge on its opening day in 1940.
narrows to less than 1.6 km wide. The location is also just south of Tacoma, a major city. A bridge at the Tacoma Narrows would cut travel across the Sound by more than 100 km for some trips. But could they build a bridge across such deep water and swift tides? Construction on the Tacoma Narrows Bridge did not begin until the late 1930s. Before that time, it was hard to convince many people that reducing travel time justified the high cost of a bridge. Then World War II began heating up, and a short route between military facilities on opposite sides of the Sound became a priority. Plans to build the bridge were put into action. Engineering teams submitted their possible designs. Decision makers chose the design that cost the least to build. Was this a good choice? Even though some people expressed concerns about that particular design, construction on the Tacoma Narrows Bridge began in 1938. On July 1, 1940, the Tacoma Narrows Bridge opened to public traffic with great fanfare. Over 7,000 people came to celebrate, and cars lined up to cross the bridge.
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Designed for Disaster Shortly after opening day, travelers began to notice what construction workers and engineers had observed as they were finishing the bridge. Winds, even light winds, caused waves in the bridge’s roadway. Riding across the bridge felt like bouncing up and down on a galloping horse. Often, the wave peaks in the concrete roadway reached about one meter high -- sometimes even higher! The rippling could last a few seconds or several hours. People soon began to call the Tacoma Narrows Bridge “Galloping Gertie.” While the rippling bridge gave some travelers motion sickness, most people did not suspect that Galloping Gertie might be unsafe. In fact, many people paid the toll to cross the bridge just for fun, as if it were a roller coaster ride. But engineers visited the bridge for another reason. They were studying the waves in the bridge so that they could modify the design to stop Gertie’s gallop. Engineers planned to place curved pieces of metal around the sides of the bridge roadway to deflect the wind. But their planned solution came too late. On November 7, 1940, winds at 67 km/h caused the bridge not only to heave up and down as it usually did but also to twist. After the bridge started twisting, the large steel cables holding up the roadway snapped. Concrete and steel plunged into the water as loose cables snaked through the air. Only four months after opening, Galloping Gertie sank to the bottom of Puget Sound. Luckily, the few people who were on the bridge escaped unharmed.
Winds made waves in the Tacoma Narrows Bridge, and this eventually led to the collapse of the bridge. Before Galloping Gertie collapsed on November 7, 1940, the roadway of the bridge began to twist.
Only four months after the bridge opened, the cables holding up the roadway snapped, causing the roadway to crash into the water below. The winds that brought down the bridge were reported to be as fast as 67 km/hr.
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Designing Sturdy Gertie Newspapers across the country shouted out headlines of Galloping Gertie’s demise. People speculated about the cause of the collapse. The bridge’s design had doomed the bridge, but engineers needed to understand exactly why before rebuilding the bridge. Mere opinions would not ensure the safety of a new bridge. Understanding the Failure To investigate why the bridge failed, the remaining tangled cables and broken bits were taken and studied. One of the last men to escape from the collapsing bridge was called upon to help. He was an engineer who was on the bridge on November 7 to gather data about its waves. With only bits and pieces of the original bridge remaining, he could no longer go out to the bridge to collect data. He needed another way to study how the bridge behaved in strong winds. To study Galloping Gertie, he built a scale model of it and placed it in a wind tunnel. Tests on the model confirmed why the bridge collapsed. They showed that the roadway was too flexible because it was relatively light, narrow, and not very deep. Its solid sides were like sails in the wind. As a result, strong winds transferred a large amount of energy to the bridge to make waves. The bridge was not strong enough to withstand the waves caused by the powerful winds that blew through the Tacoma Narrows. Based on the tests in the wind tunnel on models of the bridge, engineers redesigned the roadway of the bridge. They made it wider, deeper, and heavier, and added supports to make it less flexible. They made the sides open so that they would not act like sails in the wind.
Improving the Design Now that engineers understood why the bridge failed, they could design a new bridge that could withstand the winds without any wild waves forming in the bridge. The new bridge design called for a roadway that was wider, heavier, and deeper. Instead of solid sides, the roadway would be supported by an open network of steel beams. The new design seemed to solve all of the problems of Galloping Gertie’s design. But engineers still had more work to do before building the new bridge.
Comparing the 1940 Bridge with the 1950 Bridge 1940 Bridge
1950 Bridge Wider roadway
Narrow roadway which formed waves in the wind
Closed sides caught the wind like sails
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Heavier and sturdier construction materials
Open sides that let the wind pass through
Testing the New Design Bridge designers learned a valuable lesson from the collapse of Galloping Gertie. They had not tested how the original bridge would stand up to winds, and they were not going to make the same mistake again. They built a scale model of the new bridge design and tested it in the wind tunnel. The new model did not twist at all, even at high winds speeds. But the engineers felt they could still improve the design. They added shock absorbers at key locations on the bridge to absorb energy and reduce wave motions even more. With tests to show that it could withstand high-speed winds, the new Tacoma Narrows Bridge opened on October 14, 1950, without any galloping motion. Meeting New Needs If you look out at the Tacoma Narrows today, you will see two bridges crossing the Puget Sound side-by-side. Did the bridge built in 1950 fail, too? No, it is still standing sturdy as it was in 1950. But the cities around the bridge have grown, creating a new problem—traffic congestion. A second bridge was built so that traffic can flow across the Sound more quickly. Now, people traveling from Tacoma to the Olympic Peninsula travel across the 1950s bridge, and people traveling to Tacoma travel across the new bridge. And nobody is getting a roller coaster ride. ◆
The 1950s Tacoma Narrows Bridge was built to be sturdier than Galloping Gertie. Models of the bridge were tested in a wind tunnel before the bridge was built. Today, two bridges span the Tacoma Narrows. A second bridge was built to relieve traffic congestion caused by growing population.
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