1 Physics 1103 Wave Interactions (picture of beach on screen) Today, we go back to the beach to investigate more wave interactions. For example, what makes these waves change direction as they approach the shore? And although two objects like these bumper boats cannot be in the same place on the water at the same time, water waves can. Why is that? How can waves pass right through other waves, affecting each other for a moment, and then continuing on, unchanged? In today s program, we ll answer all these questions and more. (Read objectives on screen.) Oh, man, I m here in our classroom when I d really like to be at the beach. But I d like to be there for a good reason No, really, I d like to be at the beach so we could continue our study of wave interactions. We ve seen what happens when waves hit a boundary and are turned back. That s reflection. Now let s see what happens when the wave goes on through to another medium. (springs on screen) For this demonstration we re coupling together a heavy spring and a lighter one. Since the springs are very similar, most of the wave will go right through the boundary into the new medium. Watch what happens when a single pulse moves from the heavy medium into the lighter one. It speeds up. Now, a continuous wave moves from the slower medium on the right to the faster one on the left. What do you notice about the wavelength? The wavelength increases as the velocity of the wave increases. Notice that the frequency of the wave does not change. Frequency is not affected by the medium. Rather, it only depends on how fast the spring is shaken. The wave equation shows that wavelength is directly proportional to a wave s velocity. So when velocity increases, wavelength increases. Now waves on springs go straight through the boundary into the new medium. But what happens when waves approach the new medium at an angle? For that, we ll need to look at wave fronts. And an analogy can help you understand. So put your pencils down. We ll tell you when to take notes. (diagram on screen) Let s go back to our marching band. These are the rows of band members, all marching in step. So each row is like a wave front. Now part of the practice field is paved and part is covered in mud, about ankle deep. So the marchers will slow down when they reach this new medium. If they approach the mud straight ahead, all the marchers in a row will slow down at the same time.
2 So the distance between rows, or wavelength, will decrease on the mud side of the boundary. As velocity decreases, wavelength decreases. But what if the marchers approach the boundary obliquely, or at an angle? When this marcher reaches the mud, he slows down. But the rest of the row is still on pavement. So this end of the row will travel faster than this end, and the whole line will bend, like this. These arrows represent the directions of the waves, which are perpendicular to the wave fronts. Now let s draw a normal line all the way through both mediums. You can see that at the point of incidence the wave turns or bends toward the normal. This bending is called refraction. Look at this animation and then you ll take some notes. We can understand refraction by looking at this diagram. When a wave goes from a high speed material to a slower speed material at an angle, the wave changes direction. In this example, the right side of the wave reaches the slower material first. As a result of the left side traveling faster than the right, the wave pivots or shifts slightly to the right. As the wave leaves the slower material and enters the faster material, the opposite occurs, making the wave pivot to the left and then resume its original direction in the faster material. (green chalkboard on screen) Refraction is defined as the bending of a wave s path as it enters a new medium obliquely, or at an angle. Refraction is caused by a difference in the speed of a wave in the new medium. If the wave enters a slower medium, its path will bend toward the normal. If it enters a faster medium, the opposite will happen, making the path bend away from the normal. Let s go back into the lab to see water waves refract as they enter a new medium. This time, they ll put a shelf in part of the tank to make the water more shallow. Remember that water waves move slower in shallow water because of friction with the bottom of the tank or the floor of the ocean. (students on screen) Our students place a thick plastic shelf in the ripple tank to make a section of shallow water. Wave pulses will be sent from the bottom of the TV screen straight toward the top. The pulses will hit the boundary of the shallow water at an angle. (wave fronts on screen) You can see the wave fronts moving straight up the screen toward the boundary. When they pass into the new medium at an angle, the path of the wave fronts changes. And the wavelength, or distance between the fronts, decreases in the slower medium. By drawing a normal line, perpendicular to the boundary, and drawing arrows to represent the path of the waves, you can see that the wave path bends toward the normal. When waves go from fast to slow, they bend toward the normal. And the angle of incidence is greater than the angle of refraction. 2
3 (diagram on screen) Let s see how you would draw the diagram for what you saw in the ripple tank. The first thing you do is draw a normal line all the way through both mediums at the point of incidence. Now, put your ruler on the incident wave, like this, and then decide which way to bend it. From fast to slow, bend toward the normal. So turn the ruler closer to the normal line and draw the refracted wave. Label angles of incidence and refraction. Next, we ll draw a few wave fronts, perpendicular to the direction the wave moves. Remember that the faster the wave, the longer the wavelength. So draw the fronts far apart in the fast medium and closer together in the slow medium. Now, you try this diagram. Come back when you ve finished. Local Teachers, turn off the tape and give students problem set number one from the facilitator's guide. (Pause Tape Now graphic) (diagram on screen) In this case, the wave passes from a slow medium to a faster one. So it bends away from the normal, like this. And the wavelength is greater in the faster medium. As velocity increases, wavelength increases. (photo of beach on screen) Have you ever noticed that ocean waves seem to curl around the shoreline, coming in parallel to the beach? Why is that? Well, off shore, the waves are in a certain direction. As they approach the shore, the ocean gets more shallow, so the waves slow and refract, bending toward the normal. Since the water gets more shallow gradually, the waves keep bending toward the normal, a little at a time. So the fronts gradually become more parallel to the shore. That s the reason for the curling. We ll get back to refraction in future units on sound and light. For now, let s go on to the next wave interaction, diffraction. We ll start with the definition of diffraction. (green chalkboard on screen) Diffraction is the spreading of waves around the edges of or through an opening in a boundary. Save room for more notes later. For now, let s go into the lab and look at the diffraction of water waves in our ripple tank. 3
4 (students on screen) First, our students stand one small paraffin block in the center of the ripple tank. They will send pulses up from the bottom of the TV screen. You can see the waves bending around the corners of the obstacle. The straight wave fronts become curved due to diffraction. Now let s see what will happen when our students place two blocks in the middle of the tank with an opening between them. The straight wave fronts approach the opening from the bottom of your TV screen. When they pass through the opening, the edges curve. As the opening becomes smaller, you can see that the curving becomes greater, so that straight wave fronts become circular ones. The smaller the size of the opening compared to the wavelength of the waves passing through it, the greater the diffraction. (diagram on screen) Here s a wave diagram representing diffraction for your notes. I remember the term, DIFFRACTION, because the waves look so DIFFERENT after they pass through the opening. Put this in your notes as your second bullet. Diffraction is greatest when the size of the opening is smaller than the wavelength of the waves passing through it. Diffraction is the reason you can hear around corners and the reason you can t get a clear picture of tiny particles, such as viruses, with a regular microscope. We ll talk about that in future units on, you guessed it, sound and light. But now it s time to go on to our last wave interaction: interference. Unlike objects, waves can travel right through each other. And when they are at the same place at the same time, their effects on the particles of the medium can either add up or cancel each other out. It s called superposition. Let s go back to the lab before you get notes on superposition and interference. (students on screen) To show interference between waves, we ll have both students send pulses down the same side of the spring, so that crest will meet crest. Watch as the pulses meet each other. What happens to the amplitude of the combined pulses? This slow motion close-up shows the separate pulses, of equal amplitude, as they approach each other. As they meet, each wave lifts the coils of the spring independently. And the instant the two pulses are at the same place on the spring, their displacements add up to produce a single pulse with twice the amplitude. Next, we ll have our students send identical pulses on opposite sides of the spring, so that crest will meet trough. 4
5 Watch again in slow motion. The instant the two opposite pulses meet, their displacements cancel out. But after the pulses pass through each other, they continue on, unchanged. Watch the whole process again, in real time. (green chalkboard on screen) The principle of superposition states that the displacement of a medium caused by two or more waves is the algebraic sum of the displacements of the waves alone. The result of the superposition of two or more waves is called interference. When crest meets crest, or trough meets trough, the result is constructive interference. The amplitudes add up. When crest meets trough, the result is destructive interference. Amplitudes subtract. (diagrams on screen) Your teacher will turn off the tape now and give you these diagrams. For each, show the superposition of the pulses the instant they meet, and then draw the pulses after they pass through each other. Local Teachers, turn off the tape and give students problem set number two from the facilitator's guide. (Pause Tape Now graphic) (diagrams on screen) The first diagram is of two crests, one taller than the other. When they meet, the resulting amplitude is the sum of the two. After they pass through each other, the tall one continues to move to the left and the shorter one to the right. The result of crest and trough with equal amplitude is complete destructive interference. After they meet, each continues on its way. Finally, the tall trough and smaller crest will form a trough with an amplitude equal to the difference of the two. After they pass through each other, they proceed unchanged. Here s a close-up of these pulses traveling along a spring. The real thing should match your drawings. When two circular water waves travel in the same medium at the same time, the interference pattern they make is interesting. Watch this. (circular wave fronts on screen) 5
6 Two points are vibrated together to send out identical circular waves. When the waves meet and overlap, an interference pattern is formed, with both constructive and destructive interference. This line traces one of the regions of maximum constructive interference. All points along this line have equal path lengths from the sources of the waves, so they arrive in phase, crests meeting crests. Along this adjacent line, the water is undisturbed. No wave exists here due to complete destructive interference. The path lengths from the sources to points along this line differ by one half a wavelength. So crests meets troughs along this line. A similar interference pattern can be seen when straight waves pass through two small slits. This pattern is the result of both diffraction and interference. (diagram on screen) Put your pencils down and let me show you how the lines of total constructive and destructive interference are formed. In this pattern, crests are represented by the blue lines and troughs by the red lines. So a wavelength would be from blue to blue or red to red. Now look at the superposition of the two circular waves. All along this line, crests are meeting troughs, for total destructive interference. This is called a nodal line. Nodal lines are lines of destructive interference. Here crest meets crest, trough meets trough, crest meets crest, and so on. So all along this line, we have total constructive interference. Antinodal lines are lines of constructive interference. The medium is still along these lines. Nodal and antinodal lines repeat to make a sunbeam pattern like this. The last thing I want to show you today is the result of both reflection and interference. It s called a standing wave. As you can see, when I shake the end of the spring with a certain frequency, the spring vibrates up and down, but the wave doesn t travel from one end of the spring to the other. That s why it s called a standing wave. If I double the frequency, you can see the spring vibrating up and down in two sections and a point in the middle that doesn t move at all. What would you call this point? Tell your teacher. It s called a node. That s where nodal line comes from. Got it? Here s what happens to make a standing wave. I send a wave down the spring. It hits the fixed end and is reflected. The two waves interfere with each other, and this is the result. Get some notes and then we ll show you the details and some examples. (green chalkboard on screen) A standing wave results when two waves of the same frequency, wavelength, and amplitude travel in opposite directions and interfere. 6
7 It consists of nodes, where the medium is stationery, and antinodes, at which the largest amplitude occurs. Only certain frequencies can produce standing waves.. You ll see why only certain frequencies can produce standing waves later. For now, put your pencils down and watch this animation showing how standing waves are produced on a string. (diagrams on screen) Let s consider the wave form predicted by the principle of superposition. At the top, we see the two component waves of the same velocity, amplitude, and wavelength, traveling in opposite directions. At the bottom, we see the resultant of the superposition of the two component waves. If we move the components ¼ wavelength at a time, we see that the resultant waves goes through alternate periods of constructive and destructive interference. Even though the components move, it appears that the resultant is not moving at all. Instead, there are fixed points in which complete destructive interference occurs at all times. The points of maximum displacement appear to oscillate back and forth at fixed points along the wave. (diagrams of standing waves on screen) Now you should be able to see why only certain frequencies will produce standing waves. Standing waves on strings will have nodes at both ends, and at least one antinode between the nodes. This represents one half a wavelength. Now if you double the frequency, you ll make this, which equals one whole wavelength. Tripling the frequency will make this one. No frequencies in between will work because you have to have nodes on each end. (apparatus on screen) Watch as this string is vibrated at different frequencies. At first no standing wave is observed. Then the frequency is adjusted to produce a wavelength half the length of the string. When the frequency is increased, the standing wave disappears and then reappears once a wavelength equal to the length of the string is produced. When you pluck the string of a guitar or blow across the top of a bottle, you make standing waves. We ll talk more about that in the next unit on sound. But I ll bet you didn t know that the sweet spot on baseball bat has something to do with a standing wave. When a ball hits a bat, it sends vibrations up and down the bat, and a standing wave is produced. About 15 centimeters from the end of the bat is the sweet spot, actually a node on the standing wave, where the bat doesn t vibrate. If the ball hits here, none of the energy goes into making vibrations, so the ball will travel slightly faster coming off the bat. If the ball hits closer to you hands or off the end of the bat, the vibrations created can really sting your hands. And if the bat has a weakness, the large vibrations can actually make the bat break. That s 7
8 one more real life situation explained by physics. That s it for our study of waves, so now, it s time to SHOW WHAT YOU KNOW!! Jot down your choice for each question. Your local teacher will go over the correct answers with you. (Read Show What You Know question on screen) Bummer. That s it for our study of waves. I ll miss the beach, won t you? Well, that s OK because we ll come back to the beach at least once during our study of (Sound Effects: a medley of sounds, one after the other : horn honking, baby crying, thunder, music, etc.) sound. Who s got the ear plugs? 8