Objectives Unit 7: Waves and Sound Identify the crest, trough, wavelength, and amplitude of any wave, and distinguish transverse and longitudinal wages. Given two of the following quantities of a wave, determine the third: period or frequency, wavelength, wave speed. Characterize sound waves. Describe the consequences of waves combining with each other Describe refraction of waves. Activity 1: Worksheet Purpose How do we describe waves? How do the different quantities describing waves relate to each other? This worksheet reinforces vocabulary and gives you practice working with the numbers describing waves. Materials Worksheet for each group member, two sides (pp 81 82). Overview The period of a wave is the time it takes the wave to pass through one complete cycle; it is the repeat time of the wave. The frequency is the reciprocal of the period; it is the number of complete cycles occurring in a specified time period. The wavelength of a wave is the length of one complete cycle of the wave, or the distance the wave travels in one cycle. The speed of a wave is the speed that any particular part of a wave travels through space; it is the distance the wave travels in some specified time period. Procedure Do the worksheet. Everyone should complete her or his own copy. Questions to consider If I know the period of a wave, how can I find its frequency? If I know the period and wavelength of a wave, how can I find the wave speed? PHYS 1090 69
Activity 2: Java applet Purpose In this activity you will investigate how waves add together to make a new wave. Materials Java-enabled computer with internet access; computer worksheet Overview A key feature of waves is that when different waves encounter each other, the movements making up the waves add together to make a new wave that is the sum of the individual waves. This java applet allows you to see this for the very simple case of two sine waves adding together. Even though the waves adding together are simple, the different effects you will see can appear quite complicated! Procedure Start your web browser and go to the PHYS 1090 web page (http://www.barransclass.com/phys1090). Under Weekly Units, select the Waves unit. From there, under Resources, select wave superposition applet. You should now see an applet containing three graphs of waves atop each other. Beneath them are fields for entering numbers. The numbers entered in the fields control the parameters of the waves in the top two graphs; the bottom wave is the sum of the top two. If the waves aren t moving, position your cursor anywhere over the graphs and click once with either mouse button. This toggles wave movement on and off. Set the wave parameters to convenient values: w 1 = 0.2, k 1 = 0.1, A 1 = 30; w 2 = 0.2, k 2 = 0.1, A 2 = 30. To signal the applet that parameters are changing, hit return or click on a button. Now the top two waves should be identical. The inputs are such that controlling the waves is not intuitive. Here s how it works: the w parameters control the frequencies of the waves: higher w means higher frequency. That means that the greater the w, the less time it takes for the wave at a fixed location to rise and fall. The k parameters control the wavelengths of the waves: higher k means shorter wavelength. That means that the greater the k, the shorter the distance between successive wave crests. The A parameter actually makes sense: it is the amplitude, which is how high and low the waves get. Because you control wave length and frequency independently, the wave speeds can change unexpectedly. Ordinarily, with many physical waves, waves of different wavelength have the same speed. Instead, here the speed is determined by both w and k: speed is w/k. Because we want both waves to have the same speed, we must give them the same w/k ratio, that is w 1 /k 1 = ±w 2 /k 2. Then, their speeds will be the same. Each group member should complete a worksheet, which includes four parameter sets of your choice. Give both waves the same speed for your personal choices! That means w 1 /k 1 = ±w 2 /k 2. For your individual choices, you are welcome to vary the amplitudes. PHYS 1090 70
Questions to consider How did the waves combine when they had frequencies that were close to each other but not quite the same? How did waves combine when they had the same frequency but moved in opposite directions? Did the waves combine in a predictable way when they had very different amplitudes? PHYS 1090 71
Activity 3: Springs and Slinkys Purpose In this activity you will observe transverse and longitudinal waves in one-dimensional media. Materials Long coil spring or stretch cord, Slinky, stopwatch. Overview You will explore the propagation of waves in a spring and in a slinky, and qualitatively see the factors that affect wave speed and wavelength. You will create and observe two limiting types of waves: transverse and longitudinal. Procedure Coil spring or stretch cord 1. Have two people hold a long spring, one at each end.. (It works best if the ends are firmly fixed, for example by bracing your hand against your body, a tabletop, or a wall.) Have one person quickly move her or his end up and down once. Or, pluck the spring by holding the end fixed and lifting a nearby point, ( ) then letting go. What happens? (This kind of wave is called transverse, because the spring moves in a different dimension than the wave.) 2. Stand farther apart so that there is more tension on the spring. Again, move one end up and down quickly. Is there any difference from the previous time? 3. Now have one person hold her or his end of the spring fixed against a table or something like that; we want as much reflected wave energy as possible. Generate a single pulse from the other end. What happens to the pulse when it reaches the fixed end? PHYS 1090 72
5. Move the free end up and down, slowly at first, and then faster. With a little practice, you should be able to produce the patterns illustrated at the right. These are called standing waves because parts of the spring are actually standing still, and the parts between them are moving the most. The still parts are called nodes, and the maximally moving parts antinodes. 6. At what frequencies do these patterns occur? (How can you measure the frequencies?) 7. Remain where you are and change the tension in the spring or cord by feeding or taking up some slack. Create the same standing wave patterns as before. Record the frequencies of the different patterns. 8. The frequencies should be different from before. How have they changed? 9. Change the tension again. Again make the same standing wave patterns. Now what are their frequencies? 10. Verify that you can also make standing waves by moving the spring side-to-side rather than up and down. Slinky Please do not over-stretch the Slinky. 1. Now look at a Slinky. Lay it on a smooth surface such as a tabletop or the floor. Have two people hold it, one at each end. Verify that you can make transverse waves (where the spring moves side-to-side) just as you did with the long spring. PHYS 1090 73
2. Now make a different kind of wave with the Slinky. Instead of moving one end perpendicular to the travel of the waves, push and pull the Slinky along the direction of its length. Watch the rest of the Slinky for a disturbance that travels along it. What do you see? (This kind of wave is called longitudinal, because the spring moves along the same dimension as the wave.) 9. Create a single pulse by pushing or pulling the end once. Then stretch the Slinky so that it is under greater tension and create a single pulse again. How does tension affect the pulse? 10. You should be able to make standing longitudinal waves in the Slinky. How many nodes can you make? Questions to consider What affects the speed of a transverse wave in the spring? What affects the speed of a longitudinal wave in the Slinky? With either wave, what is the relationship between frequency and wavelength? Under what conditions can you make standing waves? What are standing waves? How are standing waves related to traveling waves? Only certain specific oscillations create standing waves. What characteristics do the allowed waves share? Is the concept of propagation speed meaningful for standing waves? Describe and distinguish transverse and longitudinal waves. PHYS 1090 74
Activity 4: Sound Purpose You will investigate some of the wave properties of sound. Materials Metal bars, string, golf ball, corrugated plastic tubing, bottle, water, drinking straw Overview Sound is a longitudinal wave! When sound is produced by a vibrating object, the frequency the sound wave is the object s frequency of vibration. Sometimes, however, standing waves of sound are set up inside containers of the appropriate size and shape, and the wavelength of the sound is determined by the size of the container. Sound waves can combine to make new sounds. Procedure Chime 1. Predict: when you hit a chime, it makes a sound. What determines the pitch of the sound? 2. Suspend a metal bar from a string tied exactly around its center. Adjust the position of the string so that the bar balances. Hit the bar lightly with a golf ball. (Try not to let the bar swing very fast.) What do you hear? 3. Similarly hit suspended bars of different metals and lengths. How does the sound you hear differ? 4. Does the sound depend on where on the bar you hit it with the golf ball? PHYS 1090 75
5. Is the sound different if you hit a suspended metal bar with another metal bar? Singing tube 1. Now use the corrugated plastic tube. Hold it by the flared end and swing it in a circle. Be sure not to hit anyone with the swinging tube! Do you hear a sound? 2. Change the speed of swinging. Try to produce a different note. How many different notes can you make? 3. How are the different notes you produce related? Slide whistle 1. Fill the bottle with water. Place the straw in the bottle. Make a tone by blowing across the top of the straw. It probably won t be very musical, just a breathy hiss with a barely discernable pitch. While blowing, lower the bottle and continue to blow. What do you hear? 2. Repeat, this time allowing the straw to come completely out of the water. What do you hear when the straw leaves the water? PHYS 1090 76
Questions to consider How does the sound from the metal rod differ when it is struck with something hard (like another metal rod) or something softer? When you swing the corrugated plastic tube faster or slower, does the pitch of the sound it makes change continuously or abruptly? What is the effect of changing the height of the slide whistle? How do things change when the slide whistle straw comes completely out of the water? PHYS 1090 77
Activity 5: Wave pans Purpose How do waves behave in two dimensions? Here you will observe waves on the surface of water. You will also observe how these waves move near obstacles and barriers. Materials Flat pan, plastic drop cloth, water, bucket or gallon jug, large funnel, cafeteria tray Overview Water surface waves are complicated! The crashing surf at the beach is obviously different from a simple sine wave. Nevertheless, they do illustrate some features common to all types of waves. We use water surface waves in this activity to look more closely at the reflection of waves from barriers. Procedure Make sure that the table top is covered with a sheet of plastic. Put some water in the pan. Allow enough for the entire bottom to be covered to at least 5 cm depth. 1. Generate circular wave pulses by dipping your finger in the water at different positions. Make wave trains by rhythmically moving your finger up and down. What happens to the waves when they reach the side of the tub? 2. Tap a side of the pan. Describe the waves that are produced. 3. Hold the cafeteria tray vertically in the pan, so that the tray is parallel to the short edge of the pan. Generate a straight wave pulse by moving the tray toward and away from the edge of the pan. How does the pulse travel across the surface of the water? PHYS 1090 78
4. Make standing waves by rhythmically moving the tray back and forth. Can you make standing waves with different wavelengths? Sketch the pattern of the standing waves you produce. 5. Does the location of the tray in the pan affect the standing waves that you can produce? 6. Can you make standing waves if you hold the tray at an angle to the side of the pan? If you can, sketch the pattern of the standing waves you produce. 7. Place an inverted funnel in the tub. Generate a single straight wave pulse and observe how it behaves when it reaches the funnel. Describe what happens. 8. Tilt the tub so that it has a shallow end and a deep end. Create a wave pulse in the deep end and observe it as it travels to the shallow end. Describe what happens. PHYS 1090 79
9. With the tub tilted as before, create a straight wave pulse that travels diagonally in the tub. Observe how it behaves as it moves from the deep end to the shallow end. Describe what happens. Questions to consider What standing wave patterns did you observe in the washtub? What happens when a straight wave hits the side of the pan? What happens when a circular wave hits the side of the pan? How does a straight wave behave when it encounters an inverted funnel? How does a straight wave behave when it encounters shallow water? PHYS 1090 80
Activity 6: Wave Tank Purpose The tank allows you to see a water wave from the side as it moves. You will specifically see how water waves behave when their water depth changes. Materials wave tank, water, piston, block Overview This continues your experiments with water waves for the previous activity, but the shape of the tank restricts the waves to one dimension. The advantage is that the tank allows you to see the profile of the wave very clearly. Procedure If the tank springs a leak, get it to the sink and drain it as neatly as you can. First practice making waves with the piston. You can make waves by moving the piston up and down or from side to side. If you hold the piston at the end of the tank, a wave can travel the entire length of the tank before hitting the far end. Find a technique that gives you a single pulse. You want things as simple as possible. 1. Make a single pulse and watch it as it travels the length of the tube. Does the pulse change as it moves? 2. Set the far end of the tank on a block so that the water is shallower there. Make a single wave pulse and watch it as it travels the length of the tube. Does the wave change as it moves? Are there any differences from when the water depth was constant? Questions to consider When the tank is level, what does a wave do when it reaches the end? When the far end of the tank is shallow, how does the wave change as it travels? PHYS 1090 81
Activity 7: Ripple tank Purpose In this activity you will observe the behavior of regular waves in two dimensions. Phenomena you will observe include the interference of two circular wave trains, the passage of straight waves through a narrow opening, and the interaction of waves emanating from parallel slits. Materials ripple tank, water, battery pack, variable resistor, two-point vibration source, straight wave source, straight barriers, plastic ruler Overview Waves in two and three dimensions have all the properties of waves in one dimension, but they also display phenomena that cannot be observed in one-dimensional waves. The wave generator can be configured to produce either two sets of circular waves or one train of straight waves. The sets of circular waves are coherent: they always have the same phase difference at the same time. Procedure Circular wave trains 1. Configure the wave source so that the two ball-terminated arms touch the surface of the water. Connect the wave source and variable resistor in parallel to the battery pack. Adjust the resistor to generate regular oscillations. Circular wave trains should emanate from the two balls in the water. Although the waves move across the water, they create an interference pattern that does not change. Look for nodes, places where the water does not move up or down. What shape do they take? 2. Slowly adjust the setting of the resistor to change the frequency of the wave source. How do the interference patterns change? 3. Sketch the interference patterns resulting from several different wave frequencies. PHYS 1090 82
Single-slit diffraction 1. Configure the wave source so that its two arms hold the edge of a straight bar at the surface of the water. Adjust the resistor so that the source makes a train of straight waves. Set two straight barriers in the path of the wave train, leaving only a slit for the waves to pass through ( ). Observe the waves that pass through the slit. What do the waves do after they emerge from the slit? Are they still straight? Do they remain as narrow as the slit? 2. Move the barriers to make the slit wider. Do the waves passing through the slit behave any differently? 3. Adjust the resistor to generate wave trains with low and high frequencies (long and short wavelengths). Observe these different wave trains pass through wide and narrow slits. Sketch the patterns of short- and long-wavelength waves through narrow and wide slits. Double-slit interference 1. Continue with the wave source generating straight wave trains. Configure the straight barriers to make two openings ( ) in the path of the wave train. Observe the waves as they encounter the barrier and pass through the slits. What do the wave trains do after they pass through the slits? PHYS 1090 83
2. Adjust the resistor to generate long- and short-wavelength wave trains. Does changing the wavelength have any effect on how the waves behave on the other side of the barrier? Questions to consider What patterns form when two circular wave trains combine? How do the circular wave trains interfere with each other in the different regions of the pattern? What happens to straight waves when they pass through a single narrow slit? A single wide slit? How do they transition from one behavior to the other? What sort of wave trains are produced when a train of straight waves passes through a double slit? Are the wave trains emerging from a double slit coherent? What sort of pattern is produced by waves emerging from a double slit? PHYS 1090 84
Name: Wave Applet Worksheet Using the Adding Simple Harmonic Waves II applet, describe the three waves you obtain using the parameters given. Choose and describe your own wave parameters for the last four cases, making certain to keep w 1 /k 1 = ±w 2 /k 2 for all of them. Keep wave amplitudes at 30 for all but the last four cases. w 1 k 1 w 2 k 2 Description 0.2 0.1 0.2 0.1 0.2 0.1 0.4 0.2 0.2 0.1 0.6 0.3 0.2 0.1 0.8 0.4 0.2 0.1 0.22 0.11 0.2 0.1 0.24 0.12 0.2 0.1 0.26 0.13 PHYS 1090 Spring 2009
w 1 k 1 w 2 k 2 Description 0.2 0.1 0.21 0.105 0.2 0.1 0.2 0.1 0.2 0.1 0.24 0.12 Remember: keep w 2 /k 2 = ±w 1 /k 1! PHYS 1090 86