LAB #11: RESONANCE IN AIR COLUMNS
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1 OBJECTIVES: LAB #11: RESONANCE IN AIR COLUMNS To determine the speed of sound in air by using the resonances of air columns. EQUIPMENT: Equipment Needed Qty Equipment Needed Qty Resonance Tube Apparatus 1 Tuning Forks 2 600mL Beaker 1 One-Meter Stick 1 SAFETY REMINDER Follow all safety instructions. Keep the area clear where you will be working and walking. THINK SAFETY ACT SAFELY BE SAFE! INTRODUCTION: In this lab you will determine experimentally the speed of sound in air by determining the wavelength of the wave formed by each of two tuning forks with known frequencies. PROCEDURES: Answer all of the questions on this handout. PART 1: Determining the speed of sound with Tuning Fork #1 You have been given two tuning forks. We will refer to the tuning fork with the lower frequency as Tuning Fork #1, and the tuning fork with the higher frequency as Tuning Fork #2. 1. What is the frequency of Tuning Fork #1? To start the tuning fork vibrating, hold the handle and strike the fork on the heel of your hand. Do not strike the fork on the lab bench or anything hard. This can damage the tuning fork. To determine the wavelength of the wave created by the tuning fork, we are going to create a standing wave in the air column. This allows the wave reflected off of the water s surface to
2 combine with the wave coming from the tuning fork to form a louder sound. By listening for this increase in loudness, we fill find the correct length for the air column. To understand this better, consider Figures #1-3. Figure #1 Figure #2 Figure #3 When a vibrating tuning fork is placed above an air column, the fork starts the air vibrating. If the water height is adjusted to the correct position, a standing sound wave is created. This occurs when the wave moving downward from the tuning fork combines with the wave moving upward, that has been reflected off of the water. This can happen when the length of the air column is equal to ¼ of the wavelength of the sound wave, see Figure #1. We show this by drawing vertically one-quarter of a wave in the air space. The water surface corresponds to a node in the wave, and the open end of the tube corresponds to an anti-node. This is called a sound wave resonance. Another resonance will occur when the length of the air column is equal to ¾ of the wavelength 5 of the sound wave, see Figure #2. Also, when the length of the air column is equal to 4 of the wavelength of the sound wave, see Figure #3. You have been given tuning forks that will form at least the ¼ and ¾ wavelength resonances within your air columns. Other resonances may be too long to fit in the tube.
3 By finding these resonances, we will be able to determine the wavelength of your sound waves, and given the sound s frequency, we can then determine the speed of sound. It will help us find these resonances if we have some idea of where to look. Using an approximate value for the speed of sound, 350.m/s, determine an approximate value for your wavelength using 2. What is your approximate value for λ? λ approx = v approx / f. 3. What is your approximate value for ¼ λ? 4. What is your approximate value for ¾ λ? Your answers to Questions #3 and 4 will give you a starting point for looking for the resonances. Notice that your resonance tube apparatus has a hose connected at the bottom which leads to a plastic beaker. The beaker is held in place with a ring clamp. Move the ring clamp so that the center of the plastic cup is about 10cm or so below your answer to Question #3 as read on the scale on the side of the tube. This will be your starting water height. Pour some water into the plastic cup until the water level in the resonance tube is up to this point, that is, 10cm or so below your answer to Question #3. Notice that you can move the plastic cup up and down and by doing so easily change the water height in the resonance tube. Strike Tuning Fork #1 on the heel of your hand and hold it near the top of the resonance tube. You will get the best results if you hold the fork horizontally with one prong above the other, as in Figure #4. While the tuning fork is vibrating, have another lab member raise and lower the plastic cup so that the water level in the tube moves through the position given as answer to Question #3. You should notice that the volume (loudness) of the sound increases and decreases as the water level changes. Notice at what level the sound is the loudest. Repeat this allowing the water level to move through this area more slowly and try to determine as accurately as possible the level at which the sound is the loudest. This may require you to strike the tuning fork several times and allow the water to raise and lower a number of times. 5. What is the length of the air column for your first resonance?
4 This is your value for ¼ λ. From this, determine λ. 6. What is your first experimental value for λ? Now adjust the water height to about 10cm below your answer to Question #4. This may require pouring some water out of your plastic cup. Following the same procedure, determine where the second resonance is. 7. What is the length of the air column for your second resonance? Figure #4 This is your value for ¾ λ. From this, determine λ. 8. What is your second experimental value for λ? 9. What is your average value for λ? 10. Using your average λ and your tuning fork frequency, what is the speed of sound? Although the water makes a very good node for the waves, the opening at the top of the tube may not be the exact location for the anti-node. Another way to find λ from your answers to Questions #5 and 7 is to subtract them and use the difference for ½ λ. This helps cancel any error that might occur due to the anti-nodes being above or below the opening of the tube. 11. What is your value for λ using twice the difference between the resonance lengths?
5 12. What is your value for the speed of sound using the λ from Question #11? It has been shown experimentally that the speed of sound varies with temperature so that where T is the room temperature in Celsius. v sound = (331.5 m/s) + (0.607m/s o C) T, 13. What is room temperature (in o C) according to the thermometer at the back of the room? 14. What is the speed of sound using this temperature? 15. Assuming your answer to Question #14 is the correct v sound, what is the error for your v sound from Question # Assuming your answer to Question #14 is the correct v sound, what is the error for your v sound from Question #12. PART 2: Determining the speed of sound with Tuning Fork #2 You will now go through the same procedure with Tuning Fork # What is the frequency of Tuning Fork #2? Using this frequency, and the approximate value for the speed of sound, determine an approximate value for your wavelength.
6 18. What is your approximate value for λ? 19. What is your approximate value for ¼ λ? 20. What is your approximate value for ¾ λ? Use your answers to Questions #19 and 20 as starting points to find your resonance lengths. 21. What is the length of the air column for your first resonance? This is your value for ¼ λ. From this, determine λ. 22. What is your first experimental value for λ? 23. What is the length of the air column for your second resonance? This is your value for ¾ λ. From this, determine λ. 24. What is your second experimental value for λ? 25. What is your average value for λ?
7 26. Using your average λ and your tuning fork frequency, what is the speed of sound? 27. What is your value for λ using twice the difference between the resonance lengths? 28. What is your value for the speed of sound using the λ from Question #27? 29. Assuming your answer to Question #14 is the correct v sound, what is the error for your v sound from Question # Assuming your answer to Question #14 is the correct v sound, what is the error for your v sound from Question #28. Notice that although we did use an approximate value for the speed of sound to help us find the location of the resonances, it wasn t absolutely necessary to do that. With patience, and enough time, the resonances can be found without a starting point, and from them the speed of sound can be accurately determined. Clean-Up Pour out as much of the water from the resonance tube apparatus as you can, wipe up any spills, and return all of the equipment to the arrangement in which you found it.
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