Name: _______________________________________ Lab Section: ___________ Lab Partners: ___________________________________________________ Grade: ____________Lab 3: Resonance in an Open-Closed TubePre-LabIntroduction One resonating system we all carry with us where ever we go, the vocal tract, can be modeled as a system of resonating tubes. For the vocal tract, as is true of the resonances of other tube systems like brass and woodwind instruments, many frequencies are inputted into the tube, but only those that meet the resonance condition can be heard. Forwind instruments, often the tube is lengthened or shortened during playing in order to change the pitch. That is, the condition for resonance has purposely been changed to select a different resonant frequency. In this lab, you will be investigating a open-closed resonating tube in very different way. You will be inputting just one frequency, and changing the length of tube in order to keep this single frequency in resonance with the system. For any traveling wave of just one frequency, the speed is given by v fl= (1)where f is the frequency of oscillation and is the wavelength. So, you will be holding the frequency constant, and the velocity of the wave, which is the speed of sound, will also be constant.1) Why will the velocity of sound be constant for this experiment? What are the only ways to change it?2) So if the velocity and frequency are constant throughout the experiment, what does that tell you about the wavelength throughout the experiment?1Visualization Case 1: Let’s assume a tube of length L that is closed at one end and open at the other and is entirely filled with air. This open-closed tube always has a node at the closed end and an anti-node at the open end. Let’s also assume thatthis length meets the resonance condition where you have three nodes along the tube length. So the resonant length for this case is L. Draw a diagram of the tube with the resonating wave. Near your diagram, write down how many wavelengths arepresent for this mode, and solve for the wavelength in terms of L. Case 2: Imagine you have filled your tube with water, thereby shortening the length, such that you will hear resonance again. Draw this. Near your diagram, write down the new length (as a fraction of L) required for this next resonance. Again, write down how many wavelengths are shown in you diagram and solve for the wavelength in terms of L. Case 3: Repeat what you did for Case 1 and 2 for the next shorter length that gives you resonance.Case 1:Case 2:Case 3:3) What do you notice about your analytical solutions for wavelength for each case? Is this what you expected? Can you get this information from the picture without doing any math? Explain.24) From the pattern you see, what is the next shorter length that gives resonance? Note that there might not be one, at some point you run out of tube.The cases you drew on the previous page correspond to lengths of the tube that will allow for resonances at a fixed input frequency. 5) From your pictures and calculations, by how much of a wavelength do you need to change your tube in order to get the next resonance?6) Conceptual Picture: If you aren’t at one of these resonant lengths, what happens? Basically, why don’t all lengthswork? What is going on in terms of the transmitted waves from the tuning fork and reflected waves off the ends of the tube. If it helps, contrast this with what happens at one of the resonant lengths. Draw some pictures below. Think sine waves and superposition. Just describe in words and pictures.37) Conceptual Picture: So what happens to a tube where you introduce many frequencies (you try to drive it at many at once; this is what happens when you blow into it). Why does it pick out ones that it “likes”? Again, just words and pictures.4Name:_______________________________________ Lab Section: ___________ Lab Partners: ___________________________________________________ Grade:____________Lab 3: Resonance in an Open-Closed TubeIntroduction One resonating system we all carry with us where ever we go, the vocal tract, can be modeled as a system of resonating tubes. For the vocal tract, as is true of the resonances of other tube systems like brass and woodwind instruments, many frequencies are inputted into the tube, but only those that meet the resonance condition can be heard. Forwind instruments, often the tube is lengthened or shortened during playing in order to change the pitch. That is, the condition for resonance has purposely been changed to select a different resonant frequency. In this lab, you will be investigating a open-closed resonating tube in very different way. You will be inputting just one frequency, and changing the length of tube in order to keep this single frequency in resonance with the system. For any traveling wave of just one frequency, the speed is given by v fl= (1)Experiment: Calculating the Speed of SoundTo experimentally measure the speed of sound, assume the frequency value stamped on the tuning fork to be correct and devisea way to measure the wavelength from finding the lengths of tube that meet the resonance condition. You can then use equation(1) to calculate the speed of sound from your measured value of wavelength. 1) How do you intend to use information about the different resonant lengths to calculate a value of wavelength? Note that in reality there is a correction factor on any open end of a resonant tube. It’s as if the open end is really a bit longer than the physical end by 0.61r, where r is the radius of the tube. However, depending on how you decideto find wavelength, you may not need the absolute length of the tube and therefore don’t need to worry about this factor. Use your drawings to help.In order to locate the lengths for which resonance occurs, raise the water level (by raising the can) until it is near the top of thetube. Strike the tuning fork with the rubber mallet (never use a hard object). Lower the water level, listening for a sudden increase in the intensity of the sound indicating a resonance. Use a string to mark the position of the water level at which the sound intensity is at its highest. Slowly move the water level past the string a few times to improve the accuracy of the measurement. Continue lowering the water level until you have found the other resonances. Record the position of the resonances and the uncertainty of the position. Repeat the