1. Standing sound waves in a tube - an analog to a quantum mechanical particle in a box Objective: For a simple tube, use an oscilloscope to compare the sound

input by a speaker at one end to the sound received by a microphone at the other end. Equipment Required: TeachSpin Quantum Analog System: Controller, V-Channel & Aluminum Cylinders Sine wave generator capable of producing 1-50 kHz with a peak-to-peak voltage of 0.50 V Two-Channel Oscilloscope Adv. Man. Rev 1.1 4/09 Setup: Make a tube using the tube-pieces. Put the end-piece with the speaker on one end and the end- piece with the microphone on the other. Attach a BNC splitter to SINE WAVE INPUT on the Controller. Connect the output of your sine wave generator to one side of the splitter. Use a BNC cable to send the sound signal to the Channel 1 input of your oscilloscope. Plug the lead from the speaker end of your experimental tube to SPEAKER OUTPUT on the controller. The same sine wave now goes to both the speaker and Channel I. Connect the microphone output of the tube array to MICROPHONE INPUT Connect AC MONITOR on the Controller to Channel 2 of the oscilloscope. Channel 2 will display the sound signal received by the microphone. Trigger the oscilloscope on Channel 1. Use the ATTENUATOR dial on the Controller to keep the signal on Channel 2 from going off scale. (Appendix 1 describes the function of each part of the Controller.) Experiment: Start at low frequency (100 Hz or less), and slowly increase the frequency. Question: What are you observing? How can you tell that you are at a resonance? Did you notice the phase- shift when going through a resonance? (Note that, due to unknown phase shifts in the speaker, microphone, and electronics, the absolute phase between input and output channel can not be interpreted.) Experiment: Change the length of the tube and repeat the experiment. Question: Do the resonance frequencies change? Are they higher/lower when the tube is longer/shorter? ADVISOR INFORMATION: The shorter the tube, the higher the resonance frequencies. Take a full set of data for one tube length: Measure and record the length of the tube. Measure the first 20 resonance frequencies. Assign the lowest resonance frequency the index number n = 1, and plot the resonance frequency f, as function of its index number, n. 1-1 Adv. Man. Rev 1.11 05/09 2.1 Measure resonances in the spherical resonator and determine their quantum numbers Objective: Determine the resonance frequencies for the spherical resonator and gather data to determine their angular-momentum quantum numbers. Equipment Required: TeachSpin Quantum Analog System: Controller, Hemispheres, Accessories Sine wave generator capable of producing 1-50 kHz with a peak-to-peak voltage of 0.50 V Two-Channel Oscilloscope Setup: Assemble the hemispheres so that the speaker is in the lower hemisphere and the microphone in the upper. Attach a BNC splitter to SINE WAVE INPUT on the controller. Connect the output of your sine wave generator to one side of the splitter. Use a BNC cable to send the sound signal to Chann 1 of the oscilloscope. Plug the lead from the speaker on the lower hemisphere to SPEAKER OUTPUT on the controller. The same sine wave now goes to both the speaker and Channel I. Use a BNC cable to connect the microphone output from the upper hemisphere to MICROPHONE INPUT. Connect AC MONITOR on the controller to Channel 2 of the oscilloscope to display the sound signal received by the microphone. Trigger the oscilloscope on Channel 1. Use the ATTENUATOR dial on the Controller to keep the signal on Channel 2 from going off scale. (Appendix 1 describes the function of each part of the Controller.) Adjust the position of the upper hemisphere so that a 180° on the scale is at the reference mark. In this position, the microphone and speaker are at opposite ends of a diameter. Experiment: Start at a low frequency and sweep the frequency up to about 8 kHz (8000 Hz). Write down all the resonance frequencies you observe. (If you listen carefully, you may actually hear some of them.) ADVISOR INFORMATION: At this angle between speaker and microphone, the resonances with high angular quantum number are visible with intensities higher than those observed at any other angle. Depending on the temperature, you will find resonances near the following frequencies: 2291 Hz, 3678 Hz, 4968 Hz, 6210 Hz, 6539 Hz, 7425 Hz, 8023 Hz... 2-4 Adv. Man. Rev 1.11 05/09 Objective: Observe, qualitatively, the way the amplitude of the resonance signal depends on the location of the microphone. Experiment: We will now gather data that will allow us to infer the angular quantum numbers of the resonances. Go to the second resonance, at about 3680 Hz. Fine-tune the frequency until it is as close as possible to the peak of the resonance. Shift the curves on the oscilloscope horizontally so that a maximum of the microphone signal (Channel 2) is located in the center of the image and marked by a vertical line. Now, watching the signal on the oscilloscope, slowly rotate the upper hemisphere, with respect to the lower one, from a = 180° to α = 0°. Questions: How did the amplitude change? Did the signal change its sign? Determine the angle where the amplitude is zero. At which angles is the signal maximal? Do both extrema have the same amplitude? Note: Do not warm the aluminum parts too much by touching them with your hands. The speed of sound is temperature-dependent, and, in consequence, the resonance frequency would shift with temperature. While analyzing the angular dependence, the chosen generator frequency should remain on top of the resonance. ADVISOR INFORMATION: The amplitude changes sign and has a node at about a = 100° corresponding to the node in the Legendre Polynomial at 0= 125.26°. The maximum at a = 0° (0 = 90°) has half the magnitude of the maximum at a = 180° (0 = 180°). Experimentally, the results are quite sensitive to the adjustment of frequency and the positioning of the upper hemisphere. Pressing gently on the upper hemisphere will give you a feeling for the experimental sensitivity in the measurement of these amplitudes. Analyze the data: The angle a read on the scale is not a suitable angle for comparison with theory. To analyze the data, you must first use a to calculate the polar angle, , which we have used for polar coordinates. Both the speaker and microphone are at an angle of 45° with respect to the horizontal plane between the hemispheres. By rotating the hemispheres with respect to each other, the angle can be changed from 0-90° (at a = 0°) to 8 = 180° (at a = 180°). Intermediate angles can be calculated using the formula 0= arccos(cosa - 1). 2-5 (2.15) You have measured the 6-dependence of the spherical harmonic function Y," (0,p) with 1 = 2 and m = 0. Now we need to learn more about the spherical harmonics to compare the experiment with theory. 6:16 Peer Grading Rubric PHSX 516 Date Reviewer Good Quality of data Cross checked data and worked to improve results. Evokes interest in physics Title Abstract " Introduction Method Results Uncertainties Summary Writing Author Improvements from draft Clearly states what was done, provides final result & explains significance Sets current experiment in physics context of the time. Explains theory or theories that are relevant. Ncitations > 2 Reader feels that they really understand how to repeat the experiment. Diagram of apparatus is clear. This section begins with "Figure 2 shows stopping voltage..... "Figures are clear and uncluttered. Legend font at least 12pt Each fig cited. Systematic & statistical uncertainties estimated. X² is reasonable Recapitulates what was measured and why it matters. Compares to other results Spelling & grammar correct. Paper gradually builds up an argument-based on data. Final report addresses all concerns Title of paper Fair Completed all aspects of experiment but no attempt to cross check Plain statement of what was done States what was done but with no physics context Explains theory but does not highlight significance of experiment Ncitations = 1 Most steps are explained but some missing. Figure may be poor. Figure are cited but for some Figures no conclusions are made about the data. Captions are incomplete. Legends smaller than 12pt text. X² unreasonable States final result but does not put it in context A few grammar mistakes. Text doesn't clarify what can be learned from data. Some corrections applied. Poor Followed manual, no attempt to fix issues Misleading Does not include final result nor put the result into context Poor explanation of theory Ncitations = 0 Explanation is garbled Figure is missing or very poor. Figures are not cited in text. Captions are unclear, Figures are cluttered with legends smaller than 12pt text in paper. No uncertainty analysis Missing or makes claims not supported by data. Many grammar mistakes. Text does not make a coherent argument. Final report essentially the same as draft