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Resonance: Standing Waves Essay

2442 words - 10 pages

abstract the objective of this study is to determine the speed of the propagating wave in the wire and then using the obtained values show how different tensions of the wire affect the speed of this wave. For this purpose the experimental setup consisting of a wire fixed at one end and with a movable fixed point at the other end, a mass bar hanging over a pulley, a magnet placed at the fixed end, and a function generator (Agilent 33120A, 15MHz Function/Arbitrary Waveform Generator) connected to the wire was used. The results obtained after fitting the experimental values with theoretical curve show the trend in increase of the velocity of the propagating wave with increase of the wire ...view middle of the document...

Therefore, the standing wave resonances occur at evenly-spaced frequencies, known as harmonics [1].(3)The velocity of the wave cs is also affected by wire tension and is generally described bycs = ,(4)where T is tension of the wire and μ stands for the mass per unit length of the wire. We started this project with some phenomenological formula relating the speed of the propagating wave cs and the wire tension Tcs = a T b ,(5)where a and b are constants. We performed the following experiment to extract coefficients a and b according to Eq. (4).3. MethodsIn this experiment we used the setup that consisted of a wire that was fixed at one end and had a movable fixed point at the other end. Tension of the wire was provided by a mass bar hanging over a pulley at the adjustable end. A magnet was placed at the fixed end of the wire and a function generator (Agilent 33120A, 15MHz Function/Arbitrary Waveform Generator) was connected to the wire (Fig. 1). The function generator was passing alternating current through the wire. The AC current in the presence of the magnet produced an alternating force on the wire, which was actually driving this harmonic oscillator. When the function generator was operating at frequencies that matched the resonant frequencies of the wire, in this case a standing wave could be observed.First, we made all necessary adjustments of the setup. We placed the magnet at the fixed of the wire, and then we checked that the function generator is connected to our setup. The wire was exactly in the pulley at the adjustable end of the wire.We decide to start with an intermediate tension of the wire, provided by mass bar of m = 200 g, which value was later changed in that way varying the tension. The length of the wire was set to l = 0.86 m. Then we began to explore the range of the resonant frequencies, whose experimental values could be observed on the on the display of the function generator. We were able to identify first and second harmonics of the wire represented by standing waves with two and three nodes, respectively. Then we repeated the previous procedure for l = 0.7, 0.6, and 0.5 meters. For l = 0.5 m we were able to observe only first harmonics. For each particular standing wave we were giving 1-2 minutes before recording the corresponding values in order to let the transients, impeding accurate determination of the resonant frequencies, die out.After that we increased tension of the wire, raising the mass of the mass bar to m = 300 g, and then we collected our experimental data, basically repeating the procedure we had in our first.Then, we decreased tension, using the mass bar of m = 150 g and took the values of the resonant frequencies of first and second harmonics for l = 0.86 m and l = 0.70 m. For l = 0.60, 0.50, 0.40, and 0.30 meters we took the values only for first harmonics, as close to second harmonics for these wire lengths the wire was vibrating rather violently, without pronounced resonance (presumably...

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