Lab 8 - Standing Waves

Lab 8 - Standing Waves - PHYSICS 133 EXPERIMENT NO. 8...

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PHYSICS 133 EXPERIMENT NO. 8 STANDING WAVES Introduction In this experiment we study standing waves on a long rubber band stretched between fixed supports. These standing waves are similar to those produced in a guitar string when it is plucked, except that in the present experiment, we will continuously drive them so that they will not die out. If one end of a long rubber band is subjected to forced periodic vibrations, traveling waves will propagate down the rubber band with velocity v = ( T / μ ) (1) where T is the tension in the rubber band and is the mass per unit (stretched) length of the rubber band. The wavelength λ is related to the frequency f of the driving force and the velocity of propagation v as λ = v / f. Waves reflecting off the far end of the rubber band interfere with incident waves, and for certain driving frequencies a stable pattern emerges, characterized by fixed points of destructive interference (nodes) and constructive interference (anti-nodes). The condition for this to occur is L = n λ /2, with n = 1, 2, 3, . .. ( integer ) (2) This condition “quantizes'' the system, so that only certain wavelengths (and thus only certain frequencies) can excite these “normal” vibrational modes of the system. Measurement The rubber band is stretched over a pulley, and the tension T is provided by a weight. The total (not just the part between the supports) mass of the rubber band is recorded on a label on the small motor for each apparatus, so you can calculate the linear mass density by measuring the rubber band’s total stretched length. (Note: this length will vary with the weight applied!) Start with the rubber band as long as possible (about 2 m). A small electric motor driven by a variable power supply produces the oscillatory driving force near one end of the rubber band. The period of the oscillations is determined by a photogate and an electronic timer, the operation of which your TA will explain. If computers are available, use the “Precision Timer” program, choose “miscellaneous timing modes” from the main menu, and then choose “strobe timer.” This mode will measure the time from one interruption of the photogate to the next. When you start the measurement by pressing the “enter” key, a series of numbers will appear on the screen, each of them equal to the period T
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This note was uploaded on 09/26/2008 for the course PHY 131 taught by Professor Rijssenbeek during the Fall '03 term at SUNY Stony Brook.

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Lab 8 - Standing Waves - PHYSICS 133 EXPERIMENT NO. 8...

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