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7B: Standing Wave In Strings - 1 6: S TANDING W AVES I N S TRINGS 1. T HE S TANDING W AVE A PPARATUS It is difficult to get accurate results for standing waves with the spring and stopwatch ( first part of the lab ). In contrast, very accurate results can be achieved using the apparatus provided in the lab room. A string is driven by a speaker which is controlled by the function generator. 1. Hang a 700g mass from the end of the string that runs over the pulley. Turn on the function generator. Set the frequency to 90 Hz and turn the amplitude all the way up. Move the clear plastic “bridge” until you get a fundamental standing wave. Play with it until you get the largest possible amplitude. If the hanging mass which provides the tension is swinging around, it will make it hard to adjust, so you may want to stop the mass if it is swinging. Once you get the best standing wave, do not move the bridge until you see you should do so in the manual . Record the length of the string. L = 2. It is important to know the frequency of the fundamental as accurately as possible. If your function generator does not read exactly 90 Hz, record the frequency here. 3. Turn the dial on the function generator to increase the frequency until you get the next standing wave, which should have two humps . Record the frequency in the table below. 4. Continue in this way until you get to the seventh harmonic. Then turn down the amplitude while you do the calculations in the next part. # humps f (Hz) f / f 1 Harmonic number 1 2 3 4 5 6 7
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6:Standing Wave in Strings- 2 Calculate f / f 1 . You should find that these values are very close to being whole numbers. Round these values to whole numbers and put the result under “Harmonic Number.” It should be obvious that the number of humps is the number of the harmonic for a string fixed at both ends. Use this knowledge to predict the frequency that will be necessary to create the 8th harmonic. Then try it. 2. S PEED AND H ARMONICS The speed of a wave on a string depends on the stiffness, density, and tension in the string. It does not depend on the wavelength of the wave sent down the string. In the same way, the speed of sound in air does not depend on the type of sound. When standing waves are created on a string, the wavelength, frequency, and speed are
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This note was uploaded on 01/20/2012 for the course P 109 taught by Professor Staff during the Fall '08 term at Indiana.

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