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HW 12 Tips

HW 12 Tips - HW 12 Tips PHY 131 Sect 10 11 15 Fall 2010...

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1 HW 12 Tips; PHY 131 Sect. 10, 11, 15; Fall 2010 Prof. Pascuzzi HW 12 covers Waves, Resonance and Sound (Ch.15, 16) Problem 1 “Standing Waves on a Guitar String” This problem describes some of the basic features of standing waves on a string, a synopsis of which is briefly shown below. The fundamental frequencies of such a wave are as shown in the box, where “ n ” is the number of antinodes (AN) as shown in the diagrams. Resonant wave frequencies along strings under tension obey the following relationship; , where n = # of antinodes or half wavelengths along the string, v = the wave speed and L = the length of the string which is resonating. Fundamental frequencies for Standing Wave Harmonics along a String; n = 1 (i.e. 1 antinode or 1 (½) wave exists n = 2 (i.e. 2 antinodes or 2 (½) waves exist along the string) ( Fundamental or 1 st Harmonic ) along the string) ( 2 nd Harmonic ) n = 3 (i.e. 3 antinodes or 3 (½) waves n = 4 (i.e. 4 antinodes or 4 (½) waves exist along the string) ( 3 rd Harmonic ) exist along the string) ( 4 th Harmonic ) Fundamental frequencies of standing waves on a string

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2 Part A). This part is basically asking you to look at the diagram and read the length of one wave. Part B). Here, you need to use the equation above (for the fundamental frequencies of the standing waves on a string) and solve it for . When you do that, look carefully at which n value will give the largest wavelength, then solve using the given numbers. Part C). Here, you can use either the equation or to determine the wave speed on the string. Note that when you see “fundamental” frequency, the antinode number ( n ) is 1. Part D). Check the diagrams above, or make your own! Notice that the overtones start after the fundamental, and the first overtone (or harmonic) has two antinodes, not one. Thus, count accordingly. Part E). The lowest frequency must be the fundamental, and remember that octaves are exact multiples in the ratio of 2:1. Thus, you can easily figure out the situation with the higher frequencies listed for this part. Problem 2 “Two Identical Pulses along a String” Part A). This is very basic, as long as you remember that when waves reflect off fixed boundaries, they invert, returning 180° out of phase. When waves reflect off a weak (or loose) boundary, they reflect non-inverted, or go back with the amplitude pointing in the same direction (in phase with the original pulse).
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HW 12 Tips - HW 12 Tips PHY 131 Sect 10 11 15 Fall 2010...

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