Variable Values R2(k) R1-3(k) I(mA) V1-2(V) V2-3(V) Meas 1 0 1 4,94 5 0 Meas 2 1 2,08 2,55 2,54 2,43 Meas 3 4 5,27 0,96 0,94 4,03 Meas 4 8 8,85 0,56 0,99 0,88 Meas 5 10 11,45 0,44 0,99 10,15 constant values R1 V1-3 1 5 V1-2 vs I 6 5 V1-2 (V) 4 3 V1-2 vs I 2 1 0 0 1 2 3 4 5 6 I(mA) 6 5 I(mA) 4 3 2 1 0 0 2 4 6 8 R2 and R1-3 10 12 14 R1 R2 1 1 1 1 1 C 0 1 4 8 10 2R2 1 1 1 1 1 0 2 8 16 20 (R1 +2R2)C f 1 1,46 2 0,73 5 0,292 9 0,162222 11 0,132727 R2 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 C 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 2R2 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 2 4 6 8 10 12 14 16 18 20 22 24 26 28 30 32 34 36 38 40 42 44 46 48 50 52 54 56 58 60 62 64 66 68 70 72 74 76 78 80 82 84 86 88 90 (R1 +2R2)C 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 f 1,46 0,73 0,486667 0,365 0,292 0,243333 0,208571 0,1825 0,162222 0,146 0,132727 0,121667 0,112308 0,104286 0,097333 0,09125 0,085882 0,081111 0,076842 0,073 0,069524 0,066364 0,063478 0,060833 0,0584 0,056154 0,054074 0,052143 0,050345 0,048667 0,047097 0,045625 0,044242 0,042941 0,041714 0,040556 0,039459 0,038421 0,037436 0,0365 0,03561 0,034762 0,033953 0,033182 0,032444 0,031739 1,6 1,4 1,2 f(Hz) R1 0,8 0,6 0,4 0,2 1 1 1 1 1 46 47 48 49 50 1 1 1 1 1 92 94 96 98 100 47 48 49 50 51 0,031064 0,030417 0,029796 0,0292 0,028627 f vs R2 1,6 1,4 1,2 f(Hz) 1 0,8 0,6 0,4 0,2 0 0 10 20 30 R2(KOhm) 40 50 60 R1 C 1 1 1 1 1 1 1 1 1 1 1 1 1 f 1 1 1 1 1 1 1 1 1 1 1 1 1 Cf 0,2616 0,2772 0,2937 0,3111 0,3296 0,3492 0,37 0,392 0,4153 0,44 0,4662 0,4939 0,5233 R1/2 0,2616 0,2772 0,2937 0,3111 0,3296 0,3492 0,37 0,392 0,4153 0,44 0,4662 0,4939 0,5233 0,5 0,5 0,5 0,5 0,5 0,5 0,5 0,5 0,5 0,5 0,5 0,5 0,5 0.23/Fc 0,879205 0,829726 0,783112 0,739312 0,697816 0,658648 0,621622 0,586735 0,553817 0,522727 0,49335 0,465681 0,439518 R2 0,379205 0,329726 0,283112 0,239312 0,197816 0,158648 0,121622 0,086735 0,053817 0,022727 -0,00665 -0,03432 -0,06048 1. Select one tune to be played during the competition. 2. Determine 6 frequencies needed 3. Decide which team will generate which frequencies and using what method and record the frequencies in Table 1. Assign lower frequencies to beams and higher frequencies to electronics. Table 1: Frequency Assignments Group 1 Group 2 Team A Team B Team C Team D Electronic Note 1 (Hz) A: 440.0 B: 493.9 E: 329.6 F: 349.2 Electronic Note 2 (Hz) D: 587.4 E: 659.2 G: 392.0 G#: Beam Note (Hz) E: 329.6 G: 392.0 C: 261.6 415.3 D: 293.7 Table 2 lists the frequencies of musical notes from middle C to C’. The frequencies are based on the so called A 440 scale (440 Hz corresponding to the A note), which is the most widely used1 in music. Table 2 Frequencies of musical notes Musical Frequency Note: If your tune contains notes outside the one octave shown, you Note (Hz) will need to research your frequencies. C C# D D# E F F# G G# A A# B C 261.6 277.2 293.7 311.1 329.6 349.2 370.0 392.0 415.3 440.0 466.2 493.9 523.3 Group A: Team A and Team B Happy 6 Notes (6 Frequencies) Needed: E: 329.6 G: 392.0 A: 440.0 B: 493.9 D: 587.4 E (one octave above the lower E): 659.2 Group B: Team C and Team D Ode Joy 6 Notes (6 Frequencies) Needed: C: 261.6 D: 293.7 E: 329.6 F: 349.2 G: 392.0 G#: 415.3 Project 2-HW 2: Musical Machine Due on Wed., November 16th (Submit Electronic Copies only) 1. Thoroughly read the instruction manual's "Reference" section on mechanical vibration of cantilever beams, tubular chimes, and palm pipes. Write Excel application which can calculate and graph theoretical first harmonic frequency of a cantilever beam as calculated from (Eq. 1) fi = K1 2 L 2 ΕΙ PA as a function of the beam length L. The application should take the values listed in Table 6, convert all values to SI units and calculate fi. a. To verify that the Excel gives correct results, calculate by hand the single frequency for all the values listed in Table 6 and for L = 4 inches. Make sure that all the units are consistent. Compare your result with the result from Excel. a. 2. Use the Excel application you created to investigate the f1(L) relation for three cases: (a) Steel beam described in Table 6; (b) steel tubular chime described in Table 7; (c) Copper tubular chime described in Table 7. For each case: Create a table with two columns: L (in) with at least 10 values, and fy with the corresponding calculated frequency (Hz). Adjust the range of L so that the frequency is approximately between 100 and 500 Hz. b. Graph fi(L) using 'scatter' plot in Excel. Add labels, units, etc. C. Determine the value of the theoretical beam length L, which will result in the assigned target frequencies assigned to your team (Refer to attached file). 3. In a similar fashion, determine the fi(L) relation and the target pipe lengths for palm pipes, as described by (Eq. 4) in the instructions.
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