Berekening dimensionering <Tubo> Robot Diapason : 440 Hz Materiaal: aluminium buis 2699 kg/m3, Youngs modulus: 69GPa note = midi note number f = frequency of the fundamental l_eff = empiric exact length of the tube suspension point at distance from end outer tube diameter inner tube diameter attack-pitch Olson-constant 1/2 lambda resonator length 48 130.81 Hz 1624.37 364.18 60 / 50 65.2 1.1129 1.28 49 138.59 Hz 1578.13 353.82 60 / 50 66.2 1.1129 1.206 50 146.83 Hz 1533.2 343.74 60 / 50 67.2 1.1129 1.136 51 155.56 Hz 1489.55 333.96 60 / 50 68.2 1.1129 1.07 52 164.81 Hz 1447.15 324.45 60 / 50 69.2 1.1129 1.008 53 174.61 Hz 1405.95 315.21 60 / 50 70.2 1.1129 .949 54 185 Hz 1328.47 297.84 57 / 47 71.2 1.1129 .894 55 196 Hz 1290.66 289.36 57 / 47 72.2 1.1129 .842 56 207.65 Hz 1253.91 281.13 57 / 47 73.2 1.1129 .792 57 220 Hz 1218.22 273.12 57 / 47 74.2 1.1129 .746 58 233.08 Hz 1183.54 265.35 57 / 47 75.2 1.1129 .702 59 246.94 Hz 1149.84 257.79 57 / 47 76.2 1.1129 .66 60 261.63 Hz 1040 233.17 50 / 40 77.2 1.1129 .627 61 277.18 Hz 1010 226.44 50 / 40 78.2 1.112 .59 62 293.66 Hz 980 219.72 50 / 40 79.2 1.1092 .556 63 311.13 Hz 952 213.44 50 / 40 80.2 1.1089 .523 64 329.63 Hz 925 207.39 50 / 40 81.2 1.1092 .492 65 349.23 Hz 898 201.33 50 / 40 82.2 1.1075 .462 66 369.99 Hz 773 173.31 40 / 30 83.2 1.1135 .441 67 392 Hz 751.5 168.49 40 / 30 84.2 1.115 .415 68 415.3 Hz 730 163.67 40 / 30 85.2 1.1146 .39 69 440 Hz 709 158.96 40 / 30 86.2 1.1139 .367 70 466.16 Hz 689 154.47 40 / 30 87.2 1.1145 .345 71 493.88 Hz 668.5 149.88 40 / 30 88.2 1.1116 .324 72 523.25 Hz 602.5 135.08 35 / 25 89.2 1.1121 .309 73 554.37 Hz 585 131.16 35 / 25 90.2 1.1107 .291 74 587.33 Hz 567 127.12 35 / 25 91.2 1.1055 .273 75 622.25 Hz 551 123.53 35 / 25 92.2 1.106 .257 76 659.26 Hz 535 119.95 35 / 25 93.2 1.1047 .241 77 698.46 Hz 519 116.36 35 / 25 94.2 1.1015 .227 78 739.99 Hz 466.5 104.59 30 / 20 95.2 1.1247 .217 79 783.99 Hz 453.6 101.7 30 / 20 96.2 1.1266 .204 80 830.61 Hz 440 98.65 30 / 20 97.2 1.1231 .192 81 880 Hz 426.5 95.62 30 / 20 98.2 1.118 .18 82 932.33 Hz 414.5 92.93 30 / 20 99.2 1.1187 .169 83 987.77 Hz 402 90.13 30 / 20 100.2 1.1149 .159 84 1046.5 Hz 391.5 87.77 30 / 20 101.2 1.1203 .149 85 1108.73 Hz 380 85.2 30 / 20 102.2 1.1182 .14 86 1174.66 Hz 369 82.73 30 / 20 103.2 1.1171 .131 87 1244.51 Hz 357 80.04 30 / 20 104.2 1.1078 .123 omit 88 1318.51 Hz 347.5 77.91 30 / 20 105.2 1.112 .115 omit 89 1396.91 Hz 336 75.33 30 / 20 106.2 1.1014 .108 omit 90 1479.98 Hz 326.5 73.2 30 / 20 107.2 1.1019 .101 omit 91 1567.98 Hz 316.8 71.03 30 / 20 108.2 1.0991 .094 omit 92 1661.22 Hz 307.73 68.99 30 / 20 109.2 1.0987 .088 omit 93 1760 Hz 298.72 66.97 30 / 20 110.2 1.0969 .082 omit 94 1864.66 Hz 290.36 65.1 30 / 20 111.2 1.098 .077 omit 95 1975.53 Hz 281.18 63.04 30 / 20 112.2 1.0909 .071 omit 96 2093 Hz 272.3 61.05 30 / 20 113.2 1.0839 .067 omit 97 2217.46 Hz 264.1 59.21 30 / 20 114.2 1.0802 .062 omit 98 2349.32 Hz 256.62 57.53 30 / 20 115.2 1.0805 .058 omit 99 2489.02 Hz 249.14 55.86 30 / 20 116.2 1.079 .053 omit 100 2637.02 Hz 238.9 53.56 30 / 20 117.2 1.0511 .05 omit 101 2793.83 Hz 234.22 52.51 30 / 20 118.2 1.0704 .046 omit 102 2959.96 Hz 227.28 50.96 30 / 20 119.2 1.0679 .042 omit 103 3135.96 Hz 219.96 49.32 30 / 20 120.2 1.0597 .039 omit 104 3322.44 Hz 213.2 47.8 30 / 20 121.2 1.0547 .036 omit 105 3520 Hz 206.7 46.34 30 / 20 122.2 1.0504 .033 omit 106 3729.31 Hz 199.62 44.75 30 / 20 123.2 1.0379 .03 omit 107 3951.07 Hz 194.08 43.51 30 / 20 124.2 1.0394 .028 omit 108 4186.01 Hz 188.34 42.23 30 / 20 125.2 1.0371 .025 omit