Inverse Eigenvalue Experiments for Beaded Strings

This web page provides supplementary data sets for experiments described in:
"One Can Hear the Composition of a String: Experiments with an Inverse Eigenvalue Problem"
Steven J. Cox, Mark Embree, Jeffrey M. Hokanson
Department of Computational and Applied Mathematics, Rice University
(28 June 2010 revision of Rice CAAM Tech Report 08-10, July 2008,
with an appendix on inversion using continued fractions).

Experimental Apparatus

Photographic overview of the experimental apparatus.

The collet vise, normally used in machine shops to hold drill bits, is used here to impose Dirichlet boundary conditions. The collet has a 0.010in diameter hole into which the 0.015in diameter string fits.	The photodetector mount. Within, two Fairchild QVE00034 photointerrupters are mounted perpendicular to each other. For each interrupter, one end emits an infrared beam which is measured by a photo-diode on the other side. As the string vibrates, it occults more or less of the beam, translating into more or less current passing through the device.

Data Sets

Using the two photointerruptors described above, we record string displacement data in two axes. Each of the plots that follow below show data for both axes: one plotted in blue, the other in green. (In some cases, the green data obscures the blue.)

Each data set is accompanied by a *.mat file and contains two variables, y and info. The variable y contains a two column vector of string displacement in micrometers (1 µm = 1e-6 meters), one column for each of the axes measured by the photointerruptors. Each entry in the vector is separated by the reciprocal of the sample rate, stored in info.sr. The structure info also contains:

• omega - Peaks in the Fourier transform by our estimation, in angular frequency (1/sec).
• tension - Tension of the string in Newtons.
• L - Total length of the string in meters.
• sr - Sample rate of the data stored in y in samples per second.

Two bead data
D0132 dataset solution
	ω = 162.73, 224.31 sec-1 Λ = 26483, 50315 σ = 125.3 N , L = 1.124 m
D0134 dataset solution
	ω = 143.26, 227.45 sec-1 Λ = 20522, 51734 σ = 126.1 N , L = 1.124 m
D0166 dataset solution
	ω = 133.20, 200.43 sec-1 Λ = 17743, 40174 σ = 163.1 N , L = 1.124 m
Four bead data
D0139 dataset solution
	ω = 118.12, 206.72, 315.42, 429.14 sec-1 Λ = 13953, 42732, 99487, 184162 σ = 191.8 N , L = 1.124 m
D0142 dataset solution
	ω = 135.72, 233.11, 284.63, 395.84 sec-1 Λ = 18419, 54338, 81013, 156690 σ = 191.2 N , L = 1.124 m
D0144 dataset solution
	ω = 139.49, 223.68, 303.48, 363.17 sec-1 Λ = 19457, 50033, 92099, 131891 σ = 192.5 N , L = 1.124 m
D0146 dataset solution
	ω = 151.42, 256.35, 313.53, 360.65 sec-1 Λ = 22929, 65717, 98302, 130072 σ = 192.5 N , L = 1.124 m
D0148 dataset solution
	ω = 142.63, 244.42, 382.65, 534.70 sec-1 Λ = 20343, 59739, 146418, 285903 σ = 154.2 N , L = 1.124 m
D0149 dataset solution
	ω = 166.50, 276.46, 343.06, 495.12 sec-1 Λ = 27724, 76430, 117691, 245139 σ = 154.0 N , L = 1.124 m
D0151 dataset solution
	ω = 169.65, 264.52, 361.91, 453.02 sec-1 Λ = 28780, 69972, 130980, 205225 σ = 152.9 N , L = 1.124 m
D0152 dataset solution
	ω = 164.62, 273.32, 339.92, 490.09 sec-1 Λ = 27100, 74703, 115546, 240187 σ = 152.9 N , L = 1.124 m
Six bead data
D0154 dataset solution
	ω = 98.02, 175.93, 305.36, 373.85, 398.98, 437.94 sec-1 Λ = 9607, 30951, 93246, 139763, 159187, 191790 σ = 166.0 N , L = 1.124 m
D0158 dataset solution
	ω = 99.90, 175.30, 338.04, 380.76, 412.81, 446.73 sec-1 Λ = 9981, 30730, 114268, 144979, 170408, 199572 σ = 161.4 N , L = 1.124 m