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Some experiments are conveniently performed in the time domain, some in the frequency domain, and some use a hybrid approach. Does the domain make any difference in the ultimate resolution of the experiment? Or can the details of the experiment always be tweaked so that the different approaches give the same answer? We consider a simple optics experiment and consider both time and frequency measurements and take into account the influence of noise, finite dynamic range, attenuation, and the duration of the measurement. (c) 2005 American Association of Physics Teachers. [DOI: 10.1119/1.1891172]

The presence and nature of fractures can have a profound impact on the elastic and mechanical properties of materials. Whether it is a fracture-induced loss of strength or the creation of a long-wavelength anisotropy, being able to infer the presence and properties of fractures in a material has many applications. Detecting changes in the spectra of mechanical resonances due to the presence of fractures is not difficult. A more interesting issue is which elastic moduli are sensitive to the presence of these fractures and how are these moduli related to the stiffness of the material? Resonant ultrasound spectroscopy was performed on acrylic cylinders with internal cracks. Inversions were performed for both isotropic and anisotropic moduli. Good agreement was obtained between isotropic moduli and projected (optimal isotropic moduli obtained from anisotropic moduli) for nonverlapping cracks. The same projections yielded poorer agreement for the sample with overlapping cracks. The results also show that the degree of anisotropy depends upon the amount of crack overlap, and that the isotropic shear modulus is a reliable measure of decreasing stiffness. [ABSTRACT FROM AUTHOR]