Waves Of Different Wavelengths Research Articles

Light-scattering in homogeneous media regarded as reflexion from appropriate thermal elastic waves

Attributing the scattering of light in a homogeneous transparent liquid to the local fluctuations in density, and the latter to the superposition of the thermal elastic waves of different wave-lengths maintained in the enclosure, one may, following Einstein, evaluate the scattering coefficient of the liquid along any given direction. The expression for the scattering coefficient involves a triple infinite series, which Einstein evaluates by suitably replacing it by a triple integral. The series, however, can be directly summed, and the contributions from different progressive waves to scattering studied in detail. This method brings out prominently the appropriateness of regarding scattering as regular Bragg reflexions from suitable elastic waves, and also reveals some interesting features which are missed when the summation is replaced by integration. The intensities of the Brillouin components are calculated on this basis, both in a fluid medium and in a crystal; and in the latter case the expression for the overall intensity of the Brillouin components is shown to be identical with the well-known expression of Waller in X-ray scattering.

An improved numerical method of two-dimensional fourier synthesis for crystals

It is shown that a two-dimensional Fourier summation for a crystal without a centre of symmetry can be resolved into one-dimensional summations, and these latter can be calculated very rapidly by using a set of printed strips which give cosine and sine waves of different wave-lengths and amplitudes. The most useful interval of division of the strips, and various features concerning their use, are described.

The Pathology of Navicular Disease

The geometry of a rectangular plate used in a structural application is an important design parameter that influences the vibrational response of the plate when it is subjected to an impact. In this study, the influence of a cross-sectional discontinuity on the vibration characteristics of viscoelastically supported plates was investigated. The discontinuity was induced at a specific location in the length-wise span. Experimental studies were performed to identify the effect of the discontinuity on the plate vibration response. The mode shapes and damping ratios of the plates with and without discontinuities in the cross-section were measured and compared. Forced vibration responses and modal properties were predicted using a numerical model. The variation in cross-sectional geometry was modeled to determine the changes in bending stiffness. The translational and rotational viscoelastic stiffnesses at the plate edges were used for modeling the vibration damping at the boundaries. This damping occurred at the contact surface between the plate and the fixtures. To investigate the effect of support stiffness on the vibration damping, flexural wave propagation analysis was performed with different boundary conditions. The ratio between the incident and reflected waves from the boundaries was predicted for flexural waves of different wavelengths. The predicted reflection ratios of the plate with and without the discontinuities were compared to the predicted loss factors using numerical analysis. The vibration energy dissipation at the viscoelastic supports was proportional to the measured modal damping.