Longitudinal and transverse waves

“Longitudinal and transverse waves” discusses vector-amplitude waves in isotropic media, as exemplified by plasma waves and by plane sound waves. Transverse and longitudinal polarizations are identified with amplitudes that are divergence-free or curl-free. These conditions pick out polarization states that are “pure”, meaning not contaminated by the other possibility.

Reflection of elastic waves at the boundary with the specified stresses

The problem of elastic waves reflection at the boundary at given constant stresses is considered. Provided that the reflection laws are fulfilled, analytical expressions are obtained for the reflection coefficients of longitudinal and transverse waves, which allow us to determine the deformations amplitudes at the boundary. The dependences of the reflections coefficients and strain components at the boundary on the angle of incidence of the wave are calculated at nonzero values of normal and tangential stresses at the boundary and the specified wave parameters. The obtained results are analyzed and compared with the known results for the free surface.

Non-destructive ultrasonic method of testing the strength of backfill concrete at deep Talnakh mines

In underground mining with backfilling of mined-out areas, it is necessary to analyze the filling mass quality. Since coring and testing would make a complex process, the method of express analysis comes in handy. As the mechanical methods of express quality analysis are not very accurate, the best option would be to use an acoustic method. But before the latter can be used, it is necessary to conduct a series of laboratory tests in order to under stand the empirical correlation between strength and acoustic pro perties. This paper describes the results of laboratory tests that were carried out for samples of backfill concrete after 7, 28, 45, 70, 90 days of curing to test their strength and acoustic properties. A correlation has been found between the uniaxial compressive strength of the fill and the ultrasonic wave propagation rates. Some field measurements have been taken to determine the propagation rates of longitudinal and transverse waves in the filling mass. Calibration curves have been built for both longitudinal and transverse waves. It was established that for the filling mass that hasn’t cured for 90 days it is the propagation rate of transverse waves that correlates most accurately with the strength; whereas for the filling mass that is older than 90 days it is the propagation rate of longitudinal waves.

Omnidirectional THz Mirror on a One-Dimensional Porous Silicon Thermocrystal

We have designed a thermocrystal that reflects phononic thermal radiation. In the THz range, heat is kinetic energy carried predominantly by phononic vibrations. These mechanical vibrations have wavelengths that produces interferences within the internal interfaces of a phononic crystal. We determined conditions to obtain gaps simultaneously for longitudinal and transverse waves in a porous silicon multilayer. We propose a one-dimensional crystal with an omnidirectional mirror that reflects all phononic vibrations in the THz.