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A molecular vibration is a periodic motion of the atoms of a molecule relative to each other, such that the center of mass of the molecule remains unchanged. The typical vibrational frequencies range from less than 10 13 Hz to approximately 10 14 Hz, corresponding to wavenumbers of approximately 300 to 3000 cm −1 and wavelengths of approximately 30 to 3 μm.
where ν is the frequency of the wave, λ is the wavelength, ω = 2πν is the angular frequency of the wave, and v p is the phase velocity of the wave. The dependence of the wavenumber on the frequency (or more commonly the frequency on the wavenumber) is known as a dispersion relation.
Rayleigh waves have energy losses only in two dimensions and are hence more destructive in earthquakes than conventional bulk waves, such as P-waves and S-waves, which lose energy in all three directions. A Love wave is a surface wave having horizontal waves that are shear or transverse to the direction of propagation.
Vibration (from Latin vibrāre 'to shake') is a mechanical phenomenon whereby oscillations occur about an equilibrium point.Vibration may be deterministic if the oscillations can be characterised precisely (e.g. the periodic motion of a pendulum), or random if the oscillations can only be analysed statistically (e.g. the movement of a tire on a gravel road).
The energy of each phonon, as given earlier, is ħω. The velocity of the wave also is given in terms of ω and k . The direction of the wave vector is the direction of the wave propagation and the phonon polarization vector gives the direction in which the atoms vibrate.
A shock wave is a type of propagating disturbance. When a wave moves faster than the local speed of sound in a fluid, it is a shock wave. Like an ordinary wave, a shock wave carries energy and can propagate through a medium; however, it is characterized by an abrupt, nearly discontinuous change in pressure, temperature and density of the medium ...
The water molecule has three fundamental molecular vibrations. The O-H stretching vibrations give rise to absorption bands with band origins at 3657 cm −1 (ν 1, 2.734 μm) and 3756 cm −1 (ν 3, 2.662 μm) in the gas phase. The asymmetric stretching vibration, of B 2 symmetry in the point group C 2v is a normal vibration.
A mode of vibration is characterized by a modal frequency and a mode shape. It is numbered according to the number of half waves in the vibration. For example, if a vibrating beam with both ends pinned displayed a mode shape of half of a sine wave (one peak on the vibrating beam) it would be vibrating in mode 1.