Bending wave is a dispersive wave and the wave velocity is different from that of the longitudinal wave
. Waves reflecting from the crack surface interferes with that from the inner and outer surfaces of the DP.
In case of the perfect fluid only displacement [u.sub.n] excites the longitudinal wave
in outer fluid.
Nonlinear longitudinal wave
was monitored at different positions along the length direction of tensile specimens for each sample.
Table 4 summarizes the range of density, longitudinal wave
velocity, and porosity of samples.
One can generalize the phase velocity of a longitudinal wave
for all states of the matter
We denote the displacement of the reflected longitudinal wave
by [u.sub.1], the lateral displacement produced by the flexural wave by [v.sub.1] in beam 1, the longitudinal displacement in string 2 by [u.sub.2], the lateral displacement in string 2 by [v.sub.2], the longitudinal displacement in beam 3 by [u.sub.3], and the lateral displacement in beam 3 by [v.sub.3].
Where m* is the band-edge effective mass, k is Boltzmann constant, T is the lattice absolute temperature, h is Plank constant divided by 2, Tu* Tu gives the tunneling probability density of the outgoing electron, F is Fermi energy level, l is energy of the electron associated with longitudinal wave
vector of the electron in the conduction band, V is the applied voltage.
For example, longitudinal wave
, transversal wave and some types of surface waves are observed in bulk specimen.
As shown in Figure 3, the longitudinal wave
velocity and density of the sandstone specimens heat treated at 800[degrees]C were both lower than those at room temperature, with difference amplitudes of 66.68%-71.84% and 5.31%-11.02%, respectively.
The nonzero elements [b.sub.13], [b.sub.24] of the matrix B determine the mutual transformation of longitudinal and transverse waves polarized along x-axis, whereas elements [b.sub.15], [b.sub.26] describe the relationship between transverse waves polarized along y-axis and longitudinal wave
. Nonzero element [b.sub.45] defines the mutual transformation between the waves of transverse polarization.
Thus, the spread speed of the longitudinal wave
of the ultrasound in the drilling mud is [c.sub.L].
where E is ultrasonic Young's modulus, G is Kirchhoff's modulus, [mu] is Poisson's Ratio, [rho] is apparent density, [C.sub.L] is speed of a longitudinal wave
, and [C.sub.T] is speed of a transverse wave.