Harmonisation of Classical Wave Equation

2021 ◽  
Author(s):  
Alireza Jamali
Keyword(s):  
Wave Equation ◽  
Short Note ◽  
Scalar Fields ◽  
Nonlinear Pde ◽  
Classical Wave ◽  
Classical Wave Equation

In this short note we present a technique using which one attributes frequency and wavevector to (almost) arbitrary scalar fields. Our proposed definition is then applied to the classical wave equation to yield a novel nonlinear PDE.

Radiation and Response of Cylindrical Beams Excited by Sound

1972 ◽  
Vol 94 (1) ◽  
pp. 139-147 ◽  
Author(s):  
J. R. Bailey ◽  
F. J. Fahy
Keyword(s):  
Wave Equation ◽  
Pure Tone ◽  
Experimental Program ◽  
Acoustic Excitation ◽  
Resonant Response ◽  
Reverberation Chamber ◽  
At Resonance ◽  
Classical Wave ◽  
Theoretical Predictions ◽  
Classical Wave Equation

The sound radiated from an unbaffled cylindrical beam vibrating transversely at resonance is calculated by solution of the classical wave equation subject to the boundary conditions imposed by the motion of the beam. The interaction of sound and vibration is then demonstrated by using a theory based on the principle of reciprocity to predict the resonant response of a cylindrical beam to acoustic excitation. The results show that radiation and resonant response are highly frequency dependent. An experimental program is also reported. The power radiated from three cylindrical beams vibrating at resonance and the resonant response of the beams to pure-tone acoustic excitation are measured in a reverberation chamber. The experimental results agree well with the theoretical predictions.

Classical wave equation in fluid filament stretching

1988 ◽  
Vol 27 (5) ◽  
pp. 466-476 ◽  
Author(s):  
S. Kase ◽  
T. Nishimura
Keyword(s):  
Wave Equation ◽  
Filament Stretching ◽  
Classical Wave ◽  
Fluid Filament ◽  
Classical Wave Equation

The Effect of Wall Motions on the Governing Equations of Contained Fluids

1990 ◽  
Vol 57 (3) ◽  
pp. 783-785 ◽  
Author(s):  
Roger Ohayon ◽  
Carlos A. Felippa
Keyword(s):  
Wave Equation ◽  
Finite Elements ◽  
Governing Equation ◽  
Equations Of Motion ◽  
Governing Equations ◽  
Displacement Potential ◽  
Classical Wave ◽  
Classical Wave Equation ◽  
Acoustic Fluid

The equations of motion for an acoustic fluid enclosed in a moving or flexible container are studied. It is shown that the determination of the reference state must account for the surface-integrated effect of the wall motions. The governing equation of transient motions about this state in the displacement potential does not generally reduce to the classical wave equation unless special adjustments are made. The results are relevant to finite elements formulations based on the displacement potential.

On Bessel Polynomials

1954 ◽  
Vol 6 ◽  
pp. 410-415 ◽  
Author(s):  
R. P. Agarwal
Keyword(s):  
Wave Equation ◽  
Spherical Coordinates ◽  
Bessel Polynomials ◽  
Classical Wave ◽  
Classical Wave Equation ◽  
Image Position

Recently a number of papers have been written on Bessel polynomials which arise as the solutions of the classical wave equation in spherical coordinates. Krall and Frink (5) studied in some detail the properties of these polynomials yn(x, a, b) defined as(1) .

scholarly journals Wave-equation traveltime inversion with multifrequency bands: Synthetic and land data examples

Geophysics ◽  
2018 ◽  
Vol 83 (6) ◽  
pp. B305-B315 ◽  
Author(s):  
Han Yu ◽  
Sherif M. Hanafy ◽  
Gerard T. Schuster
Keyword(s):  
Wave Equation ◽  
Velocity Model ◽  
Inversion Method ◽  
Data Sets ◽  
Traveltime Inversion ◽  
Numerical Tests ◽  
Classical Wave ◽  
Classical Wave Equation ◽  
Zero Offset ◽  
Starting Model

We have developed a wave-equation traveltime inversion method with multifrequency bands to invert for the shallow or intermediate subsurface velocity distribution. Similar to the classical wave-equation traveltime inversion, this method searches for the velocity model that minimizes the squared sum of the traveltime residuals using source wavelets with progressively higher peak frequencies. Wave-equation traveltime inversion can partially avoid the cycle-skipping problem by recovering the low-wavenumber parts of the velocity model. However, we also use the frequency information hidden in the traveltimes to obtain a more highly resolved tomogram. Therefore, we use different frequency bands when calculating the Fréchet derivatives so that tomograms with better resolution can be reconstructed. Results are validated by the zero-offset gathers from the raw data associated with moderate geometric irregularities. The improved wave-equation traveltime method is robust and merely needs a rough estimate of the starting model. Numerical tests on the synthetic and field data sets validate the above claims.

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