Acoustics

Yazarlar: Oskar Bschorr, Hans-Joachim Raida

Konular:-

DOI:10.3390/acoustics3020021

Anahtar Kelimeler:Spherical wave,One-way wave equation,Two-way wave equation,Spherical coordinates,Nabla operators: gradient,Divergence,Laplace,Impulse flow equilibrium,Force equilibrium,Wattless near field,Spherical Bessel functions,Longitudinal/transversal wave propagation

Özet: The coordinate-free one-way wave equation is transferred in spherical coordinates. Therefore it is necessary to achieve consistency between g r a d i e n t , d i v e r g e n c e and L a p l a c e operators and to establish, beside the conventional radial Nabla operator ∂ Φ / ∂ r , a new variant ∂ r Φ / r ∂ r . The two Nabla operator variants differ in the near field term Φ / r whereas in the far field r ≫ 0 there is asymptotic approximation. Surprisingly, the more complicated gradient ∂ r Φ / r ∂ r results in unexpected simplifications for – and only for – spherical waves with the 1 / r amplitude decrease. Thus the calculation always remains elementary without the wattless imaginary near fields, and the spherical Bessel functions are obsolete.

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