What question did this study set out to answer?

To establish an approximate solution for general linear second-order differential equations that accurately models wave reflection in inhomogeneous media without encountering singularities at function zeros.

November 15, 1954Physical Review

Reflection of Waves by an Inhomogeneous Medium

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Authors

VBV.A. BaileyUniversity of Oklahoma

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Implication

Theoretical modeling demonstrates singularity-free wave solutions in inhomogeneous media, indicating an accurate method for calculating reflection coefficients.

Key Points

To establish an approximate solution for general linear second-order differential equations that accurately models wave reflection in inhomogeneous media without encountering singularities at function zeros.
Formulated a fundamental pair of simple approximations ($u_1, u_2$) to replace classical Liouville-Rayleigh-Jeffreys solutions.
Designed an iterative mathematical process to refine initial reflection coefficient approximations ($\rho_1$) into a rapidly converging sequence ($\rho_2, \rho_3, \dots$).
Applied the differential approximation $u_1$ to derive an expanded-range analytical solution for the Hankel function $H_n^{(2)}(nz)$.
Derived approximations $u_1$ and $u_2$ maintain general agreement with Liouville-Rayleigh-Jeffreys solutions while remaining finite at zeros.
Iterative reflection approximations systematically and rapidly converge toward the exact reflection coefficient $\rho$ for specified inhomogeneous media.
The resulting Hankel function approximation matches classical formulations by Debye, Hankel, and Carlini while achieving a broader range of analytical validity.

Cite This Study

V.A. Bailey (1954) studied this question.

synapsesocial.com/papers/6a9253bd5ab1441fe3c8106a https://doi.org/10.1103/physrev.96.865

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Implication

Theoretical modeling demonstrates singularity-free wave solutions in inhomogeneous media, indicating an accurate method for calculating reflection coefficients.

Reflection of Waves by an Inhomogeneous Medium

Discussion

Member takes

Implication

Key Points

Cite This Study

Reflection of Waves by an Inhomogeneous Medium

Discussion

Member takes

Implication

Key Points

Cite This Study

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