### Abstract

This report presents the WKB approximation for the curvilinear horn (CH) equation, numerical comparisons of horn theories, and a model of viscothermal effects for acoustic wave propagation in axisymmetrical horns. The WKB solution is presented for the hyperbolic horn. The numerical comparisons for a hyperbolic horn profile show that the CH equations are more accurate than the plane-wave horn equation or previous spherical-wave horn equations. The CH equation using spherical coordinates has only small errors compared to the CH equation using oblate spheroidal coordinates. A variational derivation of viscothermal losses is constructed based upon the concept of wall admittance using orthogonal coordinates. The important case of the spherical-wave horn equation is considered as a special case using the first-order WKB theory. Differences from existing theory are observed near the apex of the cone.

Original language | English (US) |
---|---|

Pages (from-to) | 285-XI |

Journal | Acustica |

Volume | 85 |

Issue number | 2 |

State | Published - Dec 1 1999 |

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### ASJC Scopus subject areas

- Acoustics and Ultrasonics

### Cite this

*Acustica*,

*85*(2), 285-XI.

**Acoustic propagation in flaring, axisymmetric horns : II. Numerical results, WKB theory, and viscothermal effects.** / Keefe, Douglas H; Barjau, Ana.

Research output: Contribution to journal › Article

*Acustica*, vol. 85, no. 2, pp. 285-XI.

}

TY - JOUR

T1 - Acoustic propagation in flaring, axisymmetric horns

T2 - II. Numerical results, WKB theory, and viscothermal effects

AU - Keefe, Douglas H

AU - Barjau, Ana

PY - 1999/12/1

Y1 - 1999/12/1

N2 - This report presents the WKB approximation for the curvilinear horn (CH) equation, numerical comparisons of horn theories, and a model of viscothermal effects for acoustic wave propagation in axisymmetrical horns. The WKB solution is presented for the hyperbolic horn. The numerical comparisons for a hyperbolic horn profile show that the CH equations are more accurate than the plane-wave horn equation or previous spherical-wave horn equations. The CH equation using spherical coordinates has only small errors compared to the CH equation using oblate spheroidal coordinates. A variational derivation of viscothermal losses is constructed based upon the concept of wall admittance using orthogonal coordinates. The important case of the spherical-wave horn equation is considered as a special case using the first-order WKB theory. Differences from existing theory are observed near the apex of the cone.

AB - This report presents the WKB approximation for the curvilinear horn (CH) equation, numerical comparisons of horn theories, and a model of viscothermal effects for acoustic wave propagation in axisymmetrical horns. The WKB solution is presented for the hyperbolic horn. The numerical comparisons for a hyperbolic horn profile show that the CH equations are more accurate than the plane-wave horn equation or previous spherical-wave horn equations. The CH equation using spherical coordinates has only small errors compared to the CH equation using oblate spheroidal coordinates. A variational derivation of viscothermal losses is constructed based upon the concept of wall admittance using orthogonal coordinates. The important case of the spherical-wave horn equation is considered as a special case using the first-order WKB theory. Differences from existing theory are observed near the apex of the cone.

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UR - http://www.scopus.com/inward/citedby.url?scp=0033279505&partnerID=8YFLogxK

M3 - Article

VL - 85

SP - 285-XI

JO - Acta Acustica united with Acustica

JF - Acta Acustica united with Acustica

SN - 1610-1928

IS - 2

ER -