Exact evaluation of an ultrasonic scattering formula for a rigid immovable sphere

Farhad Jafari; Ernest L. Madsen; James A. Zagzebski; Mitchell M. Goodsitt

doi:10.1016/0301-5629(81)90040-5

Exact evaluation of an ultrasonic scattering formula for a rigid immovable sphere

Farhad Jafari, Ernest L. Madsen, James A. Zagzebski, Mitchell M. Goodsitt

Research output: Contribution to journal › Article › peer-review

8 Scopus citations

Abstract

It has been discovered that three theoretically derived plots of acoustic scattering for rigid immovable spheres appearing in two standard reference works are only qualitatively correct and therefore could be misleading. The reason for the inaccuracy is shown to be premature truncation of the infinite series resulting from the theory. Quantitative plots resulting from exact computations and those corresponding to premature truncations are displayed. The main purpose of this note is to alert others, who may wish to check their programming of theoretical expressions for scattering of ultrasonic waves from spheres, to the error of using the plots in the standard reference works and to suggest that they use the exact results presented here.

Original language	English (US)
Pages (from-to)	293-296
Number of pages	4
Journal	Ultrasound in Medicine and Biology
Volume	7
Issue number	3
DOIs	https://doi.org/10.1016/0301-5629(81)90040-5
State	Published - 1981
Externally published	Yes

Bibliographical note

Funding Information:
Acknowledgements--Our work was supported by NCI Grants 5-PO1-19278-2 and 5-RO1-CA-25634-01. The authors thank Orlando Canto for generating the figures and to Kathy McSherry for typing the manuscript.

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abstract = "It has been discovered that three theoretically derived plots of acoustic scattering for rigid immovable spheres appearing in two standard reference works are only qualitatively correct and therefore could be misleading. The reason for the inaccuracy is shown to be premature truncation of the infinite series resulting from the theory. Quantitative plots resulting from exact computations and those corresponding to premature truncations are displayed. The main purpose of this note is to alert others, who may wish to check their programming of theoretical expressions for scattering of ultrasonic waves from spheres, to the error of using the plots in the standard reference works and to suggest that they use the exact results presented here.",

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AU - Jafari, Farhad

AU - Madsen, Ernest L.

AU - Zagzebski, James A.

AU - Goodsitt, Mitchell M.

N1 - Funding Information: Acknowledgements--Our work was supported by NCI Grants 5-PO1-19278-2 and 5-RO1-CA-25634-01. The authors thank Orlando Canto for generating the figures and to Kathy McSherry for typing the manuscript.

PY - 1981

Y1 - 1981

N2 - It has been discovered that three theoretically derived plots of acoustic scattering for rigid immovable spheres appearing in two standard reference works are only qualitatively correct and therefore could be misleading. The reason for the inaccuracy is shown to be premature truncation of the infinite series resulting from the theory. Quantitative plots resulting from exact computations and those corresponding to premature truncations are displayed. The main purpose of this note is to alert others, who may wish to check their programming of theoretical expressions for scattering of ultrasonic waves from spheres, to the error of using the plots in the standard reference works and to suggest that they use the exact results presented here.

AB - It has been discovered that three theoretically derived plots of acoustic scattering for rigid immovable spheres appearing in two standard reference works are only qualitatively correct and therefore could be misleading. The reason for the inaccuracy is shown to be premature truncation of the infinite series resulting from the theory. Quantitative plots resulting from exact computations and those corresponding to premature truncations are displayed. The main purpose of this note is to alert others, who may wish to check their programming of theoretical expressions for scattering of ultrasonic waves from spheres, to the error of using the plots in the standard reference works and to suggest that they use the exact results presented here.

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Exact evaluation of an ultrasonic scattering formula for a rigid immovable sphere

Abstract

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