Sound radiation from a resilient spherical cap on a rigid sphere

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Abstract

It has been argued that the sound radiation of a loudspeaker is modeled realistically by assuming the loudspeaker cabinet to be a rigid sphere with a resilient spherical cap. Series expansions, valid in the whole space outside the sphere, for the pressure due to a harmonically excited cap with an axially symmetric velocity distribution are presented. The velocity profile is expanded in functions orthogonal on the cap, rather than on the whole sphere. As a result, only a few expansion coefficients are sufficient to accurately describe the velocity profile. An adaptation of the standard solution of the Helmholtz equation to this particular parametrization is required. This is achieved by using recent results on argument scaling of orthogonal (Zernike) polynomials. The approach is illustrated by calculating the pressure due to certain velocity profiles that vanish at the rim of the cap to a desired degree. The associated inverse problem, in which the velocity profile is estimated from pressure measurements around the sphere, is also feasible as the number of expansion coefficients to be estimated is limited. This is demonstrated with a simulation.
Original languageEnglish
Pages (from-to)2262-2273
Number of pages13
JournalJournal of the Acoustical Society of America
Volume127
Issue number4
DOIs
Publication statusPublished - 2010

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spherical caps
velocity distribution
acoustics
caps
radiation
loudspeakers
orthogonal functions
expansion
Helmholtz equations
coefficients
pressure measurement
rims
series expansion
polynomials
Sound
Radiation
scaling
simulation

Cite this

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title = "Sound radiation from a resilient spherical cap on a rigid sphere",
abstract = "It has been argued that the sound radiation of a loudspeaker is modeled realistically by assuming the loudspeaker cabinet to be a rigid sphere with a resilient spherical cap. Series expansions, valid in the whole space outside the sphere, for the pressure due to a harmonically excited cap with an axially symmetric velocity distribution are presented. The velocity profile is expanded in functions orthogonal on the cap, rather than on the whole sphere. As a result, only a few expansion coefficients are sufficient to accurately describe the velocity profile. An adaptation of the standard solution of the Helmholtz equation to this particular parametrization is required. This is achieved by using recent results on argument scaling of orthogonal (Zernike) polynomials. The approach is illustrated by calculating the pressure due to certain velocity profiles that vanish at the rim of the cap to a desired degree. The associated inverse problem, in which the velocity profile is estimated from pressure measurements around the sphere, is also feasible as the number of expansion coefficients to be estimated is limited. This is demonstrated with a simulation.",
author = "R.M. Aarts and A.J.E.M. Janssen",
year = "2010",
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language = "English",
volume = "127",
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journal = "Journal of the Acoustical Society of America",
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Sound radiation from a resilient spherical cap on a rigid sphere. / Aarts, R.M.; Janssen, A.J.E.M.

In: Journal of the Acoustical Society of America, Vol. 127, No. 4, 2010, p. 2262-2273.

Research output: Contribution to journalArticleAcademicpeer-review

TY - JOUR

T1 - Sound radiation from a resilient spherical cap on a rigid sphere

AU - Aarts, R.M.

AU - Janssen, A.J.E.M.

PY - 2010

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N2 - It has been argued that the sound radiation of a loudspeaker is modeled realistically by assuming the loudspeaker cabinet to be a rigid sphere with a resilient spherical cap. Series expansions, valid in the whole space outside the sphere, for the pressure due to a harmonically excited cap with an axially symmetric velocity distribution are presented. The velocity profile is expanded in functions orthogonal on the cap, rather than on the whole sphere. As a result, only a few expansion coefficients are sufficient to accurately describe the velocity profile. An adaptation of the standard solution of the Helmholtz equation to this particular parametrization is required. This is achieved by using recent results on argument scaling of orthogonal (Zernike) polynomials. The approach is illustrated by calculating the pressure due to certain velocity profiles that vanish at the rim of the cap to a desired degree. The associated inverse problem, in which the velocity profile is estimated from pressure measurements around the sphere, is also feasible as the number of expansion coefficients to be estimated is limited. This is demonstrated with a simulation.

AB - It has been argued that the sound radiation of a loudspeaker is modeled realistically by assuming the loudspeaker cabinet to be a rigid sphere with a resilient spherical cap. Series expansions, valid in the whole space outside the sphere, for the pressure due to a harmonically excited cap with an axially symmetric velocity distribution are presented. The velocity profile is expanded in functions orthogonal on the cap, rather than on the whole sphere. As a result, only a few expansion coefficients are sufficient to accurately describe the velocity profile. An adaptation of the standard solution of the Helmholtz equation to this particular parametrization is required. This is achieved by using recent results on argument scaling of orthogonal (Zernike) polynomials. The approach is illustrated by calculating the pressure due to certain velocity profiles that vanish at the rim of the cap to a desired degree. The associated inverse problem, in which the velocity profile is estimated from pressure measurements around the sphere, is also feasible as the number of expansion coefficients to be estimated is limited. This is demonstrated with a simulation.

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