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The directivity index DI (explained in the text) of a rigid spherical cap with various aperture angles of the cap: 5π/32 rigid (solid, black curve), π/8 (dotted, red curve), and π/10 (dashed-dotted, blue curve). The long-dashed, green curve starting for kR=0 at 3 (dB) is the directivity for a rigid piston in an infinite baffle, using the far-field response in Fig. 1, n=0.
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![Figure 8. The power Re[P]c/(2πρ 0 a 2 R 4 ) [dB] vs. kR (log. axis) of...](profile/R-Aarts/publication/279284600/figure/fig5/AS:669047662317579@1536524801653/The-power-RePc-2pr-0-a-2-R-4-dB-vs-kR-log-axis-of-a-rigid-spherical-cap-moving_Q320.jpg)
Loudspeakers are often modelled as a rigid piston in an infinite baffle. As a model for real loudspeakers, this approach is limited in two ways. One issue is that a loudspeaker cone is not rigid, and a second issue is that a loudspeaker is mostly used in a cabinet. Both issues are addressed here by developing the velocity of the radiator in terms o...
Contexts in source publication
Context 1
... Fig. 9 the directivity index DI from the spherical cap model is shown, while in Fig. 10 the DI of the measured loudspeaker is given. This directivity index is a qualitative measure of how directive a particular sound radiator is: it is the 10 log 10 of the ratio of the modulus squared pressure on the axis in the far field produced by the ...
Context 2
... Fig. 9 the directivity index DI from the spherical cap model is shown, while in Fig. 10 the DI of the measured loudspeaker is given. This directivity index is a qualitative measure of how directive a particular sound radiator is: it is the 10 log 10 of the ratio of the modulus squared pressure on the axis in the far field produced by the ...
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Citations
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Surrounding spherical microphone arrays have recently been used in order to model the radiation pattern of acoustic sources that are assumed to be at the center of the array. Source centering algorithms are applied to the measurements in order to reduce the negative effect of acoustic source misalignment with regard to the physical center of the microphone array. Recent works aim to minimize the energy that is contained in the high-order coefficients of the radiation pattern in the spherical harmonics domain, in order to directly address the problem of increased order and spatial aliasing resulted by this misalignment. However, objective functions which directly minimize the norm of these coefficients were shown to be convex only when employed on sources with low-order radiation patterns. This work presents a source centering algorithm that operates on plane sections and aims to achieve a convex objective function on every plane section. The results of the proposed algorithm are shown to be more convex than the previous algorithms for sources with higher-order radiation pattern, usually at higher frequencies.
