By Jens Ahrens
This e-book places the focal point on serving human listeners within the sound box synthesis even if the procedure should be additionally exploited in different functions similar to underwater acoustics or ultrasonics. the writer derives a primary formula in accordance with usual vital equations and the single-layer capability strategy is pointed out as a great tool with the intention to derive a normal answer. He additionally proposes extensions to the single-layer strength method which enable for a derivation of particular ideas for round, planar, and linear distributions of secondary resources. in response to above defined formula it truly is proven that the 2 demonstrated analytical methods of Wave box Synthesis and Near-field Compensated better Order Ambisonics represent particular recommendations to the final challenge that are coated via the single-layer strength answer and its extensions.
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Additional info for Analytic Methods of Sound Field Synthesis
Thus, the wavenumber k represents the length of the propagation vector k = [k x k y k z ]T . 8) can be rearranged to read k 2y = k 2 − k x2 − k z2 . 9) provided that they are real (Williams 1999, p. 21). 10) ⎩ ±i k 2 + k 2 − k 2 for k 2 + k 2 ≥ k 2 x z x z since k is non-negative. 10) represents a propagating or homogeneous plane wave. The vector k points into the direction of propagation. Refer to Fig. 1a for a simulation. 10) (with complex k y ) represents an evanescent or inhomogeneous wave.
Warusfel, O. (2008, May). Objective and subjective analysis of localization accuracy in wave field synthesis. In 124th Convention of the AES (p. 7361). Start, E. W. (1997). Direct sound enhancement by wave field synthesis. PhD thesis, Delft University of Technology. Steinberg, J. , & Snow, W. B. (1934a, January). Auditory perspective—Physical factors. Electrical Engineering, 12–17. Steinberg, J. , & Snow, W. B. (1934b). Symposium on wire transmission of symphonic music and its reproduction in auditory perspective: Physical factors.
At positions closer to the expansion center more energy is apparent at higher time frequencies than at farther positions. This circumstance is illustrated in Fig. 9, which shows the amplitude of a 5-th order plane wave (N = 6), which propagates inside the horizontal plane. 9 is essentially a broadband extension of Fig. 7d. It can be seen that the spatial extent of the sound field under consideration can shrink to only a few centimeters at some kHz. 5 0 0 5 10 n 15 −2 −2 −1 0 1 2 x (m) Fig. 8 Angular weighting for reduction of the Gibbs phenomenon apparent in Figs.