Room Acoustical Fields by Fridolin Mechel

By Fridolin Mechel

This ebook provides the idea of room acoustical fields and revises the replicate resource tools for useful computational use, emphasizing the wave personality of acoustical fields. The offered better tools contain the recommendations of “Mirror element assets” and “Corner resources which permit for a great approximation of complicated room geometries or even built rooms.
In distinction to classical description, this ebook extends the idea of sound fields describing them by means of their advanced sound strain and the particle speed. This process allows actual descriptions of interference and absorption phenomena.

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By Fridolin Mechel

This ebook provides the idea of room acoustical fields and revises the replicate resource tools for useful computational use, emphasizing the wave personality of acoustical fields. The offered better tools contain the recommendations of “Mirror element assets” and “Corner resources which permit for a great approximation of complicated room geometries or even built rooms.
In distinction to classical description, this ebook extends the idea of sound fields describing them by means of their advanced sound strain and the particle speed. This process allows actual descriptions of interference and absorption phenomena.

Show description

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12) . ð2Þ ð2Þ Therewith and with h1 ðzÞ h0 ðzÞ ¼ ð1 þ jzÞ=z the reciprocal cross impedance becomes: ÀZ0 vQwx 1 @pQ =@ðk0 r 0 Þ k0 h @pQ =@ðk0 r 0 Þ ¼ ¼jÁ 0Á ¼ j Á sin y Á 0 XðdÞ pQ ðr Þ k0 r pQ ðr 0 Þ pQ h   ð2Þ k0 h h00 ð2Þ ðk0 r 0 Þ k0 h h1 ðk0 r 0 Þ k0 h 1 ¼ ¼ Àj Á 0 Á ð2Þ Á 1Àj ¼jÁ 0Á k0 r pQ ðr 0 Þ k0 r h ðk0 r 0 Þ k0 r 0 k0 r 0 0 qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi wherein r 0 ¼ d2 þ ð2h À HÞ2 . 13) θ ϑ ′ ϑ Fig. 1 Point source Q in front of an absorbent wall (Notice the change of coordinates relative to Fig.

5 5 H/λ0 Fig. 02 0 Fig. 5 10 0 30 4 Modified Mirror Sources Fig. 5 5 H/λ0 Fig. 323)] or [9, Sect. e. when both source Q and field point P are close to the wall (Fig. 3a– Fig. 3d). 10) 4 Modified Mirror Sources Fig. 02 0 Fig. 02 0 Fig. 5 10 0 0 32 4 Modified Mirror Sources Fig. 5 10 5 d/λ 0 0 Summarising: • One can increase the precision for the field of a point source above an absorbent wall by the use of a suitable modified reflection factor ℜ. • Within a mirror source evaluation of room fields one will apply such reflection factors only for the final evaluation of the field in the field point P, and not for the search of mirror source positions where simpler reflection factors can be used, because in this search they are required in great number.

We symbolise the field of the same source (point or line source) Q in front of a hard plane wall with ph(r) and the field in front of the soft wall with pw(r), where r represents the coordinates of the field point P in an appropriate coordinate system. A point on the wall has the coordinates s. 1) When A ¼ const(s), B ¼ const(s) are constant on the surface, this formulation satisfies the wave equation and the far field condition (because ph(r), pw(r) do so). The correspondence of pa(r) to the volume flow of the source and the satisfaction of the boundary condition at the wall may be achieved through the appropriate choice of A, B.

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