Rr a xr 2 yr 2 Zr

Having transformed the coordinates, the directivity angles 9 and 0 follow

From these angles along with the loudspeaker-directivity data and the loudspeaker-to-receiver distance we can determine the direct-field level associated with a given receiver location. A pictorial of the resultant coordinate system is given in Fig. 18.26.

Figure 18.26 Loudspeaker Coordinate System

Figure 18.26 Loudspeaker Coordinate System

AIM POINT Xp, Tp, Zp

Multiple Loudspeaker Contributions

If the sound field due to several loudspeakers is present at a receiver location, the direct-field contribution from all sources may be combined to produce an overall direct field level. This can be done in several ways: 1) by adding the energy from each source in accordance with Eq. 2.62, 2) by combining signals in a coherent manner that accounts for the relative phase due to the difference in time, or 3) by coherently combining the energy and integrating over the frequency bandwidth.

An incoherent (energy) combination is the simplest methodology and is sufficiently accurate for most designs. It is inaccurate in that it does not account for the phase differences, but for most applications this is not a fatal flaw. The combined pressure squared is

0 0

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