A woodwind tonehole may be considered as an isotropic source [4]. Given a source-strength , the radiation pressure at a distance from such a source is:

where is the free space wave velocity. By combining (14) and (15), we can compute the pressure radiated from a woodwind tonehole as:

Note that the frequency term has disappeared in the final result. The term represents a pure time-delay (i.e., the time it takes for a radiated pressure wave to reach the ``listening point''). Thus, the radiated pressure at any distance from the tonehole can be computed by simply

where represents a delay-line of fractional length , and where is a constant. It must be noted that eq. (17) gives a good approximation at lower frequencies, but the accuracy decreases for higher frequencies. This is mainly because the WD tonehole model is based on a low-frequency approximation of the real acoustical behaviour of the tonehole. Moreover, we have assumed that the radiation is isotropic (i.e., the flow spreads out evenly in all directions). This assumption is valid for low frequencies, but for higher frequencies the effects of directivity need to be taken into account (such as described in [11]). Since the higher frequencies are relevant from a perceptual point of view, an extra filter (that compensates for the deviations described above) can be applied to the pressure calculated with eq. (17) in order to obtain a better aural result. In general, such a filter has a rather ``smooth'' high-pass amplitude response, and can be approximated with a lower-order digital filter.

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