directivity, directionality, trombone, musical instruments, radiation


Directivity animations for several partials of B♭2 (116.5 Hz fundamental), B♭3 (233.1 Hz fundamental), and B♭4 (466.2 Hz fundamental) from a played tenor trombone. The first rotating balloon plot depicts directivity levels based on normalized output auto-spectra, highlighting the effects of playing variations. The second plot portrays directivity levels based on normalized frequency response functions (FRFs), demonstrating their compensation for playing variations and elimination of longitudinal banding. Both balloon plots utilize color (see the accompanying scale) and radial extent from the origin to represent levels between −40 dB and 0 dB relative to the maximum. (Values below −40 dB were truncated.) The third rotating balloon shows coherence values for the associated FRF measurements over a range of 0 to 1. The inset arrows and the trombone graphical representation show the instrument orientation with respect to the balloons. As expected, equal-frequency partials of different notes produce balloons that are very similar. The line graph presents frequency-dependent overlays of both spatially averaged, normalized output autospectra and coherence for the played notes. A vertical bar in the graph shows the partial associated with the rotating balloon plots.

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Supplementary Materials

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Physical and Mathematical Sciences


Physics and Astronomy