Keys in woodwind- the physical cut off frequency

When a tone is produced on a wind instrument, the bore of the instrument works as a resonator, to produce a pitch, but the internal surface of the bore is not a perfect smooth parallel surface. In woodwind, the keyholes even in a closed situation, still add (drill tone hole) or attach a little bit some space (plug/attach tone hole)in the bore. The rough and uneven surface of the bore causes energy loss, especially the high frequencies with short wavelengths. Diffraction refers to various phenomena that occur when a wave encounters an obstacle or opening. The tone hole, the lattice rough surface, is the obstacle to the sound wave. When covering most and all tone holes of the woodwind instrument, short-wavelength in high frequency have trouble the get around corners and obstacles by traveling the whole length of the pipe, while the high frequencies (>1000Hz) are lost (Benada,1990). 

For fingering in woodwind instrument, it creates different patterns of open and close holes,The calculation tone-hole cutoff freqency, around this frequency is basically weaken, f = 0.11*(b/a)*v*sqrt(1/(s*(t+1.5*b))). (Benada,1990)

b = diameter of the tone hole; a = diameter of a pipe; v = volocity of air; s = the distance between holes; t = thickness of the wall.

Based on the formula above, we can explain that in a woodwind octave key or when playing the second octave of an instrument, the top hole is always released. The top key released and a series of closed tone holes makes the distance between two-tone holes is high in value, resulting in a low cut-off frequency. The dampen first partial makes the second partial stand out. For fork fingering, the complex fingering with different lengths of distance between holes provides more combinations of various cut-off frequencies. For baroque flutes without a lot of harmonic partials, the sound is duller; for double reed instruments with rich harmonic partials of the reeds, the sound is balanced back with a clearer and crispier sound.

  Benade, A. H. (1990) Fundamentals of musical acoustics. 2nd. rev. ed. New York: Dover.


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