Page 54 - Spring 2018

Woodwind Acoustics
Figure 2. a: Alto recorder. b: Japanese shakuhachi is blown longitu- dinally, with the player’s chin covering most of its open end. c: Chi- nese dizi is a transverse flute whose unusual feature is the thin mem- brane (arrow) stretched over one hole in the wall. The membrane’s nonlinear pressure-volume curve transfers power from low to high harmonics, giving it a brighter sound. d: Panpipes have a resonant duct for each note; each duct is closed at the remote end. e: Instead of a duct, the ocarina has a Helmholtz resonator. The air inside acts as a spring, and the tiny masses of air in open tone holes act, in parallel, as vibrating masses on that spring.
Figure 3.Tenor (top) and soprano (bottom) saxophones and most modern flutes are made of metal but are called woodwinds. Does the material make a difference? Not much per se, is the usual answer from acousticians. However, different manufacturing techniques and material properties lead to slightly different bore geometries. These plus different surface texture and porosity can have different acoustic effects.
Figure 4. Resonant modes in cylindrical ducts of length L. Red, acoustic pressure; blue, acoustic flow. The open-open pipe (top left) has, at both ends, pressure nodes and flow antinodes. When one end is closed (top right), this boundary condition permits no acoustic flow and allows an antinode in pressure. The longest wavelength (lowest frequency) modes are at top. See www.phys.unsw.edu.au/jw/ AT for more details.
Figure 5. Hybrid instruments, used as lecture demonstra- tions. Many people are surprised that the clarinet mouthpiece on a flute (top) plays and sounds like a clarinet and that the flute mouthpiece on a clarinet (bottom) plays and sounds like a flute. See videos at www.phys.unsw.edu.au/jw/AT.
So, with the same length, the f1 of an ideal closed-open, cy- lindrical tube is half that of the open-open tube so it plays an octave lower. Because of its bell and a flare leading to it, the clarinet does not play a full octave lower than the flute. The clarinet’s lowest note is D3 or C#3 (139 Hz) compared with C4 or B3 (247 Hz) for the flute. The available higher modes for an ideal closed-open cylinder have frequencies 3, 5, or 7 times that of the lowest. One consequence is that, for the low notes on a clarinet, the first few even harmonics are substan- tially weaker than the adjacent odd harmonics.
The different conditions at the mouthpiece have another im-
portant consequence. A flutist can play an octave of notes us-
ing the first resonance and different effective lengths for each
52 | Acoustics Today | Spring 2018
note. Then, because its resonances have f = 2f , the flutist can 21
play notes in a second octave using mainly the same finger- ings but producing a faster jet. For the clarinet, the second mode has f2 = 3f1, so the clarinetist is on the 12th note of a diatonic scale when similar fingerings can be reused.
The bores of the oboe, bassoon, and saxophone are not cy- lindrical but are mainly conical. For axial waves in a cone, the cross section varies as one over the square of the dis- tance from the apex, comparable with isotropic, spherical radiation. Consequently, the standing waves are not simple