Second-harmonic sound generation at woodwind tone holes
W. B. Richards, A. H. Benade · The Journal of the Acoustical Society of America · 1982
Keefe has observed the importance of nonlinear processes in the tone-hole lattice of a woodwind instrument. Using a probe microphone, we have investigated second-harmonic generation in the neighborhood of the first open tone hole of two cylindrical air columns driven at 200 Hz. The two lattices have tone holes with identical input impedance, but one has tone holes whose chimney height is small compared to the hole diameter, while the other has chimney height nearly the same as the hole diameter. When the SPL in the center of the bore opposite the tone hole is 107 dB, the sound waves in the two tone-hole lattices have similar second-harmonic content, −26 dB relative to the level of the fundamental. (The second harmonic contributed by the driver is 36 dB below the level of the fundamental.) When the mid-bore SPL is 122 dB, the second-harmonic level within and immediately outside the short-chimney hole rises to −11 dB relative to the fundamental, while the tall-chimney tone hole is at −17 dB. (At this level, the second harmonic at the driver is still negligible.) Streaming from the tone hole is present in all measurements, but the 3-dB width of the second-harmonic spectral component is less than 0.08 Hz at all SPL. The large second-harmonic component does not propagate away from the region of the tone hole: it drains energy from the fundamental mode of oscillation, but does not contribute to the sound field in the room nor to the operation of the flow-control valve at the top of the instrument. [Work supported by NSF.]