Results

Three basic types of results were recorded: results with no oscillation, indicating that a resonance mode was not excited, periodic oscillations, indicating that a resonance mode was excited, and strange aperiodic oscillations or oscillations with unexpected tone, that indicate either strange parameter combinations or issues with the model.

The results of the first set of mode excitation tests are summarized in Table 2. Each set of parameters is used to generate a three-second simulation. When oscillation is produced, the value of ξ_{equil_y} for which the amplitude is maximized is indicated, as well as observations of the audio produced.

f_lip (Hz)	p_max (Pa)	ξ_{equil_y} for maximum amplitude (m)	Observations of sound produced	Audio example
60	2000	0.002	Sounds like a pedal oscillation
100	2000	No oscillation	N/A	N/A
100	2500	0.002	A bit lower than the first resonant mode of the trumpet.
150	2500	No oscillation	N/A	N/A
200	2500	No oscillation	N/A	N/A
250	2500	-0.0001	Sounds like a middle C
300	2500	0.002	Sounds like a D₄
300	3000	0.002	Sounds like a D₄
350	3000	0.002	Sounds like an F, the third resonance mode of the B flat trumpet
400	3000	0.002	Really weird high-frequency component to the sound
400	3000	0.0012	Steady oscillation around a G₄
450	3500	No oscillation	N/A	N/A
500	3500	No oscillation	N/A	N/A
500	4000	No oscillation	N/A	N/A
550	4000	No oscillation	N/A	N/A
600	4000	No oscillation	N/A	N/A
600	5000	No oscillation	N/A	N/A
650	5000	No oscillation	N/A	N/A
700	5000	No oscillation	N/A	N/A

Table 2: results from testing f_lip values from 60 - 1700 Hz

As shown in Table 2, most of the lip frequency and blowing pressure did not excite an oscillation for any of the ξ_{equil_y} values tested. Only three of the six resonance modes that Adachi and Sato report having excited were excited in these trials, and some tones were excited that do not correspond to resonance peaks. There were also some tones produced that had unexpected timbres.

To attempt to excite the specific resonance modes, the peaks in the impedance were selected using a peak detection algorithm, and used directly as the f_lip values, along with the blowing pressure values given in Adachi and Sato (1996). The results of this method are in Table 3 below.

Resonance mode	Impedance peak frequency/f_lip (Hz)	p_max (Pa)	ξ_{equil_y} for maximum amplitude (m)	Sounding frequency from FFT (Hz)	Observations of sound produced	Audio example
I	86	2000	0.002	87.667	No oscillation for the first two seconds; oscillation of a pedal tone begins around the last second.
II	234.6	2500	-0.0001	237.33	Sounds around a B flat₃, the second resonance mode, but the tone decays almost like a struck instrument instead of sustaining until the end of the simulation.
III	352	3000	0.002	350	Periodic oscillation around an F₄, the third resonance mode.
IV	471.2	3500	No periodic oscillation.	N/A	N/A	N/A
V	593.6	4000	No periodic oscillation.	N/A	N/A	N/A
VI	714.4	5000	No periodic oscillation.	N/A	N/A	N/A

Table 3: results from testing f_lip values equal to resonance frequencies

Once again, the higher resonance modes are not excited at all, so that only the first three of six resonance modes produce oscillations.