PROCEEDINGS of the23rd International Congress on Acoustics
9 to 13 September 2019 in Aachen, Germany

A survey of recent Studies on initial transients infree reed oscillation
James P. COTTINGHAM1;
1

Coe College, United States

ABSTRACTIn recent decades a number of models have been proposed for sustained oscillation of free reeds, including insome cases conditions for the initiation of the oscillation, as well as experimental work testing the validity ofthe models. Typically these models involve a simplified or generic geometry of the reed tongue. In addition,
the motion of the free-reed tongue in the early stages of the initial transient has been studied experimentallywith the aim of determining the presence of higher modes and their possible role in the attack transient, aswell as the possible relation of the details of reed geometry to details of the initial transient waveform,including the rise time. Comparisons of reed tongues of different design have been made to explore the roleof these modes in the initial excitation. There is evidence that the first torsional mode and the second
transverse mode may be significant in initiating reed oscillation, so that reed design enhancing the torsionalmode may be helpful in alleviating the problem of slow attack. [Work partially supported by United States
National Science Foundation Grant PHY-1004860]
Keywords: Free Reed, Transients

1. INTRODUCTION
This report on recent work related to the attack transients of free reeds has three sections. The first
explores the importance of the higher transverse modes and torsional modes of the reed tongue in theinitiation of the attack. It will be seen that the second transverse mode and the first torsional mode areusually present and appear to be significant in determining the promptness of the attack.
The second reports a study of cases in which the reed chamber resonance can cause destructive
interference with reed vibration, inhibiting reed response. A result of this can be the phenomenon
known as “choking,” which can be a problem in higher pitched reeds in the harmonica and theaccordion.
A final topic briefly considered is research currently underway related to a suggestion that vortex
induced vibration is significant in establishing the initial transient. This research interest part of abroader investigation of predictions of a “free reed tongue tip offset theory” recently proposed byTonon [9].

2. HIGHER TRANVERSE AND TORSIONAL MODES IN THE INITIAL TRANSIENT
2.1 Measurements of Free Reed Attack TransientsFree reeds are characterized by their ability to vibrate freely through the reed plate or frame on which
they are mounted. In Western free reed instruments, such as the harmonica, accordion, and American
reed organ, the reed tongue is mounted outside of the reed frame and is blown “closed” by the airflow
initiating reed vibration [1].

air flow

Figure 1. Diagram of a Western free reed with the reed tongue mounted outside of the reed frame.
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jcotting@coe.edu

The motion of this type of reed begins with an initial displacement of the reed tongue into the reedframe. The reed then begins vibrating and grows to its steady state amplitude [2]. There has been
considerable research done on the steady-state vibration of free reeds [3-5] but, until fairly recently,
relatively little has been done on their attack transients.
The first section of this paper summarizes research on the initial transients of free reeds, in particular
the question of the importance of higher transverse modes and torsional modes in the initiation of theattack. The experimental work described in this section has been done on reeds from American reedorgans, which were manufactured with characteristic curves in their reed tongues. The manufacturers of
the reeds claimed that this curve would have two effects: (1) it provides a faster attack, and (2) it improves
the tone quality of the reed [6]. Figure 2 shows one of the reeds used in this study with the typical curved
reed tongue.
Although the motion of the reed is typically dominated by the first transverse mode, earlier researchshows that higher vibrational modes, specifically the second transverse and first torsional modes, appear in
the attack transients [2]. The research also suggests that the curve in the reed tongue helps to excite thesehigher vibrational modes, which leads to a faster attack in the curved reeds.
Of current interest is the role of higher modes of vibration in attack transients as well as the effect ofreed tongue shape on the presence of these higher modes and on the speed of the attack.

Figure 2. Photo of a reed organ reed, showing the characteristic curve in the reed tongue.

2.2

Details of an Initial Transient
Experimental results thus far have shown that torsional and higher transverse modes are present in
the early stages of free reed oscillation.
Some of the best transient analyses to date have been made using a laser vibrometer signal. Figure 3
from Reference [4] shows an oscilloscope trace of a transient of the 96 Hz F# reed suddenly released.
Results of FFT spectra of the first three segments of this transient are shown in Figures 4, 5, and 6. Ineach of these figures the graph is truncated so that the strong fundamental at 96 Hz is off scale, and theappearance of the second torsional mode (811 Hz) and the first torsional mode (1610 Hz) can beobserved.

Figure 3. Initial transient of the 96 Hz F# reed (suddenly released). The small box indicates the size of
the FFT samples shown below in Figures 4-6.

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Figure 4. FFT of first 10 cycles of oscillation.
Figure 4 shows that the second transverse mode (811 Hz) and the first torsional mode (1610 Hz) begin toappear at this early stage. In the next stage (Figure 5 – below) the torsional mode becomes the more
prominent of the two. By the third stage (Figure 6) the amplitude of the torsional mode has decreased,
and the second torsional mode is more prominent.

Figure 5. FFT of the second set of 10 cycles of oscillation. The torsional mode has become more
prominent.

Figure 6. FFT of the third set of 10 cycles of oscillation. The second transverse mode has become more
prominent, with the amplitude of the torsional mode diminished.

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3. EFFECTS OF REED RESONANCES
3.1 Reed Chamber Resonance Experiments
A problem that sometimes occurs with the higher-pitched reeds in both the accordion and harmonica
is that coupling between the reed vibration and the reed chamber resonance can inhibit the sounding of
the reed. This phenomenon has been investigated by Tonon [7], who describes it as follows: “Thevibrating reed tongue and the air within and about the cavity are acoustically coupled together. In somedesigns, the effect of the cavity on the musical tone is small or negligible, in other designs, the effect of
the cavity can significantly modify the musical tone; and in still other designs, the acoustic effect of thecavity can prevent the reed from speaking properly. As tongue vibration frequency and cavity mode
resonant frequency become closer, however, cavity air vibration can become large enough to influence
the self-excitation mechanism. Whether this influence assists or interferes with tongue vibration and theresulting musical tone depends upon the resonant mode of the cavity and how the reed is mounted inrelation to the cavity. The interference described above can completely prevent the tongue fromvibrating: the reed becomes choked. Choking is predicted, then, under certain conditions when tongue
vibration frequency is in some neighborhood of cavity mode frequency.”
This section reports on some experimental studies in which the coupling of a free reed with theHelmholtz resonance of the reed chamber was investigated to verify to what extent resonances of reedchambers can inhibit the sounding of the reed. Reeds from an American reed organ were mounted on awind chamber with Helmholtz frequency that could be varied by adding small sections of pipe. The
frequency of the reed chamber was varied to explore the ways in which the resonance of the reed chamberaffects the threshold blowing pressures.

Figure 7. A reed organ reed mounted on the variable resonance frequency reed chamber.

Figure 8. Threshold pressures TP1 and TP2 as functions of reed chamber resonance for a 268 Hz reed
mounted on a variable-resonance wind chamber.

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The results measurements made with a reed of natural frequency 268 Hz are shown above in Figure 8.
The first threshold pressure (TP1) was determined by starting at zero pressure and gradually increasing theblowing pressure until the reed began to sound. Similarly the second threshold pressure (TP2) was definedby starting at a higher initial pressure and gradually decreasing the blowing pressure until the reed would
no longer sound.
It can be seen that it is possible to excite the reed at very low pressures for most reed chamberresonance values, but for values near the reed resonance, excessive pressure (far above normal playing
pressure is required. In a few cases sounding the reed was not possible with pressures available. (One casewas observed in which the reed and chamber resonances were mismatched in such a way that the reedsounded at the frequency of its second transverse mode.) Detailed results of a few representative trials areillustrated below in Figures 9-10.

Figure 9. Oscilloscope traces showing results for a 268 Hz reed coupled to a 327 Hz wind chamber. Thereis negligible interference from chamber resonance. The two blowing pressures illustrated are within thenormal range of playing frequency.

Figure 10. Oscilloscope traces showing results for a 344 Hz reed coupled to the 327 Hz wind chamber.
There is a major effect from chamber resonance. Note the change in vertical scale of the oscilloscope
traces as compared to Figure 9, as well as the distortion in the reed vibration waveform5534

4. A CURRENT TOPIC OF INVESTIGATION
4.1 Vortex induced vibration and the initial free reed transient
Tom Tonon has recently proposed [8] that the very early initial free reed transient is a result of“vortex induced vibration, or at least periodic eddy induced vibration.” This theory uses the following
two assumptions: (1) The minimum bellows pressure Ps needed to start the eddies is that which will holdthe tongue tip into the entrance plane of the slot. (2) Small dissipation in the system allows for a high Q
resonance at the natural frequency of the reed. These assumptions lead, eventually, to the following
equation for the “start pressure”
ܽ‫ܫܧ‬
ܹ‫ܮ‬ସ
where the quantities are a = offset, E = elastic modulus, I = cross area moment of inertia, W = reed
tongue width, and L = reed tongue length.
Further calculations not detailed here result in the following equation for the frequency of eddy
formation: f=vS/W.
In this case f is the the eddy fornation frequency, v is the velocity of air moving about the tongue tip,and S the Strouhal number for this moving air. Attempts at experimental verification of these equations
and related results are underway and could provide interesting future work.
ܲ௦ ൌ 

5. SUMMARY
Experimental results thus far have shown that torsional and higher transverse modes are present in
the early stages of free reed oscillation, and generally present to a higher degree than in steady stateoscillation. Several authors have proposed models for free reed excitation, including possible initialtransients [14-16]. The models brought forward up to this point include only the fundamental transverse
mode and do not consider the possible significance of higher modes of vibration during reed attack.
It is hoped that continuing detailed experimental study of the initial transients in free reed instruments
will provide new insights into the reed excitation mechanism.

ACKNOWLEDGEMENTS
Many students contributed to the experimental work discussed in this paper. Special thanks go toDaniel Wolfe for contributing the results shown in Section 2, and to Margaret Hogan for much of theexperimental work summarized in Section 3. Financial support for this work was provided by theUnited States National Science Foundation Grant PHY-1004860.

REFERENCES
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3. Paquette A, Vines J, and Cottingham JP. Modes of vibration of air-driven free reeds in transient andsteady state oscillation. J. Acoust. Soc. Am. 114 (2003), 2348.
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topic/20667-free-reed-tongue-tip-offset-theory/&tab=comments#comment-192304
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Acoust. Soc. Am 113 (2003), 1092-1101.
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free reeds without acoustic coupling: The example of the accordion reed. J. Acoust. Soc. America
114 (2005), 2279-2289.
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