Analysis of free reed attack transients

Transcription

1 Analysis of free reed attack transients James Cottingham Physics Department, Coe College, Cedar Rapids, Iowa, United States Summary Attack transients of harmonium-type free reeds from American reed organs have previously been studied using several methods of initiating the attack, with displacement and velocity waveforms obtained using a laser vibrometer system and electronic proximity sensors. Although the fundamental transverse mode is dominant, the presence of higher transverse modes and torsional modes in the initial transient has been established. These earlier results have been augmented with the use of high-speed video, resulting in a more detailed picture of reed oscillation during the earliest part of the attack transient. This transient typically exhibits three stages. For a reed with natural frequency around 100 Hz, the motion of the reed tongue begins with a single displacement and return to the equilibrium. This is followed by a transitional period in which the amplitude of oscillation gradually increases and the frequency stabilizes at the steady state oscillation frequency. In the third stage, the amplitude of oscillation continues to increase to the steady state value. The second transverse mode and the first torsional mode are observed to be especially significant in the second stage. [Work partially supported by US National Science Foundation REU Grant PHY ]PACS no Lm, Yy 1. Introduction 1 Free 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]. Figure 1. Diagram of a Western free reed with the reed tongue mounted outside of the reed frame. The motion of this type of reed begins with an initial displacement of the reed tongue into the reed frame. The reed then begins vibrating and grows to its steady state amplitude [2]. There has been considerable research done on the steadystate vibration of free reeds [3-6] but, until recently, relatively little has been done on their attack transients. 1 (c) European Acoustics Association air flow This paper first summarizes recent research on the attack transients of free reeds, in particular the question of the importance of higher transverse modes and torsional modes in the initiation of the attack. Work on this topic thus far has used reed motion data obtained by laser vibrometry and from the use of electronic proximity sensors. Later in this paper, the possibilities of the use of high speed photography with tracking software will be discussed. This technique will facilitate the study of the details of reed vibration, in particular the possible significance of torsional and higher transverse modes in attack transients. The experimental work described here has been done on reeds from American reed organs, 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 [7]. Figure 2 shows one of the reeds used in this study with the typical curved reed tongue. Though the reed s motion is typically dominated by the first transverse mode, previous research shows that higher vibrational modes, specifically the second transverse and first torsional modes, appear in the attack transients of free reeds [2]. The same research suggests that the curve in the reed tongue helps to excite these higher vibrational

2 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 of reed tongue shape on the presence of these higher modes and on the speed of the attack. reeds pitched at 96 Hz; the second was a set of four smaller B reeds pitched at 250 Hz. Figure 2. Diagram of a reed organ reed, showing the characteristic curve in the reed tongue. 2. Previous experimental work This section summarizes some work done recently by Biernat and Cottingham [8] on attack transients of reeds from American reed organs. 2.1 Experimental method The reeds were mounted on a wind chest with two different air supplies that could be used interchangeably. The first, a commercially available organ blower (Lee ORGAVAC RO-16), supplied a realistic, high volume of air to the wind chest. The second, a laboratory blower, allowed greater variation of pressure within the wind chest. Different methods of initiating reed attacks were used; each resulting in different reed attack transients. The sudden start method involved restraining the reed and then suddenly releasing it, which resulted in the quickest reed attack. The pallet valve start used a constructed pallet valve mounted inside the wind chest. This method most realistically modeled the experience of a reed in a musical instrument. The transient motion of the reed was captured using a Polytec laser vibrometer system that measured reed velocity, and a variable impedance transducer (VIT) proximity sensor (Kaman KD SU) that measured reed displacement. A diagram showing the relative placement of the VIT sensor and laser vibrometer can be seen in Figure 3. To analyze the attack transients, the vibrometer and VIT signals were captured on an oscilloscope. The resulting waveforms were then analyzed using an FFT program written in MATLAB. Two sets of reeds were used. The first was a set of four F# Figure 3. Relative placement of the VIT sensor and laser vibrometer along the reed tongue. 2.2 Some sample results In steady state vibration, the motion of the reed is dominated by the first transverse mode, but other vibrational modes have been shown to be present in steady state free reed vibration, including higher transverse modes and torsional modes [3-6]. Previous research has also suggested that these higher modes of vibration are not only present in the transient vibration of free reeds, but may be important in initiating reed vibration [2,3,8]. To determine the vibrational modes present during attack transients, FFT frequency spectra were obtained from the vibrational waveforms using a program written in MATLAB. Figure 4 on the following page shows the displacement of an F# (96 Hz) reed during an attack initiated using the sudden start method. Portions of the transient waveform could be analyzed in sections as small as 40 ms. Frequency spectra (Figures 5a and 5b) for the portions of the waveform marked A and B were computed to compare the presence of higher modes of vibration during the initial transient with the period in which the reed begins to reach its steady state vibration. Figure 5a shows the frequency spectrum of the reed motion during the first 50 ms of the attack (segment A in figure 5), and Figure 5b shows the spectrum the corresponding spectrum after 150 ms (segment B in figure 5). The earlier spectrum shows a large peak at the fundamental frequency (96 Hz) and two smaller peaks at the frequencies of the second transverse mode (811 Hz) and the first torsional mode (1610 Hz). The spectrum of The waveform 100 ms later shows only the presence of the fundamental frequency.

3 Figure 4. Attack transient of an F# reed (96 Hz) at wind chest pressure 0.86 kpa. (from [8]) (5a) 2 nd transverse mode torsional mode (5b) Figure 5. FFT frequency spectra of portions A and B of the waveform shown in Figure 4. (5a) Spectrum of portion A of the waveform of Figure 4 showing the fundamental frequency and peaks at the second transverse and first torsional modes. (5b) Spectrum of portion B of the waveform showing the presence of only the fundamental frequency. (from [8])

4 3. Summary of current results on free reed attack transients A number of investigations have shown that higher modes of vibration are present in the attack transients of American reed organ reeds. The second transverse mode appears to always be present in the attack transient and the first torsional mode has been observed in the larger, lower frequency reeds. The degree to which these higher modes were present can depend on the suddenness of the attack. Comparing reeds with the curvature found in the American reed organ reeds with similar reeds without the curvature does not appear to affect the presence of the second transverse mode and the first torsional mode in the attack transient. Free reeds, especially the larger, low frequency reeds, have a tendency to be slow in speech. It has been found that the curve in the reed tongue does lead to a faster attack. At this point it is not clear whether this is related to stronger presence of torsional modes in the early stages of the attack transient. The examples shown here are a pair of initial transients from the same reed (F#-96 Hz) mounted on the wind chamber at 0.86 kpa and excited using either the artificial pallet valve, which imitates the result of key action in the complete instrument, or the sudden start method. The video tracking measurements were taken at two different points on the reed tongue, shown in Figures 7 and 8 below. The transient shown in Figure 9 was taken at the point indicated by the arrow in Figure 7. A point closer to the reed tip as was chosen for the second example as indicated in Figure 8 for the transient waveform shown in Figure 10. Figure 7. The point on the reed tongue, about 2 cm from the free end, tracked in the transient shown in Figure Investigating attack transients with high speed photography A promising tool for the study of the initial stages of reed vibration is the use of high speed video photography. With the use of appropriate tracking software, the motion of selected points on the reed tongue can be followed in detail throughout all stages of oscillation. This is especially useful during the early transients. A few examples of the use of high speed video are given below. These suggest the possibilities of this technique for use in more detailed subsequent investigations. The camera used was the Photron FASTCAM-SA3, capable of full resulution at 1000 frames/second (fps), with up to fps at reduced resolution. Figure 6. The high speed camera used: Photron FASTCAM SA3. Figure 8. The point on the reed tongue, about 7 mm from the free end, tracked in the transient shown in Figure 10. The two transient waveforms in Figures 9 and 10 differ in important ways. The point tracked in Figure 9 is farther from the reed tip, and the reed oscillation was initiated by a sudden increase in the pressure difference. The waveform shown in Figure 10 is from a point much closer to the reed tip, and the reed was excited by a gradual increase in the pressure difference. Naturally the displacement of the equilibrium point is greater for the point nearer the free end of the tongue, and the rise time to full amplitude is less for the sudden start method. The images were obtained at 1000 fps, and the points on the oscillating reed tongue were tracked using Tracker, open source software available at

5 Figure 9. Displacement curve for the 96 Hz F# reed with a sudden increase in windchest pressure. The point tracked is 2 cm from the free end of the reed. Figure 10. Displacement curve for the 96 Hz F# reed with a gradual increase in windchest pressure. The point tracked is 7 mm from the free end of the reed. It should be noted that, in both of Figures 9 and 10, the waveform displayed is truncated before the full steady-state amplitude is reached. The use of the high speed video images with tracking software has potential for investigating in detail the presence of torsional modes and higher transverse vibrational modes in the initial transients. In the example shown below in Figures 11and 12, two points on opposite sides of the reed tongue were tracked during a mechanical excitation of the first torsional mode at 1620 Hz. A fps image rate was used in this case. The

6 two pints tracked show out of phase motion in the x-direction as expected but lower amplitude in phase motion in the y-direction. Thr ability to track motion in two dimensions in one of the advantages of high-speed video. each of these figures the graph is truncated so that the strong fundamental at 96 Hz is off scale, and the appearance of the second torsional mode (811 Hz) and the first torsional mode (1610 Hz) can be observed. Figure 11. A view of the tip of the reed tongue with the points tracked indicated with red and green circles. At right is a trace of the motion in the x-direction during the first 100 ms of the video.. Figure 13. Initial transient of the 96 Hz F3 reed (suddenly released). The small box indicates the size of the FFT samples shown below. Figure 14. FFT of first 10 cycles of oscillation. Figure 12. Motion of the pints tracked in the x- direction (upper plot) and the y-direction (lower plot) during the first 100 ms of the video. 5. Detailed study of an initial transient Experimental results thus far have shown that torsional and higher transverse modes are present in the early stages. Some of the best transient analyses to date have been made using a laser vibrometer signal. Figure 13 show 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 14, 15, and 16. In Figure 14 on the next page shows that the second transverse mode (811 Hz) and the first torsional mode (1610 Hz) begin to appear at this early stage. In the next stage (Figure 15) the torsional mode becomes the more prominent of the two. By the third stage (Figure 16) the amplitude of the torsional mode has decreased, and the second torsional mode is more prominent This represents only a single measurement on one reed, and further study is needed to determine whether this represents a consistent pattern, and whether the torsional mode is an important component of the attack transients of free reeds. In this regard experiments with reed tongues made with differing amounts of curvature are needed.

7 Acknowledgements This project has been partially funded by US National Science Foundation REU Grant PHY Eugene Wehr has helped greatly with the implementation of the high speed video imaging and tracking. Figure 15. FFT of the second set of 10 cycles of oscillation. The torsional mode has become more prominent. Figure 16. 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. 6. Conclusions Experimental results thus far have shown that torsional and higher transverse modes are present in the early stages of free reed excitation, and generally present to a higher degree than in steady state oscillation. Several authors have proposed models for free reed excitation, including possible initial transients. [9-11] 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 detailed study of the attack transients, including the use of high speed video tracking, will provide new insights into the reed excitation mechanism. References [1] J. Cottingham: Acoustics of free-reed instruments. Physics Today 64, no. 3 (March 2011), [2] J.P. Cottingham: Modes of reed vibration and transient phenomena in free reed instruments. Proc. Meetings on Acoustics, 19 (2013), [3] A. Paquette, J. Vines, and J.P. Cottingham: Modes of vibration of air-driven free reeds in transient and steady state oscillation. J. Acoust. Soc. Am. 114 (2003), [4] J.P. Cottingham, C.J. Lilly and C.R. Reed: The motion of air-driven free reeds. J. Acoust. Soc. Am. 105 (1999), 940. [5] J.P. Cottingham: Reed Vibration in Western Free- Reed Instruments. Proc. Int.l Congress on Acoustics (ICA2007), Madrid, Spain, September [6] S.L. Behrens, W.L. Coyle, and J.P. Cottingham: Vibrational Modes of Accordion Reeds. J. Acoust. Soc. Am. 126 (2009), [7] R.F. Gellerman: The American Reed Organ and the Harmonium. Vestal Press, Vestal, New York, [8] J. Biernat and J.P. Cottingham: Attack transients in free reed instruments. J. Acoust. Soc. Am. 126 (2013), [9] T. Hikichi, N. Osaka, and F. Itakura: Time-domain simulation of sound production in the sho. J. Acoust. Soc. Am 113 (2003), [10] D. Ricot, R. Caussé, N. Misdariis: Aerodynamic excitation and sound production of blown-closed free reeds without acoustic coupling: The example of the accordion reed. J. Acoust. Soc. America 114 (2005), [11] L. Millot and C. Baumann: A Proposal for a Minimal Model of Free reeds. Acta Acustica/Acustica 93 (2007),