Analysis on the mechanism of sound production and effects of musical flue pipe

Cognitive Computation and SystemsVolume 4, Issue 1 p. 77-84 ORIGINAL RESEARCHOpen Access Analysis on the mechanism of sound production and effects of musical flue pipe Jing Jiang, Corresponding Author Jing Jiang [email protected] orcid.org/0000-0003-3532-6556 School of Applied Science, Beijing Information Science and Technology University, Beijing, China Correspondence Jing Jiang, School of Applied Science, Beijing Information Science and Technology University, Beijing 100192, China. Email: [email protected]Search for more papers by this authorJingyu Liu, Jingyu Liu School of Applied Science, Beijing Information Science and Technology University, Beijing, ChinaSearch for more papers by this authorZijin Li, Zijin Li Department of AI Music and Music Information Technology, Central Conservatory of Music, Beijing, ChinaSearch for more papers by this authorTingyu Zhang, Tingyu Zhang School of Applied Science, Beijing Information Science and Technology University, Beijing, ChinaSearch for more papers by this authorHong Yang, Hong Yang School of Applied Science, Beijing Information Science and Technology University, Beijing, ChinaSearch for more papers by this author Jing Jiang, Corresponding Author Jing Jiang [email protected] orcid.org/0000-0003-3532-6556 School of Applied Science, Beijing Information Science and Technology University, Beijing, China Correspondence Jing Jiang, School of Applied Science, Beijing Information Science and Technology University, Beijing 100192, China. Email: [email protected]Search for more papers by this authorJingyu Liu, Jingyu Liu School of Applied Science, Beijing Information Science and Technology University, Beijing, ChinaSearch for more papers by this authorZijin Li, Zijin Li Department of AI Music and Music Information Technology, Central Conservatory of Music, Beijing, ChinaSearch for more papers by this authorTingyu Zhang, Tingyu Zhang School of Applied Science, Beijing Information Science and Technology University, Beijing, ChinaSearch for more papers by this authorHong Yang, Hong Yang School of Applied Science, Beijing Information Science and Technology University, Beijing, ChinaSearch for more papers by this author First published: 17 February 2022 https://doi.org/10.1049/ccs2.12048 This paper is part of a special issue on Music Technology. AboutSectionsPDF ToolsRequest permissionExport citationAdd to favoritesTrack citation ShareShare Give accessShare full text accessShare full-text accessPlease review our Terms and Conditions of Use and check box below to share full-text version of article.I have read and accept the Wiley Online Library Terms and Conditions of UseShareable LinkUse the link below to share a full-text version of this article with your friends and colleagues. Learn more.Copy URL Share a linkShare onFacebookTwitterLinkedInRedditWechat Abstract String instruments, wind instruments and percussion instruments are three traditional categories of musical instruments, among which wind instruments play an important role. Usually, pitches of wind instruments are determined by the vibrating air column, and the musical pitches will be affected by multiple factors of the air flow. In this article, the mechanism of sound production by a pipe is analysed in terms of the coupling of the edge tone and the air column's vibration in the tube. Experiments and computational fluid dynamics numerical calculations are combined to study the influence of the jet velocity on the oscillation frequency of the edge tone and the musical sound produced by the tube, which help to gain deeper insight into the relation between physics and music. 1 INTRODUCTION The mechanism of sound generation of wind (or flue) instruments has been an intensive research subject in the area of flow dynamics and aeroacoustics. According to their acoustic characteristics, wind instruments can be classified into open-pipe instruments and closed-pipe instruments [1]. Common musical instruments such as flutes and recorders are open-pipe instruments, while other instruments such as the clarinet and bawu are closed-pipe instruments. On the other hand, wind instruments, which generate sound by vibrating columns of air, have different sound generation mechanisms. For instruments such as the clarinet and oboe, the player blows to cause a reed to vibrate, and for instruments such as the flute and xiao (a Chinese vertical end-blown bamboo flute) [2], the oscillating jet around the labium act as a dipole-type acoustic source to generate sound, and then, the jet flow shed from the edge of a cylindrical or conical bore. Different wind instruments have different timbre and tonal quality depending on the performance technique of the player. For example, wooden/bamboo flute has a bright, sharp pitch, which is rich in expressions and is suitable to a wide range of musical genres [3]. The Chinese xiao possesses a deep and mellow timbre, which is appropriate for playing lyrical melodies [4]. Even for the same kind of wind instrument, different performance techniques will give rise to different timbres. The inharmonic hydrodynamic sound during starting transients plays an important role for the subjective perception of the sound generated by the wind instrument [5, 6]. The flutist is free to tailor the tonal quality via altering the lip-to-edge distances, the angle and velocity of the airstream that strikes the embouchure hole [7]. For example, the technique of overblowing allows the player to overblow the pitch to a higher overtone with the fingering unchanged. The complex interactions between the hydrodynamic and the acoustic phenomena take place mainly at the mouth of the musical flue pipe. There are two feedback paths act on the oscillation of the air jet reported in the literature. One of them is hydrodynamic feedback of the aerodynamic sound generated by a free jet oriented to a wedge-shaped object, which is termed as the edge tone. The physical mechanism of the edge tone phenomenon has been elucidated through a number of theoretical, experimental [8-10] and numerical [11] studies and the coexistence of different hydrodynamic modes was reported. Vaik et al. [11] carried out two-dimensional computational fluid dynamics (CFD) simulations on an organ pipe foot model and found good agreement with the experimental results. As the energy accumulates and the pressure builds up, the jet is forced to oscillate under the frequency of the normal modes of the pipe resonator of the flue pipe. A feedback mechanism occurs between the air jet and the acoustical field of standing sound wave of the pipe resonator. However, the mechanism of the interaction between the vortical flow and the acoustics of the pipe resonances is still not fully understood. Many researchers have made efforts to elucidate the sounding mechanism of flue instruments through numerical simulations [12-18] and experimental studies [5]. Castellengo et al. [5, 19] carried out intensive experimental studies on the interactions between the mouth tone and the subsequent flue pipe tone. They made a parameter study changing the pressure build-up rates of the attack transients using a time-frequency approach. Tabata et al. performed a three-dimensional compressible large eddy simulations with OpenFOAM to study the energy transfers between the fluid and acoustic in an air-jet instrument [13]. Yokoyama et al. directly simulated the flow and acoustic fields in a recorder with tone holes based on three-dimensional compressible Navier–Stokes equations [12, 14]. For most of the literature mentioned above, the jet-edge system is made of the languid of the labial organ pipe. Here, a musical pipe model that generate sound by the jet oscillating against the edge of a cylindrical tube is under investigation. In this paper, we experimentally implement a musical pipe model and show the mutual relationship between the edge tone phenomenon and the pipe harmonics. The audio signal data is collected and analysed in combination with CFD simulations, which shows a close relation with the velocity of the jet flow. In this article, the simulations were performed using the ANSYS FLUENT commercial CFD software, which solves two-dimensional Navier–Stokes equations under a finite volume scheme. The description of acoustic behaviour under different parameter settings in this article may provide theoretical guidance on instrumental performance and help understand the sound generation mechanisms in realistic musical flue instruments such as the wooden flute and the xiao. 2 THE SOUNDING MECHANISM OF THE FLUE INSTRUMENTS The sound-production mechanism of a musical pipe is as follows: a jet of air with a relatively stable frequency oscillates against the edge of the tube and brings about vortices that generate audible sound, which is denoted as the edge tone [20-22], and then the jet drives and interacts with the periodic vibration of the air column inside the tube. This acoustic resonance of the tube that amplifies small perturbations to periodic oscillations with large amplitudes is denoted as the pipe tone. For flue instruments attached with a pipe resonator, there are two feedback paths acting on the vibrating air jet: the hydrodynamic feedback at the edge (labium) and the acoustic feedback of the pipe resonance [7, 23]. Specifically, the jet impinges on the edge of the pipe, and the oscillating jet forms a dipole-type acoustic source [24]. This oscillating stream is then divided by the edge and breaks into asymmetric vortex street propagating along the two sides of the edge. The airflow obstruction caused by the edge changes the velocity of each particle of the jet and brings about pressure difference. Particles with smaller jet velocity have larger intensity of pressure while particles with larger jet velocity have smaller intensity of pressure. Particles with higher acoustic pressure will move towards the particle with smaller acoustic pressure, which gives rise to collisions between vortices [25]. The frequency of a chosen particle of the vortices that pass through one side of the edge is approximately equal to the frequency of the audible edge tone [26]. This sound creates an infinitesimal disturbance on the jet emitted from the nozzle, which can be attributed to a hydrodynamic feedback loop [24]. Compared to the eigenmodes of the pipe, the edge tone is extremely weak, and its duration is quite short. The edge-tone jet initiates and couples to the subsequent pipe tone to generate audible sound that is more intense, rich in harmonics and easier to stabilise. The coupling process is as follows [13, 15-18]: the edge-tone jet that oscillating with high frequency introduces vorticity components through the shear layer, and the vortices gradually grows into larger vortices with increasing pressure. During the process of energy accumulation before the pressure is sufficient to excite the pipe resonance, the oscillation frequency of the edge-tone jet is dragged down and forced to the frequency of the normal modes of the flue pipe. The vortices shed from the pipe edge move downwards and continuously strike the back side of the cavity, which leads to complex flow disturbance that either transfers energy to, or takes away from, the resonant acoustic field inside the pipe. At the same time, this disturbance feeds back to the front side of the cavity and affects the formation of the subsequent vortices in the shear layer, which forms an acoustic feedback cycle with energy interchange (as shown in Figure 1) [27]. FIGURE 1Open in figure viewerPowerPoint Feedback loop of the jet-drive oscillations in the cavity In the following sections, we numerically investigate the influences of the factor of jet velocity and jet angle on the oscillation frequency of the edge tone and the tonal quality of the musical flue pipe. Also, experimental implementation on the acoustic response of a musical flue pipe under varying jet velocities is carried out. 3 CFD SIMULATIONS Geometry configuration, computational mesh and simulation parameters The influence of the magnitude of the jet velocity on the oscillation frequency of the edge tone is investigated by solving the incompressible, two-dimensional Navier–Stokes equations under a finite volume scheme (ANSYS FLUENT). Here, in order to explore the role of the edge tone and help explain the experimental result presented in the next section, we investigate the behaviour of air flow for a standalone jet-edge system separated from the remaining acoustic pipe resonator. The reason of separating the jet-edge system from the tube in the CFD simulation is as follows: the duration of the starting transient, which is generated by vortex shedding from the edge is quite short, extremely weak, and difficult to stabilise. As the energy accumulated the edge tone adhere to the pipe modes, and the signal becomes intense and stable. Separating the mouth system from the remainder of the pipe allow us to observe the edge-tone behaviour clearly without the overwhelming subsequent pipe resonances. The geometry configuration is illustrated in Figure 2. The distance l from the nozzle exit to the edge is 20 mm, and the width of the nozzle is 3 mm, with the centre of the nozzle aligned horizontally with the corner of the edge. In this paper, the jet velocity is varied while the distance l is kept constant. The fluid in the simulation is set to air at 25°C, with density ρ equals to 1.185 kg/m3, and dynamic viscosity μ equals to 1.831 × 10−5. The Reynolds number of the fluid can be calculated as Re = ρvd/μ. Here, the relation between the jet velocity and the oscillation frequency is investigated by two-dimensional (2D) CFD simulations. The reason of this simplification is as follows: a nozzle with high aspect ratio is used in most experimental studies [8, 10], and no three-dimensional (3D) effects have been found. Therefore, it is reasonable to assume the flow is planar because of the negligible flow and momentum transport in the third direction. Vaik et al. [28] performed 3D simulation for a jet-edge system and compared it with the 2D version; in the central region, the flow is proved to be almost perfectly two-dimensional and the 2D and 3D results are nearly identical. Due to the moderate Reynolds number (Re ≈ 3000) and the assumption of 2D flow in this work, the Direct Numerical Solution (DNS) model without turbulence modelling, which was developed mainly for 3D CFD simulations, was used. The mesh shown below in Figure 3 was fine enough to resolve the flow structures to reach the stop condition of iterations in each time step for the DNS simulation; thus, no turbulence modelling is necessary. FIGURE 2Open in figure viewerPowerPoint Velocity field of the air flow near the edge FIGURE 3Open in figure viewerPowerPoint The computational mesh The geometry and the mesh were prepared using ANSYS-ICEM software. The mesh was block-structured with extra refinement at the near-wall region in order to fully resolve the flow near the boundary. The region between the nozzle exit and the edge was covered by 40 elements (Figure 3). The wall of the nozzle and the edge were set to no-slip wall, and the nozzle exit was set to velocity-inlet. Outer boundaries were set to the opening boundary condition with prescribed static pressure. Influence of varying the jet velocity on the edge tone As shown in Figure 2, the jet flow that emanates from the nozzle oscillates as a result of the jet instability. When the jet impinges on the edge, periodic vortex shedding occurs due to the separation of the air stream. Figure 4 plots the pressure signals read out from the monitoring point (✚ in Figure 2) in the vicinity of the edge. Subplots in the left panel of Figure 4 show time history of pressure signals under varying jet velocity with the transient response omitted. The corresponding spectra calculated with Fast Fourier Transform using Matrix Laboratory software are presented in the right panel. In order to balance the accuracy of the simulation and the computational cost, we carefully determine the optimal time step τ to be 0.1 ms, and for the duration of the simulation T, according to the characteristics of the Fourier transform, T is related to the frequency resolution of the spectra (Δf = 1/T). Therefore, the value of T must be adjusted to fulfil the required frequency resolution for different oscillation frequencies. Also, we found that the duration of the transient response is inversely proportional to the jet velocity, which means the duration of the simulation could be reduced for higher jet velocity. Therefore, the duration of the simulation is varied from 0.5 to 1 s in accordance with the jet velocity. FIGURE 4Open in figure viewerPowerPoint The time history of the sound pressure signals (left panel) and the corresponding spectra (right panel). The jet velocities are (a) (b) 2 m/s, (c) (d) 4 m/s and (e) (f) 18 m/s, respectively. As illustrated in Figure 4, the sound pressure signals have complicated waveforms as a result of superposition of signals of different frequencies. Different frequency regimes of the audio signals are defined as stages. Next, we will briefly discuss about the existence of multiple stages of the edge tone phenomenon The oscillation frequency of the edge tone is mainly dependent on two factors, the exit velocity v and the nozzle-to-edge distance l. If the velocity v is increased continuously, the oscillation frequency increases continuously with the velocity within a certain range. However, further increasing the jet velocity, at certain values the frequency suddenly jumps to a higher value, along with changes of the qualitative appearance of the flow. These distinct regions of the edge tone characterised by different oscillation frequencies and flow patterns are called stages [28]. The reason of the existence of stages are as follows: the jet wave driving the flue pipe and the stimulating acoustic disturbance are subjected to certain phase relation. Beyond certain parameter region, this phase relation cannot be achieved through minor, continuous adjustment of the frequency. The frequency needs to be adjusted to a completely different value, and thus the jump from one stage to another stage. In Figure 5, the frequencies of the edge tone are extracted from the spectra depicted in Figure 4 and are presented as a function of the exit velocity. As shown in Figure 5, when the jet velocity is relatively small, there is only one pure stage. When the velocity is increased to 1.25 m/s, the frequency jumps from 29 to 60 Hz and the second stage of the edge tone appears. It can be seen that within the investigated velocity range, the lower stages remain present at higher velocities when the edge tone jumps to a higher stage. Further increase the jet velocity, when the velocity reaches 4 m/s, the frequency jumps to 318 Hz, and the first, second, and third stage coexist. Also, as demonstrated in Figure 5, within each stage of the edge tone, the frequency rises with the jet velocity but with different slopes for different stages [29, 30]. FIGURE 5Open in figure viewerPowerPoint Frequency as a function of the exit velocity As stated above, vortex shedding at the edge gives rise to the edge tone phenomenon, which exhibits sudden change of frequency towards higher stages as the jet velocity increases. This will affect the subsequent pipe resonance excited by the edge tone if the edge is affixed to a pipe resonator. In order to gain more physical insight into the interplay between the edge-tone jet and the stimulating acoustic resonance, in the next section, the acoustic response of a jet-drive musical flue pipe under varying jet velocities is studied experimentally. Influence of varying the jet angle on the edge tone Computational fluid dynamics simulations with different jet angles against the edge were also carried out. As shown in Figure 6, the nozzle was rotated by an angle α clockwise and anticlockwise about the corner point of the edge, respectively. In Figure 6, the velocity field of the jet flow near the edge and the corresponding spectra (with transient response omitted) are plotted for α = 10 ° $\alpha =10{}^{\circ}$ (upper panel) and α = − 10 ° $\alpha =-10{}^{\circ}$ (lower panel). The distance l from the corner point of the edge to the nozzle exit and the jet velocity v are kept constant (l = 20 mm, v = 4 m/s) when varying the angle of the jet flow. The spectrum with a relatively strong second stage, a weaker first stage and much weaker higher order stages was observed with α = 10 ° $\alpha =10{}^{\circ}$ . When α equals to − 10 ° $-10{}^{\circ}$ , the first stage is stronger than the second one as illustrated in Figure 6d. These observations can lead to the conclusion that the edge tone's dominant mode can be varied by changing the angle of the impinging jet flow. As a result, the player has the latitude to obtain subtle variations in the perceived tonal quality by varying the inclination angle between the jet flow and the mouthpiece of the instrument. However, since the influence of varying the angle of the jet flow on the oscillation frequencies of the edge tone is not as significant as that of the jet velocity (increasement of the frequency and jump to higher stages), here we focus on the factor of jet velocity and experimental study on the acoustic response of a jet-drive musical flue pipe under varying jet velocities is carried out in the next section. FIGURE 6Open in figure viewerPowerPoint Velocity field (left panel) and corresponding spectra (right panel) for (a) (b) α = 10 ° $\alpha =10{}^{\circ}$ and (a) (b) α = − 10 ° $\alpha =-10{}^{\circ}$ 4 EXPERIMENTAL REALIZATION OF A PIPE FLUE MODEL Experimental setup An open-ended cylindrical pipe made of acrylic glass is measured, and the geometry parameters are as follows: the inner diameter Din = 44.1 mm, the outer diameter Dout = 50.3 mm, the pipe length L = 800 mm, and the nozzle breadth δ = 5 mm. The ambient temperature is 25°C, and the humidity is 30%. As illustrated in Figure 7, the high aspect ratio is aligned with the edge of the pipe. A blower is used to pump wind to drive the pipe through bellows and the nozzle. There is a throttle valve on the reservoir to control the output pressure, and the jet velocity is then calculated by the value of the air pressure divided by the cross section of the windway. The sound pressure signal is measured by a G.R.A.S. 40PP constant current power Free-field QC microphone placed 2 cm away from the pipe exit. Signals collected by the probe microphone are then analysed by an audio signal analysis system based on LabVIEW. FIGURE 7Open in figure viewerPowerPoint Schematic of the experimental setup Influence of varying the jet velocity on the tonal quality of the flue pipe The spectrogram with varying jet velocity is demonstrated in Figure 8. The jet velocity is switched from 19.8 to 59.5 m/s and then to 79.4 m/s. It can be observed that for the duration of 0–8 s, the jet velocity is relatively low (V1 = 19.8 m/s) and the oscillation frequency of the edge tone is around the frequency of the first resonant mode of the pipe. Therefore, after the edge tone exciting and coupling to the subsequent pipe tone to generate stable sound, the fundamental resonant mode (206.5–208.0 Hz) becomes dominant in the spectra. Although in the presence of higher harmonics, the first mode has the highest energy content. The blowing velocity is further increased to V2 = 59.5 m/s in the interval from 8 to 16 s. As the jet velocity increases, the oscillation frequency of the edge tone increases with the jet velocity and jumps from the lower stage to higher stage. During this duration, the frequency of the edge tone reaches the frequency of the second harmonic of the pipe, which causes the dominant mode of the stimulating pipe resonance change to the second resonant mode (413.0–416.0 Hz). For the interval from 16 to 20 s, the jet velocity is increased to V3 = 79.4 m/s. It is found that the dominant mode of the pipe resonance becomes the third harmonic (618.5–624.0 Hz), which can be attributed to the jumping of the edge tone to a higher stage that adheres to the third normal mode of the pipe. Noticeably, when the jet velocity increases, lower harmonics of the pipe do not disappear but coexist with the higher harmonics. FIGURE 8Open in figure viewerPowerPoint Spectrogram of the flue pipe with varying jet velocity As indicated by the results of the numerical simulation, the oscillation frequency of the edge tone increases with the exit velocity. In addition, at certain value, the frequency of the edge tone suddenly jumps to a higher stage. Since the measured stable sound of the flue pipe is excited and affected by the edge tone, the change of the dominant frequency of the pipe resonance is a result of both the above two factors. 5 CONCLUSION The sound generation mechanism for a musical flue pipe can be described as follows: the jet impinges on the edge of the pipe to generate the edge tone, and then the edge tone initiates and interacts with the subsequent pipe resonances. In this work, it was found through numerical simulations that the oscillation frequency of the edge tone increases with the jet velocity and jumps to another higher stage at certain values, and the dominant modes can be altered by varying the impinging jet angle. The experimental study of a musical pipe model has been developed, and the tonal quality of the flue pipe is demonstrated to be dependent upon the changes in the oscillation frequency of the edge tone. In particular, greater amplitude and higher dominant frequencies are shown in the acoustic response of the flue pipe when increasing the jet velocity. These properties make it possible for the flutist to obtain subtle variations in the perceived tonal quality through adjustment of the blowing velocity during the attack transient, such as the technique of overblowing, where the pitch is overblown to a higher overtone while the fundamental mode is suppressed. The tonal quality of wind instruments is determined by multiple factors, including the jet velocity, the nozzle-to-edge distance, the impinging angle of the jet flow relative to the edge, the material and shape of the resonator etc. The experimental and numerical analysis on the acoustic behaviour of a flue pipe presented in this paper may facilitate the development of a comprehensive understanding of the acoustics of real wind instruments. CONFLICT OF INTEREST The authors have no conflict of interest to declare. Open Research DATA AVAILABILITY STATEMENT The data that support the findings of this study are available from the corresponding author upon reasonable request. REFERENCES 1Fletcher, N.H., Rossing, T.D.: The Physics of Musical Instruments. Springer, New York (1998) 2Wan, Y., thesis, M.S.: Acoustic Principle of Wind Instruments Orchestration in Chinese Orchestra. China Conservatory of Music, Beijing (2019) 3Malm, W.P.: Traditional Japanese music and musical instruments. 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