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Physics and Tonal Design in Pipe Organs and Air-Jet Musical Instruments

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Physics and Tonal Design in Pipe Organs and Air-Jet Musical Instruments Measurement of Velocity Profiles of the Jets Issuing from Some Flue Geometries Typical of Air-Jet Instruments Shigeru Yoshikawa and Keita Arimoto Dept. of Acoustical Design, Kyushu Institute of Design, Fukuoka, 815-8540 Japan Air-jet musical instruments may be categorized by the geometry of flue channel and flue exit: The flue of metal organ pipes is simply modelled by a vertical plate and a horizontal languid (such a flue is called "organ" here). The flue made by flute or shakuhachi players may be modelled by two thin plates corresponding to player's lips (called "short" because of short channel length). Contrary to this "short" flue, a "long" flue consisting of two long plates has been used for experimental organ pipe models. The recorder flue can be modelled as a long flue with a chamfer on the edge of the lower plate (called "chamfer"). The measurement of jet velocity profile was carried out on these flue models without using pipe resonators. The profile was measured at the distances of 2 to 25 mm from the exit when the initial jet velocity was varied from 10 to 50 m/s. The flue height was 2.2mm throughout the measurement. The profile difference between the “short” and “long” flues is distinctive as inferred from the top-hat and Poiseuille profiles at the exit. The profile from the "chamfer" flue tends to change from the "long"-type profile for lower jet velocities to the "short"-type one for higher velocities. The "organ" flue indicates an asymmetric profile for shorter distances from the exit. The "organ" jet directs downwards when the languid is 5 mm thick, while directs upwards when it is 1 mm thick. The experimental results are compared with the theoretical Bickley profile on a laminar two-dimensional jet and an empirical Nolle profile more squarish than the Bickley profile. INTRODUCTION anemometer when the probe is precisely dislocated with a 3-D adjustable traverser. The measurement parameters were set as follows : Tones of air-jet instruments are considerably Initial center line velocity (U00) 10, 20, 40, 50 m/s affected by the jet velocity profile which depends on Distance from the flue exit (x) 2, 4, 8, 15, 25 mm the geometry of the flue channel and flue exit. The transverse velocity profile of the jet was measured However, there are very few reports that give for the fixed U00 and x values. quantitative measurement of the velocity profile or some correlation between the flue geometry and the 2h foot 98mm foot 2h velocity profile. Our aim is to make the comparison of 100mm the velocity profiles resulting from some flue 5mm geometries typical of air-jet instruments such as the (a) long (b) short pipe organ, flute, and recorder. 2mm 2h 2h foot 1mm 5mm, MEASUREMENT 1mm (c) chamfer (enlarged near the flue exit) (d) organ5 , (e) organ1 The flue geometries used in our experiment are Fig.1 Flue geometries used in our experiment. illustrated in Fig. 1 . The “long” has a long and uniform flue channel and flat exit. Such a flue is often used in RESULTS experimental organ pipe models. The “chamfer” has the same flue geometry except for the chamfer on the Figure 2 shows the profiles of the “long” and lower side of flue exit. The flue geometry of “short” “short” obtained at the same experimental condition may give a simplified model of shakuhachi or flute (U00= 10 m/s, x = 4 mm). These profiles are well player’s lips. The “organ5” and “organ1” are different approximated by from each other in the thickness of languid (5mm and U (x, z) = U (x)sech 2 (z / b)n (n = 1,2,3 ⋅ ⋅ ⋅), (1) 1mm). The flue height 2h is 2.2mm in all of the flue 0 geometries throughout the measurement. where U0 defines the centerline jet velocity and b The velocity profile is measured by using a hot-wire the jet half-thickness. The profile from the “long” flue Poiseuille profile top-hat profile Fig.2 Velocity profiles of “long” and Fig.3 Channel flow at the flue Fig.4 Velocity profiles for U00 = “short” for U00 =10 m/s and x=4 mm . exit of the “long” and “short” flues. 20 m/s and x= 8 mm. Fig.5 Velocity profiles for U00 Fig.6 Velocity profiles of “organ5” Fig.7 Velocity profiles of “organ1” =40 m/s and x=8 mm. for U00 =20 m/s and x=2, 8, 15 mm. for U00 =20 m/s and x=2, 8, 15 mm. has n=1 and shows the so-called Bickley profile; the changes from the “long”-type profile (cf. Fig.4) to the “short”-type profile (cf. Fig.5) when the initial jet “short” flue has n=3 and shows the so-called Nolle velocity U00 increases from 20m/s to 40m/s. profile. The difference between the profiles is inferred (2) The jets of “organ5” and “organ1” do not run from the difference in channel flow at the flue exit, as straight along the x axis as illustrated in Figs.6 and 7. illustrated in Fig.3 . It may be supposed that the More interestingly, the “organ5” jet gradually deviates channel flow has reached the following Poiseuille downwards (about –10 degrees) , while the “organ1” profile at the flue exit of the “long” flue. jet deviates upwards ( about 10 degrees) . (3) Initial velocity profiles (at x= 2 mm) are also U (x, z) = U (x)(h2 − z 2 )/ h2 z ≤ h (2) 0 different between the “organ5” and “organ1” as On the other hand, the top-hat profile may be assumed indicated in Figs. 6 and 7. The “organ5” profile is at the flue exit of the “short” flue. The above asymmetrical and distorted, although it becomes mentioned difference between the velocity profiles symmetrical as the jet travels downstream. The from the “long” and “short” flues is held up to x= 8 “organ1” profile is symmetrical and it is close to the mm and U00 = 20 m/s (the Reynolds’ number Re≈ top-hat profile rather than the Nolle profile. 3000). Figures 4 and 5 indicate the profile difference at x= CONCLUSIONS 8 mm between five flue geometries for U00 = 20 m/s and 40 m/s, respectively. We may easily recognize the Velocity profiles of the jets issuing from five kinds individuality (or separation) of the profiles (although of flue geometries were measured and compared. The the profiles of “chamfer” and “organ1” are partly individuality of five profiles was recognized in the range of 10 ≤ U00 ≤ 20 m/s and 2 ≤ x ≤ 8 mm. overlapping for |z| > 1mm) when U00 = 20 m/s. However, the profiles seem to be divided into two, the When U00 was increased to 40 m/s, four profiles except for the “long” one tended to make up one group, “long” profile and the other profiles when U00 = 40 m/s. Also, all the profiles at x ≥ 15 mm approach to which may be roughly represented by the “short” one. the Bickley profile regardless of flue geometry. Some Finally, all the profiles at x ≥ 15 mm approached to characteristics typical in other flue geometries are the theoretical Bickley profile. Also, significant effects summarized as follows; of the languid thickness were recognized from the (1) The behavior of the jet from the “chamfer” “organ1” and “organ5” profiles. Can wall vibrations alter the sound of a flue organ pipe? M. Kob Institute of Technical Acoustics, Technical University Aachen, D-52056 Aachen, Germany The prediction of changes in the perceived sound of a blown pipe due to wall vibrations is made difficult by the multitude of interac- tions. Excitation, shape, and sound radiation of structural modes depend on a number of parameters like material, voicing technique, geometry and fixing of the pipe. This article presents experimental work on comparison of vibrations and sound radiation from a tin-rich pipe in two cases: with damped and undamped wall vibrations. It was found out that changes in sound pressure level at certain frequencies in the spectrogram coincide with eigenfrequencies of both air modes and structural modes and thus support the assumption of mode coupling being responsible for sound changes. INTRODUCTION shown to the right. In this spectrogram, the clouds are still present but the sound pressure level at certain frequencies Although most organ builders agree to organ pipe vi- has been reduced by approx. 10 dB at 1250 Hz, 1550 Hz brations being audible, this is in contradiction to many and 1800 Hz in the first 100 ms of the sound. Smaller experiments that were carried out on modern organ pipes differences between the damped and the undamped pipe (for an overview, see [1]). A reason why this question sound can be observed in the stationary part of the sound is not easy to answer is the multitude of parameters (e.g. at those frequencies. foot pressure, voicing) and boundary conditions (e.g. pipe support, temperature) that are difficult to control during an experiment. In addition, modern flue organ pipes are rather thick-walled compared to pipes of the 17th or 18th century. Stationary sound This work presents some measurement results indi- cating that eigenmodes of the air column, further called As a second approach the pipe was mechanically ex- air modes, and eigenmodes of the pipe body, structure cited with a shaker at the labium (c.f. Fig. 2). The sound modes, are likely to interact at some frequencies. pressure at the upper (passive) end of the pipe has been recorded and the ratio to the applied force has been calcu- lated.
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