James P. Cottingham

Variation of frequency with blowing pressure for an air‐driven free reed

In free reed instruments, an approximately linear decrease of playing frequency with increasing blowing pressure is normally observed. Laboratory measurements on harmonium‐type reeds from an American reed organ have shown additionally that at very low pressure there is a small region of increasing frequency with increasing blowing pressure, and at extremely high blowing pressures, the frequency of reed vibration increases rapidly with increasing pressure. Measurements of growth and damping rates confirm the previously reported result [A. O. St. Hilaire, T. A. Wilson, and G. S. Beavers, J. Fluid Mech. 49, 805–815 (1971)] that at low air‐flow rates aerodynamic forces add to the mechanical damping of the vibrating reed, but at higher flow rates, the aerodynamic forces contribute negative damping, resulting in self‐sustained oscillations. Measurements of reed damping or growth rates have been made over a wide pressure range. Incorporation of these values along with other appropriate parameters in Fletcher’s m...

The motion of air‐driven free reeds

An earlier study on free reeds from reed organs [P. D. Koopman and J. P. Cottingham, Reed Organ Soc. Bull. 15, No. 3–4, 17–23 (1997)] yielded information about the variation in amplitude of reed vibration with pressure, but few further details on the reed motion. A more thorough set of measurements of the motion of these reeds has been done, including the use of a variable impedance transducer to measure reed displacement and a laser vibrometer system to measure reed velocity. For reeds from reed organs, at low to moderate blowing pressures, the reed motion at each point is nearly sinusoidal and the reed profile at maximum amplitude closely approximates that calculated for a cantilevered beam vibrating in the first mode. At blowing pressures considerably higher than normal playing pressure, strong indications of the presence of the second beam mode are observed. The nearly sinusoidal reed motion at normal pressure contrasts with the sound pressure waveform near the reed which, as a result of the valve act...

Bamboo in Asian musical instruments.

The acoustical properties of bamboo, along with its widespread availability, have made it one of the most commonly used materials for the construction of musical instruments worldwide. Among its properties important for acoustics, bamboo has a relatively low density and elastic modulus and a significant difference between the elastic moduli parallel to and perpendicular to the bamboo fibers. An extensive general review of the acoustically relevant properties of bamboo has recently been published [U. G. K. Wegst, Annu. Rev. Mater. Res. 38, 323–349 (2008)]. This paper presents some recent results on measured physical properties of bamboo as used in Asian wind and percussion instruments. The mechanical properties of the bamboo reeds used in some free reed wind instruments have been studied. Since a wide variety of flutes and reed wind instruments employ bamboo pipes the elastic moduli of bamboo pipes, as well as the non‐uniformity of the pipe wall material are of current interest, in particular, as related t...

The acoustics of the khaen, bawu, and gourd pipe

Mouth‐blown instruments using a free reed coupled to a pipe resonator have a long history in China, Japan, and throughout Southeast Asia. The khaen and the gourd pipe are unusual wind instruments, employing a free reed mounted in the side of a cylindrical tube open at both ends, although in the gourd pipe the player has the option of closing the bottom of the pipe so that the reed is near the closed end. The bawu is a closed cylindrical pipe with a free reed at one end, in which the effective acoustical length is varied by the use of tone holes. The playing frequency of each pipe of the khaen or the gourd pipe is typically slightly above both the resonant frequency of the pipe and the natural frequency of the reed. In the bawu, on the other hand, the pipe resonance pulls the sounding frequency well above the natural reed frequency, resulting in a striking difference in tone quality. Acoustical measurements made on these instruments include studies of reed vibration and impedance measurements of the pipes,...

Period doubling in free reeds coupled to pipe resonators

An earlier study investigated behavior of the reed–pipe combination consisting of an American organ reed installed at the closed end of a cylindrical pipe. Over a wide range of pipe lengths and playing pressures, the sounding frequency is slightly below a pipe resonance frequency and can be pulled considerably below the natural frequency of the reed. [Vines et al., J. Acoust. Soc. Am. 114, 2349 (2003)]. Additional measurements of reed vibration for these reed–pipe combinations for low frequency (48 Hz) free reeds show that as the playing pressure is increased there is typically a sudden transition to period doubling or, in some cases, tripling or quadrupling. Some pressure intervals exist in which apparently chaotic reed vibration occurs, or in which the reed will not vibrate at all. Period doubling was found to occur over varied values of pipe length, pipe diameter, and the use of two different reeds with matching resonance frequencies. General trends in the onset and steady‐states of period doubling are...

An inward striking free reed coupled to a cylindrical pipe

A number of acoustical measurements have made on a reed‐pipe combination consisting of a harmonium‐type reed from an American reed organ installed at the closed end of a cylindrical pipe. This configuration, which somewhat resembles the configuration of free‐reed organ pipes, differs from the reed‐pipe combination occurring in the mouth organs of Asia, which use symmetric (outward striking) free reeds and normally operate on both possible directions of airflow. Measurements have been made of the sounding frequency, amplitude of vibration of the reed tongue, and the sound spectrum. Of particular interest is the degree to which the reed frequency can be altered by altering the pipe length, and hence the pipe resonance frequency. In this case the sounding frequency can be pulled considerably below the natural frequency of the reed. These results can be compared with the results of similar measurements on free‐reed organ pipes [J. Braasch, C. Ahrens, J. P. Cottingham, and T. D. Rossing, Fortschr. Akust., DAGA...

Experimental investigation of air‐driven free reeds using a laser vibrometer system

Previously reported measurements of free‐reed vibration using a variable impedance transducer (VIT) gave a picture of the motion of a point on the reed throughout its cycle [J. P. Cottingham, J. Acoust. Soc. Am. 105, 940 (1999)]. A more detailed picture of the reed motion throughout its vibrational cycle has been obtained by measuring reed velocity using a laser vibrometer system. Unlike the VIT sensor, the laser vibrometer can be scanned along the reed, allowing reed profiles to be obtained. The laser system is also usable on reeds of magnetic material (e.g., steel accordion reeds) as well as reeds too small and inaccessible for the VIT. In this investigation the emphasis has been on comparison of the vibrational motion of accordion reeds with that of the reed organ reeds which had been measured in earlier studies. Some of the differences observed between the two types of reeds can be related to the structure of the reed tongues and frames.

Frequency and amplitude of vibration of reeds from American reed organs as a function of pressure.

The frequency and amplitude of vibration of a representative sample of reeds from American reed organs have been studied as functions of the (negative) static pressure difference between the interior and exterior of the windchest. Over a pressure range that includes the normal playing pressure of the instrument, the frequency tends to decrease in an approximately linear fashion with increasing pressure difference, but some anomalous effects are observed at higher pressures. Effects of constrictions to the airflow, simulating the effect of a partially opened pallet, have also been studied.

Effects of air‐jet angle and other jet characteristics on the spectral features of a jet‐driven Helmholtz resonator

Previous studies of a Helmholtz resonator excited by an air jet explored the dependence of the frequency and amplitude of the Helmholtz mode on jet speed. It was observed that there are domains of jet speed, separated by narrow transition regions, for which a single frequency Helmholtz mode occurs [R. Khosropour and P. Millet, J. Acoust. Soc. Am. 88, 1211–1221 (1990)]. In the current investigation, a series of measurements were made exploring the dependence of amplitude, frequency, and domain width on the jet angle as well as jet speed and jet width. In addition, the amplitude variations of the harmonics of the Helmholtz mode and the appearances of the first standing wave mode were studied, especially near transition regions.

The Technical Committee on Musical Acoustics: Diverse membership with a common interest

The Technical Committee on Musical Acoustics is concerned with the application of science and technology to the field of music. Topics of current interest include the physics of musical sound production, music perception and cognition, and analysis and synthesis of musical sounds. TCMU is an interdisciplinary committee with ties to architectural, psychological and physiological, signal processing, speech, physical, and structural acoustics. Members of the committee represent a variety of backgrounds and interests, yet are united by a common interest in understanding all aspects of the science of music.