R. Dean Ayers

California State University, Long Beach | CSULB · Department of Physics & Astronomy

The linear behavior of an air column can now be illustrated very easily using a personal computer. Concepts that may have been somewhat abstract become more concrete with kinetic images on the computer screen. One basic example is a representation of standing waves with imperfect nodes in terms of several dependent variables, each of which displays...

Tunes are played on the Great Highland bagpipe using the tone holes of its conical chanter. The much quieter practice chanter has holes with the same spacings on a narrow cylindrical bore. Differences between spherical waves in a cone and plane waves in a cylinder give rise to striking differences in pitch and tone quality. Drone pipes do not need...

A software program was developed to help musicians learn to tune just intonation intervals. A reference tone is played and Lissajous‐like figures present a visual representation of the interval the musician’s sound makes with the reference tone. This approach is interesting, because the musician receives coordinated aural and visual feedback in rea...

Musicians become used to equal temperament pitch intervals due to their widespread use in tuning pianos and other fixed-pitch instruments. For unaccompanied singing and some other performance situations, a more harmonious blending of sounds can be achieved by shifting to just intonation intervals. Lissajous figures provide immediate and striking vi...

Galileo Galilei showed us by example how to put hypotheses about the natural world to the test of scientific experiments. It is very likely that his attitude of healthy skepticism toward his own ideas and those of others was instilled in him by some work in musical acoustics. His father, Vincenzo (or Vincentio), was a prominent music theorist and c...

A circuit has been designed and built to provide real‐time, precisely controlled video images of a brass player’s lips during the relatively steady part of a sustained note. This should be useful for both the scientist who wishes to model the lip reed and the beginning player who is just learning how to control that driver. The circuit uses a phase...

Introductory treatments of waves usually emphasize undamped traveling waves and ideal standing waves with perfect nodes. Those are just special cases from a larger class of waves in which the crests perform a characteristic ‘‘lurching’’ or ‘‘galloping’’ motion. The variation of a terminal reflection coefficient and the constant for damping in propa...

Simple lip reed models treat the brass player's upper lip as a single mass that moves with one or two degrees of freedom. Helmholtz's outward-swinging door model operates at a playing frequency that is higher than both the lip frequency and the relevant air column resonance frequency. A simple empirical test with an isolated mouthpiece shows a very...

A brass player employs mutes in performance to modify spectral characteristics of the sound output for musical effect. An undesirable side effect is a modification in pitch center, which is easily compensated for in the trombone by a small adjustment in playing slide position. The effects of various mutes upon the sounding frequencies of the trombo...

Since 1980, a converted 27‐ft recreational vehicle has been visiting local schools filled with a variety of hands‐on science exhibits and activities. The Mobile Science Museum (MSM) has recently undergone a major renovation, including adding a generator. The MSM is now self‐contained with inside exhibits that focus on the physical sciences, includi...

There are currently three basic models for the brass player?s vibrating lips: (1) Helmholtz?s outward?striking or swinging door model, (2) a sliding door model, with motion that is transverse to the air stream, and (3) a hybrid, two?dimensional model that combines those two motions. Time?domain computer simulations of these models have been carried...

The stroboscopic technique of Daniel W. Martin [J. Acoust. Soc. Am. 13, 305–308 (1942)] has been updated by using a video camera. Improved magnification and resolution show that the upper lip’s motion is complicated: a Rayleigh wave propagates downstream in a thin, passive layer of flesh. Muscles of the embouchure are used to adjust the tension and...

Although designed particularly for music students, musical acoustics courses at American universities generally draw a ??mixed bag?? of students with a rather wide variety of backgrounds. This presents some real challenges but also some real rewards. Some of the problems in teaching musical acoustics to heterogenous classes and some of the ways the...

Mouthpieces with flat windows are used to examine the lip reed?s motion during the steady parts of notes played on brass instruments. Magnified stroboscopic images show different parts of the upper lip moving out of phase with each other. Sighting directly along the channel between the lips, one can observe a Rayleigh wave propagating downstream in...

An idealized conical bore that is complete to its apex has been used as the basic model for several wind instruments with tone holes, such as oboe,bassoon,saxophone, and cornetto. The useful playing frequencies for these relatively short instruments include those near the first peak in |Z|. A uniform pipe that is closed at both ends has been propos...

Given that a nearly harmonic alignment is a desirable condition, to what extent is it achieved in a particular brass instrument, and how do the bell and the input segment cooperate to bring it about? Answers to these questions that are easily read by human beings are not to be found in a plot of |Z|, or any aspect of the plane?wave reflection coeff...

A novel algorithm for calculating a brass instrument’s acoustic pressure response to an impulsive volume flow at the input end [R. D. Ayers, J. Acoust. Soc. Am. 100, 1190–1198 (1996)] is applied to sound simulation. The algorithm employs several impulse responses that have no multiple reflections and that decay very rapidly. These are convolved wit...

A brass instrument has three major parts: an input segment, a cylindrical or conical central segment, and a bell. (The latter two are often treated together.) It is conceptually useful to isolate the input segment from the rest of the air column and study the acoustical behavior of that complete segment rather than its components. Features in time?...

This paper generalizes the linear part of Robert T. Schumacher's approach for modeling wind instruments [R. T. Schumacher, Acustica 48, 71- 85 (1981)]. A reinterpretation of that work shows that the general problem is one of deconvolving an infinite series of multiple reflections, rather than attempting to define an anechoic termination for the inp...

The definition of effective length has been generalized to all frequencies by Pyle, working in the context of lossless plane‐wave horn theory [R. W. Pyle, Jr., J. Acoust. Soc. Am. 57, 1309–1317 (1975)]. In this paper, losses due to radiation and visco‐thermal damping are included by letting the effective length become complex. With that additional...

In the context of a plane?wave approximation for acoustic waves in an air column, the pressurereflection coefficientR is related to the relative input impedance Z/Z c by a simple bilinear transformation. At any location along the air column, the complex effective length to an open, downstream end of an equivalent cylinder is defined as L o ?(j/2k 0...

Experimental studies of impulse responses in a trumpet bore have suggested a divide‐and‐conquer approach in which the contributions of the major elements (input end, uniform pipe, and output end) can be examined and understood separately. Multiple convolutions are then used to assemble these into the time‐domain response (Green's function) of...

Recent interest in modeling nonlinear feedback control of the driver has led several researchers to examine Green's functions and reflection impulses for wind instrument bores. These are usually obtained as inverse Fourier transforms of experimental or computational results in the frequency domain. At CSULB, the focus instead has been on devel...

Arthur Benade's well‐known paperback Horns, Strings, and Harmony includes a didactic fairy tale about a bugler forced to play on a uniform pipe and stay in tune with ordinary bugles. With a bit of sawing and some impressive lipping, he manages to succeed. This story fits nicely with the prevailing view that the bell on a brass instrument causes a c...

The author has developed a minicourse for school teachers on how they can include acoustics in their teaching of science, with particular emphasis on musical sounds. The organizing theme is the direct, hands?on accessibility of many basic ideas in this area. The course is divided into three units: (1) simple vibrators, covering ideas about pitch, f...

A senior/graduate elective course on Fourier transforms and the physics of vibrations and waves has now been taught for 6 years. The textbook by Ronald Bracewell is used in the first half of the semester to lay the mathematical foundations: piecewise functions, convolution, generalized functions, the transform and the series, theorems on transform...

A survey of descriptive textbooks on musical acoustics shows a need for a legitimate, convincing explanation for the seemingly paradoxical behavior of the conical bore. We examine the differential equations and their solutions for spherically symmetric waves in three dimensions, settling on acoustic pressure as the variable of interest because it b...

An inexpensive piezoelectric transducer described earlier [M. I. Ibisi and A. H. Benade, J. Acoust. Soc. Am. Suppl. 1 72, S63 (1982)] is driven by an arbitrary (digital) waveform generator. The width and shape of the volume velocity pulse generated are controlled by Wiener (least?mean?squares) filtering [A. C. Holly, J. Acoust. Soc. Am. 75, 973?976...

The acoustic pulse generator described in the previous paper has been used to examine extended impulse responses in bores of simple geometry with relatively few, distinct discontinuities. These are pressure waveforms at the input end that result from the application of a single volume velocity pulse there. The complex input impedance curve of a bor...

A systematic study has been undertaken to identify and analyze all possible multiphonics on a popular brand of plastic recorder (Aulos, alto voice). The absence of a bell at the end of the recorder combines with the open‐hole cutoff effect to guarantee strong, nonharmonic bore resonances, and many of the forked fingerings produce stable multiphonic...

A review of textbooks and research literature reveals that there is room for improvement in the treatment of this simple but important bore shape. We use plots of acoustic pressure standing waves to show students in a descriptive course that a complete cone and an open pipe of the same length have the same natural frequencies. These plots also pred...

Fraunhofer diffraction from a planar diffracting object is explained in terms of spatial Fourier transforms and the Ewald sphere construction from solid-state physics. It is found that the most meaningful view of such a diffraction pattern is obtained by letting it fall on a spherical screen centered upon the diffracting object and then observing t...

An experiment to illustrate mechanical resonance has been designed for use in lower division laboratories. The apparatus and procedure have deliberately been kept as simple as possible. The basic experiment yields measurements of amplitude versus driving frequency, but a fairly simple elaboration allows for measurements of the phase lag as well.

A simple construction is used to relate the farfield radiation to the two?dimensional Fourier transform of the radiator's velocity distribution. This results in a convenient mapping of the (?, ?) dependence for the radiated amplitude into the k plane. The inverse transform of the contents of the ?radiation circle? of radius ?/c 0 then yields all in...

An optional, one?unit laboratory course to accompany a three?unit general?education course in descriptive acoustics has been designed to utilize some fairly sophisticated equipment available in our electronics laboratory. In the very first experiment, students become familiar with the use of the oscilloscope by following a literal cookbook to get a...

The Barcus‐Berry AudioPlate is a new type of speaker which employs a large piezoelectric element to drive a glass plate in bending motion. Tests conducted in an anechoic chamber indicate a useful frequency range extending from about 2 kHz to well above 20 kHz. Particularly prominent above 10 kHz is an unusual maximum in the radiation pattern in the...

A rotating sample technique for measuring the electrical resistivity of liquid metals is developed in some detail and is checked for accuracy and dependability by making measurements of the resistivity of indium-mercury alloys of different compositions. End corrections have been made to the rotating sample method. This method has several advantages...

A theoretical calculation for the effect of the cylinder ends on the eddy currents induced in a finite cylindrical conductor by a magnetic field rotating perpendicular to the cylinder axis has been carried out. The conditions assumed here, i.e. that the conductor is a solid and that the eddy currents do not significantly alter the magnetic field, a...