Introduction to Acoustics

from master to apprentice even today. That is certainly
the way that the Italian masters must have worked, without
the aid of any scientific measurements beyond the
feel and the sound of the individual plates as they are
flexed and tapped.
Scientific Scaling
The other interesting development inspired by Carleen
Hutchins and her scientific coworkers Schelling and
Saunders has been the development of the modern violin
octet [15.126], a set of eight instruments designed
according to physical scaling laws based on the premise
that the violin is the most successful of all the bowed
stringed instruments. The aim is to produce a consort
of instruments all having what are considered to be
the optimised acoustical properties of the violin. Each
15.3 Wind Instruments
In this section we consider the acoustics of wind
instruments. These are traditionally divided into the
woodwind, played with a vibrating reed or by blowing
air across an open hole or against a wedge, and brass instruments,
usually made of thin-walled brass tubing and
played by buzzing the lips inside a metal mouthpiece
attached to the input end of the instrument.
In general, the playing pitch of woodwind instruments
is based on the first two modes of the resonating
air column, with the pitch changed by varying the effective
length by opening and closing holes along its length.
In contrast, brass players pitch notes based on a wide
range of modes up to and some times beyond the 10th.
The effective length of brass instruments can be changed
by sliding interpenetrating cylindrical sections of tubing
(e.g. the trombone) or by a series of valves, which
connect in additional length of tubing (e.g. trumpet and
French horn). The pitch of many other instruments, such
as the organ, piano-accordion and harmonium, is determined
by the resonances of a set of separate pipes or
reeds to excite the full chromatic range of notes, rather
like the individual strings on a piano.
A detailed discussion of the physics and acoustical
properties underlying the production of sound in
all types of wind instruments is given by Fletcher
and Rossing [15.5], which includes a comprehensive
list of references to the most important research literature
prior to 1998. As in many fields of acoustics,
Helmholtz [15.127]andRayleigh [15.3] laid the foundations
of our present-day understanding of the acoustics
of wind instruments. In the early part of the 20th century,
Musical Acoustics 15.3 Wind Instruments 601
member of the family is therefore designed to have
the frequencies of the main body and Helmholtz resonances
in the same relationship to the open strings as
that on the violin, where the Helmholtz air resonance
strongly supports the fundamental of notes around the
open D-string, while the main structural resonances support
notes around the open A-string and the second and
generally strongest partial of the lowest notes played on
the G-string. Several sets of such instruments have been
constructed and admired in performance, though not
all musicians would wish to sacrifice the diversity and
richness of sounds produced by the different traditional
violin, viola, cello and double bass in a string quartet
or orchestra. Nevertheless, the scaling methods have
led to rather successful intermediate and small-sized
instruments.
Bouasse [15.128] significantly advanced our understanding
of the generation of sound by the vibrating reed.
More recently, Campbell and Greated [15.129] have
written an authoritative textbook on musical acoustics
with a particular emphasis on musical aspects, including
extensive information on wind and brass instruments.
Recent reviews by Nederveen [15.130] andHirschberg
et al. [15.131] provide valuable introductions to recent
research on both wind and brass instruments. Earlier
texts by Backus [15.132] and Benade [15.133],
both leading pioneers in research on wind-instrument
acoustics, provide illuminating insights into the physics
involved and provide many practical details about the
instruments themselves. A recent issue of Acta Acustica
[15.134] includes a number of useful review articles,
especially on problems related to the generation of sound
by vibrating reeds and air jets and on modern methods
used to visualise the associated air motions. For a mathematical
treatment of the physics underlying the acoustics
of wind instruments, Morse and Ingard [15.135] remains
the authoritative modern text. Other important review
papers will be cited in the appropriate sections, and selected
publications will be used to illustrate the text,
without attempting to provide a comprehensive list of
references.
We first summarise the essential physics of sound
propagation in air and simple acoustic structures before
considering the more complicated column shapes used
for woodwind and brass instruments. An introduction
is then given to the excitation of sound by vibrating
lips and reeds, and by air jets blown over a sharp edge.
Part E 15.3