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How long should I cut my pipes?

PASINIK KRUG JOSE MIGUEL jpasinik at cec.uchile.cl
Thu Aug 28 11:21:17 EST 1997

In article <33FBA2A8.79D at sirius.com>,
Cathy Highet and Erick Gallun  <erick at sirius.com> wrote:
>thomasr wrote:
>> Could someone tell me how long to cut a one-inch pipe to get middle C?
>I will assume that this pipe is open at the end as you referred to
>primitive brass instruments.
>The frequency of middle C is about 262 cycles/sec.
>The speed of sound (at 68 degrees F) is about 344 meters/sec.

Your considerations are correct, but it must be borne in mind that
we should know the boundary conditions at both ends of the pipe.
One side is open (the "bell" side) and the condition at the
other end will depend on how thomasr intends to excite the pipe.
I see you assumed that the mouthpiece end would be closed, which 
coincides with a "brass mouthpiece" and "clarinet mouthpiece" boundary
condition. But if our friend wishes to blow into the pipe (as in a
flute, or a zampoña--this is an instrument played in the altiplano),
this way of exciting the pipe will result in an open end
boundary condition.

So, the length of the pipe will be 1/4 of the wavelength if one end
is closed and the other is open (as in a clarinet, or a trumpet).
But if it is open at both ends, the pipe length is only 1/2 of the
wavelength. So, if you want to blow into the pipe, but you want to
use short pipes, you might as well close the other end, so that the
same pipe length corresponds to double the wavelength (or half the
frequency--that is, a note an octave lower). Remember also that in
this case the sound is generated by vortices at a wedge (in this
sense a flute and a recorder are the same, but in the recorder
making it sound is easier because the air flow is directed by the
mouthpiece toward the wedge--of course this results in less freedom
and versatility of the instrument), so it would probably make
sound generation easier if you sharpen a bit a section of the end
you blow into.

This is a  _very_ interesting topic, so for those with an interest
in this theme, I reproduce now the bibliography of the book
"Instrumentos Musicales: astesania y ciencia" (Musical Instruments:
craft & science) by H. Massmann and R. Ferrer:

Articles in general interest scientific magazines:

1. The Vibrating String of the Pythagoreans, E.E. Helm; Scientific
   American, December 1967.
2. L'acoustique des salles de concert, F. Santon; La Recherche #211,
   June 1989.
3. Musical Dynamics, B. Patterson; Scientific American, Nov. 1974.
4. The Physics of the Piano, E.D. Blackham; Scientific American, Dec 1965.
5. The Coupled Motion of Piano Strings, G. Weinreich; Sci. Amer., Jan 1979.
6. The Acoustics of the Harpsichord, E.L. Kottick, K.D. Marshall, & 
   T.J. Hendrickson; Sci. Amer., Feb 1991.
7. The Physics of Woodwinds, A.H. Benade; Sci Amer, Oct 1960
8. Physics of the Flute, J. Coltman, Physics Today, vol. 21, 25 (1968).
9. The Physics of Brasses, A.H. Benade; Sci Amer, July 1973
10. Playing the Baroque Trumpet, D. Smithers, K. Wogram, & J. Bowsher;
	Sci Amer, Apr 1986
11. The Physics of Organ Pipes, N.H. Fletcher & S. Thwaites; Sci Amer,
	Jan 1983
12. The Physics of Kettledrums, T.D. Rossing; Sci Amer, Nov 1982
13. L'acoustique du gong, T. Rossing; La Recherche #230, March 1991
14. Acoustics of Drums, T.D. Rossing; Physics Today, vol. 45(3), 40, 1992
15. The Physics of Violins, C.M. Hutchins; Sci Amer, Nov 1962
16. Founding a Family of Fiddles, C.M. Hutchins; Physics Today vol. 20,
	23, 1967
17. The Acoustics of Violin Plates, C.M. Hutchins; Sci Amer, Oct 1981
18. The Physics of the Bowed String, J.C. Schelleng; Sci Amer, Jan 1974
19. Micromechanical Models of the Cochlea, J. Allen & S. Neely; Physics
	Today vol. 45, 40, 1992.

Elementary and general interest books:

1. La Musica, N. Ardley; Biblioteca Visual Altea, Altea, Taurus,
   Alfaguara S.A, Madrid, España, 1989
2. El mundo del sonido, A. Efron; Editorial Bell, Washington, Estados
   Unidos, 1971.
3. Musical Acoustics, D.E. Hall, Brooks/Cole Publ. Co., 2nd ed., Pacific
   Grove, California, 1991.
4. Science and Music, Sir J. Jeans; Cambridge University Press, London,
   England, 1953.
5. Measured Tones, I. Johnston; Adam Hilger, New York, 1989.
6. El mundo de las vibraciones y de los sonidos, C. Prelat; Editorial
   Espasa-Calpe, 1951.
7. The Physics of Music, A. Wood; University paperbacks, Methuen & Co.,
   6th ed., London, England, 1964.

I would add "Horns, Strings, and Harmony" by Arthur Benade to this
category. And of course I recommend reading the book by Massmann &
Ferrer from where I got this bibliography.

More specialized books:

1. La tecnica de la orquesta contemporanea, A. Casella y V. Mortari;
   Editorial Ricordi Americana, Roma, Italia.
2. The Physics of Musical Instruments, N. Fletcher & T. Rossing;
   Springer-Verlag, New York, 1991.
3. Instrumentation in der Musik des 20 Jahrhunderts, W. Gieseler, L.
   Lombardi, & R. Weyer, Moeck Verlag, Celle, Germany.
4. Physik für Ingenieure, E. Hering, R. Martin, & M. Stohrer;
   VDI-Verlag, Düsseldorf, Germany, 1989.
5. The Dynamical Theory of Sound, H. Lamb; Cambridge University Press,
   London, 1925.
6. Akustik und musikalische Aufführungspraxis, J. Meyer; Verlag Das
   Musikinstrument, Frankfurt am Main, Germany.

I apologize for the lengthy post.

Jose Miguel Pasini                                                   Z" ?
jpasinik at cec.uchile.cl                                  O__o_o_o%o\o-{_/!
PGP key at http://tamarugo.cec.uchile.cl/~jpasinik               \`\___  )
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