TThe effects of the mouthpiece and bell on the frequencies of the vibrating air column in a trombone can be demonstrated quite readily by first calculating the expected resonant frequencies of a piece of PVC pipe that is the same length as a trombone, then replacing portions of the PVC pipe of the same length with first a cup-shaped mouthpiece and then a flaring-bell section of a trombone. The trombone components used were from a new pBone plastic trombone1 that is not only much less expensive than a regular instrument, which is made mostly of brass, but also features components that are much lighter than those of a conventional brass trombone and is therefore easier to work with.
REFERENCES
2.
J.
Backus
, The Acoustical Foundations of Music
, 2nd ed. (Norton
, New York
, 1977
), pp. 260
–268
.3.
R. W.
Pyle
, “Effective length of horns,”
J. Acoust. Soc. Am.
57
, 1313
–1314
(1975
).4.
5.
http://www.phys.unsw.edu.au/jw/brassacoustics. html#mouthpiece.
6.
See http://hyperphysics.phy-astr.gsu.edu/hbase/hframe.html, under Sound and Hearing; Musical Instruments; Brass Instruments; Brass Concepts; Mouthpiece Effect.
7.
Ref. 4, pp. 407–409.
8.
N. H.
Fletcher
and T. D.
Rossing
, The Physics of Musical Instruments
, 2nd ed. (Springer
, New York
, 1998
), pp. 431
–433
.10.
See http://hyperphysics.phy-astr.gsu.edu/hbase/hframe.html, under Sound and Hearing; Musical Instruments; Brass Instruments; Brass Concepts; Bell Effect.
11.
Figure from http://hyperphysics.phy-astr.gsu.edu/hbase/ hframe.html, under Sound and Hearing; Musical Instruments; Brass Instruments; Brass Concepts; Forced Harmonic. Sequence used with permission of webmaster RodNave@gsu.edu.
12.
http://flexpvc.com/PVCPipeSize.shtml.
13.
Data taken with Logger Pro, Vernier Software & Technologies, http://www.vernier.com/. Data could be taken with any data collection hardware and software able to capture sound waves, display their form, and calculate frequencies.
14.
T. D.
Rossing
, F. R.
Moore
, and P. A.
Wheeler
, The Science of Sound
, 3rd ed. (Addison-Wesley
, San Francisco
, 2002
), p. 232
.16.
See http://hyperphysics.phy-astr.gsu.edu/hbase/hframe.html, under Sound and Hearing; Musical Instruments; Brass Instruments; Brass Concepts; Pedal Tone.
17.
From Ref. 14. Used with permission.
18.
Ref. 14, p. 135.
19.
An online appendix is available at TPT Online, http://dx.doi. org/10.1119/1.4849149, for teachers interested in a more mathematically advanced calculation.
© 2013 American Association of Physics Teachers.
2013
American Association of Physics Teachers
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