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Boomwhackers and End-Pipe Corrections
1.The Diatonic Set of 8 Boomwhackers by Whacky Music is vailable from vendors that you can easily find at www.amazon.com. Be sure to purchase the eight tubes for the major scale. Some pipe sets come with only five tubes. More expensive sets include a bag, stand, and a single end cap.
2.Maria Eva Amorim, Teresa Delmira Sousa, P. Simeão Carvalho, and Adriano Sampaio e Sousa, “A simple experiment to explore standing waves in a flexible corrugated sound tube,” Phys. Teach.49, 360–362 (Sept. 2011).
3.Stephen Luzader, “PC and PVC acoustics demonstrations,” Phys. Teach. 28, 469–463 (Oct. 1999).
6.M. E. Bacon and Steven Torok, “An experimental investigation of the end effects for Blue Man Group® pipes,” Phys. Teach. 49, 152–154 (March 2011).
7.Daniel R. Raichel, The Science and Applications of Acoustics, 2nded. (Springer, New York, 2006), p. 135.
8.N. H. Fletcher and T. D. Rossing, The Physics of Musical Instruments,2nd ed. (Springer, New York, 1999). Thomas D. Rossing, F. Richard Moore, and Paul A. Wheeler, The Science of Sound, 3rd ed. (Addison-Wesley, San Francisco, 2002), pp. 65–66.
10.Levine and Schwinger give 0.6133r as the correction for each open end when . From their nice plot of end correction versus kr, one finds that the end correction is a slowly decreasing function over the range of pipe lengths of interest.
11.Julian Schwinger shared the Nobel Prize in 1965 with Richard Feynman and Sin-Itiro Tomonaga for their independent work on quantum electrodynamics (QED).
12.Michael C. LoPresto, “Fourier analysis of musical intervals,”Phys. Teach. 46, 486–489 (Jan. 1994). See Table I for a complete set of whole-number ratios for the 12-tone scale (which includes the five black keys).
13.Mike Bowman from North Buncombe High School, Wayne Hamlin from T. C. Roberson High School, and Biff Spisak from A. C. Reynolds High School.
14.Judy Beck, James Perkins, Department of Physics, UNC Asheville, and the author.
15.Nicole Munger, a graduate with an associate's degree from Asheville Buncombe Technical Community College and a physics major at UNC Asheville, working in the comprehensive science teaching licensure program.
16.End caps, called “octavators” are nice to have and can be purchased separately. Then you don't have to hold your hand over one end to form a closed pipe. Also, the “octavator” sounds cool!
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End-pipe corrections seldom come to mind as a suitable topic for an introductory physics lab. Yet, the end-pipe correction formula can be verified in an engaging and inexpensive lab that requires only two supplies: plastic-tube toys called boomwhackers 1 and a meterstick. This article describes a lab activity in which students model data from plastic tubes to arrive at the end-correction formula for an open pipe. Students also learn the basic mathematics behind the musical scale, and come to appreciate the importance of end-pipe physics in the engineering design of toy musical tubes.
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