# Engineering Project: Band in a Box

Hello!  Today, I’d like to tell you a bit about my final team project in Intro. to Engineering at Arizona State University, completed with teammates John Turner and Andy Mussett.  For this project, we were asked to design and build a “Band in a Box,” to include four instruments capable of playing a four-part harmony song.  We would need to create at least one percussion, one string, and one wind instrument, and all four instruments would have to fit into a 2x2x2-ft. stage box. No more than 10 feet of pipe and 6 feet of string would be allowed to build all of the instruments, and we were limited to a \$15.00 construction budget per team member, per instrument. We chose “Ode to Joy” as our performance piece, which would have to be mixed and mastered on Audacity recording software.  Add to all of this that we were taking the course online and had to do everything remotely: no easy task!

I chose to design and build a xylophone, which is a percussion instrument. Specifications for the instrument are as follows:

Description, Underlying Physics, and Design Inspirations: The instrument is a 12-note, diatonic, wooden-barred xylophone capable of playing notes spanning over an octave from A3 to E5 (soprano-alto range). The following formula was used to determine appropriate bar lengths for the xylophone:

L = sqrt((pi*v*K*m2)/(8*fn))

where v = the speed of sound through hardwood or 3962 m/s, K = bar thickness/3.46 for flat bars = .0037 m, vM = 3.0112, and Fn = the desired frequency. This instrument closely resembles a classic, diatonic xylophone or glockenspiel with typical wooden A-frame design.  Given stringent space and size limitations, however, it was decided that only those notes needed for the performance piece would be included (i.e., the instrument would lack larger, chromatic capabilities).  Also, the instrument would not be able to have a traditional resonator box.  Instead, reverberation would be simulated by boring holes beneath the keys rather than mounting the keys atop a resonator box.

DETAILED DESIGN DESCRIPTION

Design Aspects: The bars are made of hardwood (pine) and mounted to a simple wooden A-frame with screws. The dimensions are 10.0” wide x 14.5” long x 1.5” high, making it portable enough to fit into the stage box.  One can play the instrument in the traditional manner by striking the appropriate bars with wooden, plastic, or metal mallets. It is inexpensive, easy to manufacture, and was tuned appropriately to a standard 440 Hz piano tone for uniform quality, using equal tempering. Pine was selected as the hardwood of choice (oak being the other option) for construction of the instrument since it is less expensive, cuts easier, and yet provides very similar sound quality.

Requirements and Constraints Satisfied: The xylophone features a simple design that is easy to manufacture by simply mounting the wooden bars to a wooden A-frame with screws.  It costs under \$15.00 to build, and the construction materials (pine wood and screws) are readily available.  The instrument features 12 notes, spanning over an octave from A3 to E5: fully capable of playing the high-range (soprano) part in “Ode to Joy.”  It is compact and portable, with dimensions of 10.0” wide x 14.5” long x 1.5” high, making it small enough to easily fit into the 2x2x2 stage box.  It plays like a standard xylophone or glockenspiel with traditional wooden or plastic mallets and evenly spaced keys; thus, there is no learning curve for the musician.

Design Decisions and Trade Offs: One major design addition was to provide a solution for tuning the instrument and generating a pleasing tone.  Typical xylophones feature a large resonator box, fixed beneath the bars, which captures and reflects/echoes the vibrating wooden bars.  This generates a more pleasing, fuller tone.  Without the resonator box, the xylophone would have a flat, clipped tone.  However, given the spatial constraints, it was impossible to build a full resonator box.  Thus, the solution to this problem involved boring a circular hole into the underside of each wooden bar.  This allows the bar to resonate within a small space, simulating the box.  The underside and tips of the bars were also hollowed and carved out to tune the pitches more precisely.

Note Frequencies and Appropriate Lengths

“Ode to Joy”: High (Soprano) Voice

Note                Frequency (Hz)            Bar Length  (1/2” thick x 1” wide)

D4                   293.66                                    0.42160 m.                1.3832’

G4                   392.00                                    0.36491                      1.1972’

A4                   440.00                                    0.34443                      1.1300’

B4                   493.88                                    0.32510                      1.0666’

C5                    523.25                                    0.31584                     1.0362’

D5                   587.33                                    0.29812

Theoretical Minimum and Maximum Frequencies Compared to Actual Frequencies (Lowest and Highest Note)

Note               Theoretical Min. and Max                             Actual

A4 440 Hz                  433-447 Hz                                                  442 Hz

D5 587.33 Hz            573-598 Hz                                                589 Hz

Testing and Performance: Overall, the instrument performed quite well.  Initially, the B3 key was slightly high in pitch.  Although all bars were tuned in accordance with standard equal tempering and tested against equivalent electronic piano tones for accuracy, wood glue was applied to the hollowed underside of the bar to deepen it slightly, but approximately 3 Hz, in accord with just tempering.  This solved the problem, making the tone more pleasing to the ear.  During the post-production phase, a reverberation effect was added to the xylophone part to make it sound more pleasing and not quite so clipped; i.e., helping it to sound like a larger and more expensive instrument with a genuine resonator box.

CONCLUSION

In general, the instrument was simple to design and make, and inexpensive.  It also performed well, providing a pleasing and accurate tone for its size and limitations.  Tuning posed the greatest challenge: each bar had to be carefully measured for length, hollowed out, and then bored out in the center.  This required systematic and continuous modifications until the correct pitch was finally achieved.  Mass-production would be simple regarding construction of the frame and keys; however, tuning, including required carving and boring, would require careful calibration for machine parts, and might ultimately have to be performed and tested manually.

For this particular instrument, the amount of time provided to design, construct, and test it was sufficient.  For its limitations, its tone quality was actually quite good. However, to make a better instrument, a bigger budget would be called for so that oak wood could be used in construction for better sound.  Also, greater space allowances would permit the addition of a full resonator box and additional bars for a higher-quality sound and greater performance range.

This project demonstrated the importance of careful, mathematical precision and provided an exercise in time management, teamwork and coordination, creativity, and even ingenuity.  It was a very satisfying and successful endeavor.  I’m happy to say that my team (Team 13) received a Design Award for Creativity/Innovation for our work on this project.

A link to our final presentation, as well as the mixed and mastered version of “Ode to Joy” can be found here:

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