Team Members (T3-1):Lazy Dog, Slack Dog,Slow Dog, Sloth Dog 9/24/2015

Transcription

1 UNIVERSITY OF TENNESSEE The Bucket Base EF 152 Rocky Top Project Team Members (T3-1):Lazy Dog, Slack Dog,Slow Dog, Sloth Dog 9/24/2015

2 Introduction For this project, our team was tasked with building a handmade instrument that could play the song Rocky Top. The instrument must be built using concepts from our EF 152 course. The instrument must be built using readily available materials. Our team decided to create an instrument similar to a washtub bass. A 5-gallon bucket was used along with a broomstick and a string. We named this instrument the bucket bass. Final Design: The Bucket Bass The team decided the instruments should be a stringed instrument. Original ideas included an instrument with multiple strings on a fret board, similar to a guitar or banjo, or free strings in tension like a harp. Some preliminary testing indicated significant difficulty in maintaining the correct tension in multiple strings thus leading the team to create an instrument with only one string. Changing pitch could be accomplished by altering the length of the string or by changing the tension in the string [2]. The team decided on the latter. The handle of a broomstick is placed on top of an upside down 5 gallon bucket. A string is attached to the top of the broomstick then anchored to the bucket. The tension in the string is changed due the angle of the broomstick. A suggested materials list was provided by Kuhfeld on her website on Simple Musical Instruments [1]. Materials: broomstick string 5-gallon bucket eyebolts

3 cardboard Design Details: The broomstick is 3.4ft long. A hole is drilled into the end of the stick and an eyebolt is inserted. Another hole is drilled and an eyebolt inserted into the bucket. A piece of string 4ft long is tied and connected to both eyebolts. A make-shift protractor fashioned out of cardboard is attached to the bucket to show the angle of the stick. Angles necessary for various frequencies are shown in Table 2. Analysis of the Bucket Bass The frequency of the string was obtained using the following equation: f 1 1 2L T where f 1 is the first natural frequency, L is the length of the string, T is the tension in the string, and µ is the mass per unit length. The tension in the string was determined based on the strain in the string. The strain was obtained using geometry, as shown in Figure 1.

4 Define L 0 as the initial length of the string and x a, y a as the coordinates of the anchor point of the string. The x and y coordinates of the end of the string are obtained as: x L s y L s cos sin The final length of the string, L, is obtained as: L x x y y 2 a 2 a The strain in the string is determined as: L L 0 The stress in the string would be obtained as Eε, where E is the modulus of elasticity. The tension in the string would be obtained as the cross-sectional area, A, multiplied by the stress, or: T EA To find (EA) of the string, the string was tied to the ceiling and the 5-gallon bucket was hung from the string. Increasing amounts of water was added to the bucket, and the increase in length of string was measured. The stretch in the string was measured. For a 4 ft initial length of string, the following data was obtained.

5 Table 1. Stretch of String vs. Weight Force (lb) Stretch (in) Strain AE (lb) From this data, and average value of AE was obtained as 4730 lb. The mass per unit length of the string, µ, is determined as the mass of the unstretched length of the string divided by the final length of the string. All of these calculations were put into an Excel spreadsheet, which is submitted with the report. The solver routine was used to determine the required angle θ for different frequencies. This is summarized in the following table. The second octave was used to match the capabilities of this instrument. Table 2. Angles for Frequencies Note Frequency (Hz) Angle (θ) D E F A B C # Results The Bucket Bass was easy to build and consistent in pitch. The calculated values for the angles were slightly off which can be attributed to the rough calculation of the strain, thus affecting the

6 tension calculations. The accuracy of the notes relied heavily on the athleticism of the stickmover, as faster notes made precision more difficult. Also synchronizing the pluck of the string precisely with the movement of the stick proved to be challenging at first, but practice and repetition improved performance. The actual frequencies of the notes played were measured using a tuner app on the iphone. Each note was measured and the measured values related to the theoretical calculations are found in Table 3. Table 3. Measured vs. Theoretical Frequencies Theoretical Frequency (Hz) Measured Frequency (Hz) Percent Error (%) Based on the measured and theoretical calculations, our least accurate frequencies were the 86 Hz and 90 Hz frequency. We believe that two improvements could be made to ensure a more accurate note in the future. First, we would add a protractor reading dial to our bucket base to ensure that the player could more accurately hit the correct angle needed for the note that needed to be played. Second, we would require a longer period of practice for our player to ensure that the player could have a high repeatability for playing accurate notes.

7 Conclusion A simple design and minimal construction requirements allowed more time for minor adjustments and practice. Calculating the theoretical values prior to construction improved the efficiency of the overall process instead of relying solely on trial-and-error. References 1. Kuhfeld, Ellen. (2015) Simple Musical Instruments Wikipedia: The free encyclopedia. (2015) Washtub bass.