Building and Analysis of a PVC Pipe Instrument Using Standing Waves

CASEY WILKINSON, JOHN BRINTON, AND MAX ZACHARKO

ABSTRACT

Four to six sentence, complete overview of project, noting investigation, methods used, and

results.

For this project we explored the relationship of standing waves in PVC pipes, specifically those that can be made into instruments. It is relevant to AET majors because we will come across a variety of percussive instruments, as well as other types of instruments that utilize standing waves in our work environments. By better understanding how the standing waves relate to the pitches heard, we can better understand other instruments and use that knowledge to our advantage in recording situations. To do this, we constructed a “Drumbone,” an instrument that is used by the Blue Man Group. It is constructed from PVC tubes (open on both ends) that are connected and able to slide in order to change the frequency of the instrument. By recording the instrument being hit and running a sine sweep through the Drumbone then analyzing our findings, we confirmed that our initial calculations corresponded to the actual found frequencies of the standing waves of the “Drumbone.”

0 INTRODUCTION

As audio engineering students who often come across percussion instruments as well as brass instruments such as the trombone that require standing waves in order to produce sound. Analyzing the relationship of standing waves in pipes was very beneficial to understanding these instruments and the physics behind why they work. We set out with the intention of researching, building, and experimenting with the “Drumbone,” a percussion instrument made from PVC piping that has the ability to change pitch by sliding like a trombone while being hit like a drum. The Drumbone was designed by the award-winning Blue Man Group, who use it in some of their onstage performances [1] along with many other pvc pipe instruments. The premise of the Drumbone is similar to that of a PVC xylophone of sorts. If there is a desired frequency range for the instrument, then one can calculate the lengths of pipe needed to meet those desired frequencies. This idea was investigated by Alex Mohr of Illinois University who made a scale based on the lengths of piping needed to reproduce frequencies in a certain frequency range, he included the diameters of the pipes in his calculations along with the speed of sound [2]. So, just like a trombone and its frequency variability, the drumbone’s frequency range could be calculated in a similar fashion, and then played percussively. By building this instrument, we wanted to be able to measure and analyze the frequencies that the instrument could produce and see if those measurements agreed with the calculated values that were found based on the formula for standing waves in an open tube, f=v/2(L+.8d). In this formula v equals the speed of sound in air, d equals the diameter of the pipe, and L equals the length of the pipe. Through our calculations and measurements, based upon what was learned in class and from outside resources to verify that the calculations used were correct [3], we wanted to see how one could, by using the resonant frequency calculation for standing waves in pipes, build an instrument tuned to a specific frequency or frequency range.

1 METHODOLOGY

The first piece of equipment required to complete this experiment was the Drumbone itself. This had to thus be constructed out of PVC pipes. The lengths of the pipes were 2.5’ with 3” and 4” diameter, and another 1’ section of 3” diameter pipe was cut into four 3” sections. The elbow sections of the pipe were constructed first and then the consecutive long pieces were cemented in place with the PVC cement. The biggest challenges in the construction process were mainly fitting the 4” pipe over the 3” with the couplings, since they had to be sanded down before greasing. The building instructions that were followed were found online [4] and can be found in the reference section of this paper. Also it should be noted that E-How’s instructions are similar in nature [5]. The only piece that is not mentioned in the construction is the short section of tubing that is actually hit, as seen in the video of the Blue Man Group playing the original Drumbone. It is recommended to use a thinner piece of 3” pipe for better resonance, though for our instrument, we used 1’ of the left-over thick 3” pipe. Once fully constructed, the next step was to take it into the studio in order to record the pipe’s response to being hit with a drumstick. The different sections along with the two sections combined were tested in their fully extended length and their constricted forms. We used four different microphones to record the instrument, and they were placed at the following distances: 1.9” into the pipe (the furthest we could insert the microphone without it coming into direct contact with the instrument), edge of the pipe, and 6” from the pipe’s edge. These distances were chosen to see if a difference in the measurements existed due to the interaction of the air as it enters and exits the instrument, creating nodes. The microphones used were a Neumann KM84, Schoeps SKM5, Sennheiser e604, and a Neumann U87. The KM84 and SKM5 had better frequency responses since they are small-diaphragm condenser microphones and they fit into the pipe better than the e604 and U87. Once the measures were taken, the pipe then was brought into the lab and driven with a Yamaha speaker. One end of the pipe was as close to the speaker as possible and the other end was miked with an Audix Earthworks microphone placed 1.9” into the end of the pipe. Then, using Room EQ Wizard and ProTools, a sine sweep was generated to excite the resonances of the pipe. Once all of the data was recorded, it was put into both ProTools and SHAART to be spectrally analyzed. The frequency response of the pipe was analyzed using a frequency analyzer plug-in, and SHAART was used to analyze the RT60 in order to calculate the Q factor and bandwidth for each pipe length.

2 RESULTS

Once we recorded the different sections of piping being hit with a drumstick and driven with a sine sweep, we analyzed our recordings. Our initial calculations were found by measuring each section of piping after the construction phase, and plugging the values into the equation: f=v/2(L+.8d). We accounted for the different diameters of the pipes only for the fully extended calculations since the coupling sealed off the 4” pipe from the 3” pipe when not in an extended position, meaning that the 4” pipe would not resonate since air would not move through it while the 3” pipe was inside. In order to account for the different diameters, we did separate calculations of L^1=L+.8d and added the values together, then plugged that value back into the resonant frequency calculation (f=v/2*L^1). To ensure that we did not have to do any additional calculations to compensate for the “bending” of the instrument due to the many PVC elbows we incorporated, we found that the same principle as is used with many brass instruments [6] is applicable. By pressing the buttons on a trumpet, additional length is added to the tubing of the instrument. This is how more frequencies can be created and therefore the only necessary adjustment to calculating the frequencies of our instrument was just to incorporate an estimate of the length of each elbow.

The calculated frequencies we found (see Figure 1(a) for specific measurements) were 144.8 Hz and 84.8 Hz for the short section, not extended and extended. For the long tube not extended and extended, the calculated frequencies were 90.7 Hz and 64.4 Hz. For the full combined tube not extended and extended, the frequencies we found were 55.8 Hz and 36.6 Hz.

The actual measured frequencies we found (see Figures 2(a-f)) were 149.02 Hz and 91.76 Hz for the short section, not extended and extended. For the long tube not extended and extended, the measured frequencies were 88.17 Hz and 63.04 Hz. For the full combined tube not extended and extended, the frequencies measured were approximately 52 Hz and 36 Hz respectively. Unfortunately for the lowest frequencies (the combined tube) the measurement microphone used did not respond very well at these frequencies. The resonant frequencies could be heard in the room, but they did not show up well on the graphs as seen in Figures 2 (e) and (f), so our measured frequencies for those lengths are approximate.

Utilizing the sine sweep recording for each section, the waveforms were loaded into SHAART and the RT60 was found. By doing this, the Q factor and ∆f were found (see Figure 1(b) for individual values) for each section of tubing. The average Q calculated from the measured sine sweep was 67.8 and the average ∆f was 1.21 Hz. These calculations show that the bandwidth for each section was quite small. The RT60 time varied from 1.1s for the shortest tube length to 4.84s for the longest tube length. As the length of the tube increased, generally the RT60 increased as well.

Some problems encountered during the experiment were applying the correct type of hit with enough pressure in order to make the instrument resonate and a few microphone issues. Since the PVC pipes were quite thick, they had to be hit rather hard for the tone to be heard. A rubber mallet or something similar would probably have had the best results. Thinner PVC pipes would have probably helped with this issue as well, since they wouldn’t have to be hit as hard and a regular drumstick could be used, unlike our mallet-like drumstick that was used. We utilized a few microphones when doing our initial recordings of hitting the Drumbone. We were unable to place a microphone farther into the pipe than the coupling on the end (1.9” inside the tube) so as to avoid the microphone stand or microphone itself coming into direct contact with the instrument while it was played, therefore distorting the recorded sound. The best response we gathered from our recordings were from the small condenser microphones, though we also tried an Audix e604 and Neumann U87. We selected a variety of microphones, but decided to continue to use the small condensers since the Blue Man Group’s engineer stated that’s what he uses for the instrument during live shows [7]. The Neumann U87 would not fit very well into the tube due to its size and the Audix e604 did not sound as clear as the small condensers and it seemed to not be able to pick up some of the low end that the other microphones recorded a little better.

Overall, our calculations matched up well with our measured frequencies, with an average standard deviation of only 2.3 Hz. Adjusting the .8 value to compensate for diameter of the tubes did not prove fruitful, since our values were quite close and unevenly varied in their degree of closeness to the calculated frequencies.

Figure 1(a): Resonant frequency calculations, measured frequencies, and standard deviations for all pipe lengths.

Figure 1(b): Q, RT60, and Bandwidth for all pipe lengths.

Figure 2(a-f): Graphical representation of sine sweep, showing frequency (Hz) vs. Amplitude (dB), with resonances marked.

Figure 2(a): Short Condensed:149.02 Hz

Figure 2(b): Short Extended: 91.76 Hz

Figure 2(c): Long Condensed: 88.15 Hz

Figure 2(d): Long Extended: 63.04 Hz

Figure 2(e): Combined Pipe Condensed:~52 Hz

Figure 2(f): Combined Pipe Extended: ~36 Hz

Figure 3(a-f): Graphs from SHAART showing RT60, Time (s) vs. Power (dB)

Figure 3(a): Combined pipe condensed.

Figure 3(b): Combined pipe extended.

Figure 3(c): Long pipe condensed.

Figure 3(d): Long pipe extended.

Figure 3(e): Short pipe condensed.

Figure 3(f): Short pipe extended.

3 CONCLUSION

Through this experiment of building a PVC instrument modeled after the Blue Man Group’s Drumbone, we found that it is entirely possible to select desired frequencies for an instrument and build it to spec. Utilizing the resonant frequency calculation for standing waves in open ended tubes, one could build a variety of instruments to cover a large range of resonant frequencies. The bending of the tubes did not affect our calculations except to add length and therefore decreasing the frequency of the instrument slightly, as can be found with brass instruments like trumpets. Including diameter in calculations also affected the frequency by lowering the calculated frequency, essentially doing the same thing as adding more length to the tube, though to a smaller degree. The calculated frequencies were very similar to our measured frequencies, with an average standard deviation of only 2.3 Hz.

Future experimentation could be done utilizing different thicknesses of tubes to see if some resonate better or easier than others. This turned out to be something that was not mentioned online, since there are different types of PVC piping, the thinner outdoor and thicker (and heavier) industrial PVC. By using the thinner PVC, it could yield clearer and more precise measurements, and possibly be more cost effective. Also trying different diameter pipes, perhaps by building a smaller scale drumbone, could be a potential experiment. Utilizing our calculations and instrument as a basis, further research could be done to find how much extension of the pipes needs to be made to resonate at certain frequencies between the maximum and minimum frequencies that we found in our experiment.

4 REFERENCES

[4] Building Instruction: http://willieblue.tripod.com/bluemangroup/id7.html

[6] Tube Length and Frequency http://hyperphysics.phy-astr.gsu.edu/hbase/music/trumpet.html

[1] https://www.youtube.com/watch?v=ltAk4ToydBg

[3] http://www.physicsclassroom.com/class/sound/Lesson-5/Open-End-Air-Columns

[2] Alex Mohr’s paper on Blue Man Group’s PVC instruments/ Science behind it (2004) https://courses.physics.illinois.edu/phys193/Student_Reports/Fall04/Alex_Mohr/Alex_Mohr_P199pom_Fall04_Final_Paper.pdf

[5] http://www.ehow.com/how_2238950_build-drumbone.html

[7] (http://www.audixusa.com/docs_12/sound_guys/EkkpuVlVuABIIobklZ.shtml)