Building the WHAP!-a-phone:
If it weren’t for technology there would be very little music. If that seems to be too strong a statement, think about it for a minute. The definition of technology is not limited to computers and digital instruments--even though that’s how we usually interpret its meaning today. Rather it is simply “the application of science to a useful purpose.” To a musician a useful purpose is creating something that makes music. By applying principles of acoustics, sound perception, and scientific observation, people are able to craft all sorts of devices that allow musicians to communicate musical ideas. Every musical instrument relies these principles in its construction and use.
Recently I had an opportunity to work with two bright junior high school musicians in exactly this type of project: building a playable musical device and being able to explain how and why it worked. The project was for a science fair and a few of the parameters of the musical instrument were dictated by the fair organizers. Ideally the instrument was to be capable of playing a two octave chromatic scale surrounding middle C. It was to be tuned to equal temperament based on standard A 440 (440 cycles per second). It had to be totally acoustic-- that is, without electrohnic sound generation or amplification. Other than that, the design was open.
At the fair, the builders not only had to be able to play a recognizeable tune on the instrument (Aura Lee), they had to explain how they made it and how their design related to theoretical concepts of western music. Julie, Barbara, and I are presenting this article for other students who want to understand how musical instruments work or who may even want to use this example as a springboard for their own musical science project.
Early on, Julie and Barbara decided that they wanted to develop an instrument whose adherence to scientific principles and music theory concepts was obvious. This steered them away from small wind instruments and more toward a largr form in which each tone generating part would be separate and clearly visible. After some experimentation with wood and metal xylophone-llike concepts, they settled on the idea of tubes whose air columns would resonate at various pitches when struck. Thus was born the WHAP!-a-phone.
A few preliminary concepts of sound are called for here. First, any object that is struck tends to distort a little and then return to its resting shape. If the object has good elasticity-- and almost everything does-- it tends to overshoot its resting shape, create a slightly smaller mirror of the first distortion and return again toward its original shape. This overshooting actually happens many times after an object is struck although each distortion is smaller than the previous one and eventually the object returns to its rest state. Interestingly, the distortions always take an equal amount of time even though they get smaller and smaller. This even spacing of distortions is called periodic, and the many distortions together are called vibration. Air picks up these vibrations and transmits them as pressure changes to our ears. If periodic vibrations happen at a frequency of between 20 and 20,000 times per second, people perceive them as a musical tone.
Vibration is easy to see in a string because the distortion is perpendicular to the string’s length. This is called transverse vibration. But the vibration of an enclosed column of air, although invisible, is just as real. Think of this type of vibration as a shock wave that travels back and forth through the length of the air column at the speed of sound. This is called longitudinal vibration. Even when the column of air is struck only once, the shockwave will travel 50 or more times back and forth along its length before dying away completely. The shockwave’s travel from one end to the other and back again is called one cycle. It only takes 20 or so cycles for us to recognize the pitch of a vibration.
Julie and Barbara decided to use common PVC pipe to create the air columns. PVC is cheap and it’s easy to cut into any length tube. But they needed a lot of pipe! A chromatic scale in Western music has 12 notes in each octave and the science fair parameters called for at least 2 octaves around middle C. Finding the right lengths for all 24 tubes called for some math calculations.
Here are a few more sound concepts that made calculating the correct lengths of the tubes possible: The speed of sound in air is known to be about 1128 feet per second. This speed remains the same no matter how high or low the pitch of the sound is. Remember that a shockwave in a vibrating column of air travels back and forth at the speed of sound to make one complete cycle. Given just these two simple facts, it’s easy to calculate the length of a tube needed to create any pitch.
Length of Tube = (Speed of Sound / Frequency) / 2
Using the standard note A 440 as an example, divide 1128 by 440 (to get 2.56 feet) and then divide this result by 2 (1.28 feet). Since it will be easier to accurately measure tubing in inches than in feet, multiply this result by 12. The length of the A 440 tube should be 1.28 feet or about 15.4 inches.
Julie and Barbara cut a tube to this length and used a large paintbrush to strike (WHAP!) its end. The pitch of the sound was indeed A 440. Now they had to calculate all the other lengths of tubing they would need. This called for a few more sound and music principles.
An octave above or below any given note is very easy to calculate: it is always double or half of the given note’s frequency. For example, since A 440 is the A above middle C, the A below middle C will be A 220. Using the formula developed above, it’s possible to calculate the tube length of this note as 2.57 feet or about 30.8 inches
Calculating the other notes in the octave between A 220 and A 440 calls for another simple formula. For the past 200 years Western music has used a tuning system known as equal temperament to derive all the notes of the chromatic scale. In its simplest form it means that the frequency for any note can be calculated by multiplying the frequency of the note just below it by the 12th root of 2. The 12th root of 2 turns out to be 1. 059463094 or approximately 1.06.
Next Half Step Higher = Previous frequency x 1.059463094
Using this formula and the Length of Tube formula, Julie and Barbara calculated all the frequencies and tube lengths they needed plus a couple of extra notes on the high end:
Once all the tubes were created, it was time to make the frame to support them. This entailed a good bit of carpentry for Julie and Barbara with only occasional assistance from me. Here is photo of the completed instrument and frame made from 1x4 and 1x2 lumber:
Julie and Barbara took the project to the science fair in late Spring and placed in the top ten percent of their classification. But perhaps more important, they learned about the practical application of music technology and how science merges with art in music making.