by Paul Doherty

An invited presentation at the annual AAAS meeting, San Francisco, 2001

The Presentation I began by twirling the three foot long children's toy whirly over my head playing a series of notes up and down the scale. "I fell in love with the sounds of the whirly the first time I heard children playing them in the Exploratorium store. Whirlies only play notes which sound good together. No matter how I swing it around, it only plays certain notes. It does not slide from note to note it jumps. It thus behaves like the electron in an atom which jumps between energy levels. The whirly plays quantum music." After I had played the toy whirly for a while I got tired of the same five notes and began looking for other corrugated singing tubes. I conceived of a plan to incorporate the whirly into symphony orchestras. I envisioned a whole new orchestral section based on corrugated plastic tubes: the corrugahorn section. That set me on a search for the full range of instruments from alto to bass. My first experiments were geared toward finding bass instruments. One day, my wife Ellen and I were at a friend's swimming pool. In the pool I spotted a surface vacuum cleaner trailing a long flexible corrugated hose. Ellen impressed me with her speed as she stopped me from unfolding the blade of my knife. She talked me into waiting a day and buying my own hose from a swimming pool supply store. At the store I purchased my first swimming pool vacuum hose whirly. I played a few notes and they rang out loud and clear in the room.   One day a professional whirly player came to the Exploratorium, Sarah Hopkins. She had a question for me, how do whirlies sing their songs. I was pleased to be able to give her a short complete answer,"I don't know." She laughed and said that she had already asked two physicists and received two different answers. I suggested we do some experiments. While we worked together Sarah tuned a whirly for me and taught me to play a piece of music she composed for it, "Deep Whirly Heartsong." Let me play it for you. The performance whirly filled the hall with sound. As the last note faded away the audience applauded and cheered. We began to discover how whirlies work. Sarah pointed out that whirlies didn't play their fundamental note. We then went for a ride in a car and stuck the whirly out the window we found that the frequency of the notes went up proportional to the speed of the car. We held the whirly perpendicular to the airflow out the window of the car, it did not sing, yet held pointing into the airflow it sang loudly. On stage, I blew across the end of the whirly to show it would not sing, then blew into it to make it sing. We were doing experiments and making progress. More tests were needed. We reasoned that longer whirlies would play lower frequencies. I played a whirly twice as long as the last one. "Note the lower pitch of the lowest note of the longer whirly." The whirlies only sing sound waves which fit in them exactly, longer tubes mean longer soundwaves which have lower pitch. It got to the point where my wife hated to go into hardware stores with me. I kept blowing into and whirling every piece of corrugated hose I could find; gas pipes, electrical conduit and electrical wire guides... like these." I picked up the two "Fly" whirlies. I reasoned I could play them by pushing their ends through the air. and, "I was thrilled to find something to do with my left hand." I began to play 'Fly' (another Sarah Hopkins composition.) by arcing the two whirlies from above my shoulders down across the front of my body. "When I play this I find that I can walk through all neighborhoods of San Francisco and no one will ask me for change! This motion allowed me to combine music, physics and self-defense!" I segued into the second part of 'Fly' which involves swinging the two whirlies alternately, then into the finish with arcing moves again. The audience applauded.   Just like the Mr. Toad who was stricken with automobile fever, I was smitten with whirlies. When I went to visit friends they hid their china and lamps. The children loved me though. " One day a friend made the comment that my music was not very multicultural. I took his words to heart." I picked up a toy whirly attached to a 5 gallon plastic bag. I filled the bag with air from a battery operated leaf blower. The audience giggled at the sight of a turgid bag attached to a whirly, then laughed aloud as I tucked the whirly under my arm and they figured out what I was going to do. I played the bag whirly by squeezing the bag under my arm. I was pleased to find the answer to my search for multicultural whirlies among my own Celtic roots... The bag whirly! After I played half a bagful of notes, I removed the bag from my underarm and played the whirly in my usual swinging way. The whirly sang and sucked the remaining air from the bag. The singing stopped when the bag was empty. I looked quizzically at the quiet whirly and its deflated bag and said, of course, "pardon me but my instrument seems to be a little flat tonight." (This time the audience groaned.) Whirly discoveries came fast and furious. I found my highest pitched instrument in a 7-11." I pick up a large plastic cup pull out the corrugated straw and blow a few notes making high pitched sounds. "Have you ever been thrown out of a 7-11?" "I have." I still longed for deeper notes. Then one day at a winery my attention was riveted by a piece of hosing. My wife shouted "NO!" But she was too late I had found the Mount Everest of whirlies &emdash; agricultural drain hose. It was three inches in diameter and twelve feet long." I picked up my giant whirly and held it, coiled around me on the stage looking at it in a perplexed way. The only problem was how could I play it? Normally, I would start to spin A loud low tone would grow to fill the room. However at the AAAS I didn't have enough room to play the bass whirly by spinning it. I looked at the tables filled with Bassam Shakashiri's chemical glassware, took the whirly in both hands and with a fiendish gleam in my eye said, "be afraid Bassam, be vary afraid!" Then I laughed and got out my blower and used it to play the deep notes from the bass whirly. Holding the blower close made the whirly sing high pitches, further away deep low notes. I ended with a deep low note, then said, "at last I had found all of the instruments needed to fill the corrugahorn section of the orchestra." The room erupted with cheers and applause. WOW. I sure had fun at this lecture.

The Science A corrugated plastic tube will sing notes when swung overhead. A corrugated plastic tube open at both ends Hold one end in your hand. Twirl the other end in a circle. Listen to the sound made by the tube. Vary the speed of the tube. Notice that the pitch of the whirly jumps from one note to another and increases as the speed of the twirling is increased. That is, high speed twirling creates high pitch notes. What notes does the whirly play? If you are musically trained or have a person who is musically trained in a class ask them to identify the interval between the lowest note played by the whirly and the next highest note. They will tell you it is a musical 5'th. What that translates to is that the notes have a frequency ratio of 3/2. If these two notes were the fundamental and the next harmonic they would be in the ratio of 2/1 a musical octave apart, yet they are not. Most meter long whirlies do not play the fundamental note. The reason why will not appear until later. If you have a frequency meter you can measure the frequencies directly, my tube sang at 220 Hz and 330 Hz. The interval between the second and third notes is a musical third a ratio of 4/3. Why are the musical notes of the whirly quantized? A tube open at both ends has only certain harmonic frequencies at which it will resonate. These are the frequencies at which an integer number of half-wavelengths of sound fit inside the length of the tube. At the fundamental frequency one-half wavelength fits in the tube. A physics image of the sound in a whirly, click to enlarge. A movie of air motion in a whirly, click on the image to enlarge. A 1.5 meter long tube would have a 3 meter wavelength, L, sound wave at resonance. The frequency, f, would be f = c/L where c is the speed of sound in the tube. The speed of sound in air depends on temperature but is near 340 m/s. However measurements on the whirly show that the speed of sound in the whirly is near 330 m/s. So the fundamental resonant frequency of a tube would be 110 Hz. The tube resonates to integer multiples of this fundamental frequency. Longer whirlies have a lower frequency fundamental, the harmonic frequencies are closer together, spaced apart by the lower frequency of the fundamental. Resonances of the tube Hold one end of the whirly near your ear and the other end near your mouth. Hum into the whirly. Vary the pitch of your humming while you try to keep the loudness of the humming (heard by the ear not next to the whirly) the same. Notice that at some frequencies the tone heard in the whirly is louder. When you hum at a resonant frequency of the tube your humming is amplified and sounds louder. (You can also drive the whirly with a frequency generator and a speaker.) Notice that the resonances occur at the same frequencies the whirly sings. Except for the fundamental. There is a resonant amplification of your humming at the fundamental frequency yet the whirly will not play the fundamental. What makes the whirly sing part 1 One often heard yet incorrect hypothesis for what makes the whirly sing is that air rushes past the rotating open end at a high speed creating a low pressure area due to the Bernoulli effect and that the difference in pressure between the stationary end at atmospheric pressure and the moving end pushes the air through the tube. To show that this is incorrect blow across the end of the tube with your mouth or any other blower. (Footnote: Why it is not the Bernoulli effect.) The whirly cannot be made to sing by air flowing across the end! Next blow through the tube. Hold your mouth a few inches from the end and blow, it will sing pure notes. Blow faster and the notes increase in pitch. While playing the whirly: 1. Cover the stationary end with your hand. Notice that the sound stops immediately. 2. Hold the stationary end near the burning candle, notice that the flame bends into the whirly. 3. Hold the stationary end of the whirly near a pile of confetti, or other small paper pieces. Notice that when the whirly is signing a note the paper pieces flow into the whirly and are sprayed around. Taking whirlies for a car ride. Take the whirly along with you in a car. Stick one end out the window slowly increase your speed note the speeds at which it sings each note the loudest. For my whirly I found that it sang notes at speeds near 20 mph, 30, mph, 40, mph and 50, mph. The frequencies of these notes were 220,330,440 and 550 Hz. A plot of frequency versus speed shows that the frequency of the whirly is proportional to the speed of the car. Measuring the speed of the tip of the whirly You can also play a note and find the speed of the tip of the whirly, as you spin it, estimate the circumference of the circle scribed by the end of the whirly then time how long it takes to complete the circle (I usually time 10 rotations to improve the accuracy of my measurement.) Once again a graph of frequency versus speed will show that he frequency of the whirly is proportional to the speed of the rotating end. Why spinning the tube makes air flow through it Picture the whirly full of marbles, if you swing the whirly the marbles will be launched out the moving end at high speed. The same happens to the air. Twirl the whirly and you launch the air out of it. Twirl it faster and the air moves through it faster. Longer whirlies sing two notes at once Make a longer whirly, perhaps 3 meters long. Play it. Notice that it sometimes sings two adjacent notes at once. The Bag whirly Tape a plastic garbage bag to one end of the whirly. Use a blower to inflate the bag. (You can also inflate the bag by blowing into the bag with your mouth. If you blow into the bag do not press your mouth against the whirly, hold your mouth a few inches from the end of the whirly to promote entrainment of surrounding air, this will increase the flow of air into the bag and decrease the time it takes to fill the bag.) Squeeze the bag and you can play the whirly. Squeeze hard to get high pitch notes, squeeze softly to get lower pitches. You can measure the speed of airflow through the whirly, s, in m/s by measuring the volume of the bag, V, in m3 the cross sectional area of the whirly, a, in m2 and the time it takes to empty the bag, t, in seconds while playing one note. The speed will be s = V/at. Check the units, they are meters per second. What makes the whirly sing part 2. To sing, the tube must be corrugated on the inside. Aerodynamics researchers in Japan put a whirly in a wind tunnel and used very tiny hot wire anemometers to measure the airflow near the corrugations. They discovered that air flowing over two successive corrugations in the wall of the whirly experienced "impinging shear flow instability." This is the same effect that makes a tea kettle sing. If you look at the spout of a teakettle you will see that it has two disks separated by a short gap, each with a hole in its center. When the air, or steam, flows through the first hole and then flows through the second hole it exits in vortices which cause oscillating pressure in the air, heard by the human ear as a whistle. The ridges in the whirly tube play the same role. As the air flows first over one ridge then over a second it tumbles into a vortex. The faster the air flows through the tube the higher the frequency of the sound produced by the vortex. When the frequency of the vortex matches one of the natural resonant frequencies of the tube it is amplified. But why doesn't the whirly play the fundamental note? To drive the resonant frequencies of the tube, air must flow in an eddying instability over each ridge in the whirly. This means that there must be turbulent flow of air in the tube. At low speeds the air can flow through the whirly tube smoothly, this is called laminar flow, such a smooth and quiet laminar flow will produce no turbulent eddies to create sound frequency oscillations which drive the resonant frequencies of the tube. The spiral myth There is a persistent myth that whirlies with ridges that spiral around them will not sing. However I posses several spiral ridged whirlies that sing loud clear tones. Why it is not the Bernoulli Effect Many people first guess that the air blowing across the end of the whirly reduces the pressure at the end of the whirly due to the Bernoulli effect and sucks air through the whirly. The simple experiment of blowing across the end of the whirly shows that this guess is incorrect. While the air does speed up as it flows over the end of the whirly, and while this speeding up is accompanied by a drop in pressure according to the Bernoulli effect, simple experiments given above show that this drop in pressure plays a minor role in making the air flow through the tube.

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21 Feb 2001