Sound Generation by Vortices and Turbulence
Supplement for chapter 14
Links
Schleiren simulations of turbulence, emanating from fast jet of air. *** Looks like a "strange" link target ***
A well written, informative and illustrated article by Roberto Velaquez Cabrera on various homespun noise and resonant sound generators played by mouth (including some inside the mouth). Many good projects here!
Sound files
loud_f_sound - a turbulent consonant recorded "live and then slowed down by factors of 8, 128, and 256. The resemblance to some rocket sounds at the bigger slowdowns is not accidental.
Jet cabin noise at seat 12a was recorded at 30,000 feet on a Boeing 757. In addition, Rhapsody in Blue is played overlaying the noise and also the noise reduced by 18 dB, typical of the reductions in noise canceling headsets.
[Above] Von Kármán vortex street animation, courtesy of Cesareo de La Rosa Siqueira. (Source Wikipedia)
See other interesting vortex street images at Two Views of Von Kármán Vortices (nasa.gov)
Below video is especially easy to follow. By studying this video, you can develop an intuition for the mechanics of vortex shedding.
Lip Whistle
The documentary movie Pucker Up (2005) is surprisingly entertaining; the range of whistling methods and performance is impressive.
It is also surprising how little factually correct literature there seems to be on human whistling; we discuss some of the aspects in Why You Hear What You Hear, but more research could be done. Much more is published in the engineering and fluid dynamics literature, about the analogous processes of jets emerging from pipes. Even that, however, seems mostly concerned with supersonic flows. Furthermore, the nature of the resonant cavity (if any) may be very different in engineering contexts.
We link to a mall portion of an NPR interview, with the winner of the national competition, and a sample, here.
Tacoma Narrows Bridge
The collapse of the Tacoma Narrows Bridge in Washington state, nicknamed "Galloping Gerdi" shortly after it was constructed, was a disaster of major proportions. Luckily there was no loss of human life when it finally collapsed four months after opening, although a small dog died. It was abandoned on the lurching bridge by its owner, who was bitten by the terrified animal.
The bridge roadbed, suspended across a long span, had a torsion motion with a high Q, of a frequency of about 0.33 Hz in resonance with vortex shedding from the roadbed with the wind at about 40 mph. The effect is similar to driving an aeolian harp string resonantly with wind induced vortex shedding from the string. The vortex shedding put a resonant, periodic, driving force on the roadbed, that responded by gathering more energy in the torsion mode and reinforcing the vortex shedding in sync with the torsion. High Q modes of any sort are a bad idea for bridges, but this one was particularly pernicious since it could be excited by wind alone. Scroll to near the video's end to view the bridge collapse.
Sensitive Flames
A sensitive flame comes from a smooth-walled tube containing flammable gas under pressure. If the orifice shape, diameter and the gas pressure are right, the jet of escaping gas becomes unstable (even without the flame) and turbulent rather than laminar. If such an instability is reached by turning up the gas pressure, backing off just a bit on the pressure can make the flame laminar again but exquisitely sensitive to sound, especially of high frequencies. On the threshold of turbulence, tiny disturbances can force it over the edge into turbulence, yet it returns to quiescence once the disturbance is gone.
Sensitive flames can roar, flair, become shortened, or be extinguished by even very modest sound levels of the right frequency. Some sounds may excite a sensitive flame to the extreme, but not others. Tearing a piece of paper or rattling a set of keys might excite a sensitive flame across a room. The role of the flame itself is secondary, it mainly serves to illuminate what the gas jet is doing. Sound-sensitive smoke jets have been made, for example.
Propagating sound waves involve both pressure changes and back and forth oscillation of the air. Lord Rayleigh separated the two effects and made a key observation by placing a sensitive flame near a rigid wall, with high frequency periodic sound impinging on it. The sound bounced off the wall and interfered with the incoming wave, setting up a standing wave. At the nodes of the standing wave, pressure does not fluctuate, but the motion of the air toward and away from the wall is maximal there. At an antinode in a standing wave, the air is not moving but the pressure fluctuation is maximal. Rayleigh discovered that sensitive flames are sensitive to the pressure fluctuations, not air movement. His flame flared up at the pressure nodes and settled down at the anti-nodes as he drew it through the standing wave.
Rudolph Koenig (1832-1901) was a remarkable instrument builder and scientist devoted almost exclusively to sound and its phenomena. One of his interests was presenting acoustic and perception phenomena to relatively large gatherings. Koenig became a key player in the scientific controversies of his day concerning acoustics and perception.
In 1862 Koenig developed the manometric flame, a clever combination of 19th-century technologies. This device could make every undulation of pressure in a sound wave visible. The main idea is to feed a gas flame from a chamber exposed to sound, causing pressure fluctuations in the chamber to be almost instantly transcribed into fluctuations of the flame.
The drawing show a manometric capsule transferring pressure fluctuations in a chamber (C) fed by a gas line (A) to a flame (B). If the capsule is made into a Helmholtz resonator as seen here with the chamber (D) added, it becomes a Fourier filter very sensitive to a narrow range of frequencies near the resonance. The audio frequency fluctuations of the flame can be seen in the rotating mirror as the reflection of the flame streaks across the eye.
This image shows manometric flame patterns detected in a rotating mirror Koenig apparatus (see previous image, right) for various vowels sung at different pitches. In this case the region D above was connected to a tube leading to a cone into which the singer projected his voice; it was not acting as a Helmholtz resonator but instead recorded the pressure fluctuations in a 19th century version of a modern microphone connected to an oscilloscope. The flame becomes an instant display of the wave form, with which one can immediately see the differences in two vowels at the same pitch.
Senistive Flame(?) in My Fair Lady
Although definitely misrepresented, this attempt in the Warner Bros. movie My Fair Lady to get Eliza Doolittle to pronouce her vowels correctly using a flame as feedback is charming and at least displays some of the apparatus of the late 1800's, including a sensitive flame and a rotating mirror used (but not effectively here) to make the fast oscillations of the flame individually visible.
*** Looks like an image is missing here on the live-site ***
Noise *** This repeats the top section "Sound files" *** ?
Here is a recording of the sound of "f", first played at original speed, then slower by a factor of 8, then 128, then 256. GOOD SPEAKERS/EARBUDS SHOULD BE USED TO HEAR THIS PROPERLY. At 128 and 256, the similarity with a distant large rocket launch, such as Apollo, is remarkable. Sound generation by chaotic turbulence is very similar no matter on what scale it is produced, provided that time is stretched appropriately to make the time between major fluctuations similar.
The sound file "Jet cabin noise seat 12A" demonstrates cabin noise in a Boeing 757 at 30,000 feet, and the same noise 18 dB reduced in volume, for comparison. Then, the same two files are overlaid with a short section of ``Rhapsody in Blue'', by George Gershwin; identical sound files were copied into the noise tracks in both cases.
Mach 2 Turbulence
One of the beautiful aspects of this schlieren photograph of turbulence is the sound waves generated by the Mach 2 helium jet, heading out in the surrounding air caused by turbulent "punches" or acceleration to the air at the air-jet surface. Since the billows of helium are traveling at roughly Mach 2, or twice the speed of sound in air, the sound pressure wave fronts they have an angle of about 63 degrees to the horizontal (think about this). Something else to notice -and its ubiquitous and important. Note that the sound pressure waves are closer together if they come from the base or jet entrance region, and farther apart (and therefore of lower frequency) if as the are generated further along the flow. This not only says a lot about the turbulence but is a common experience, if you care to listen for it neat a jet of ait (Be careful!) or, in the case of a water jet in a pool, "feel" it. Placing your hand close to the entrance of a water jet below the surface, you will notice lower and low frequency turbulence as you move your hand away from the source.
