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Flue Pipe Acoustics (The Physics Behind the Sound of Flutes, Organ Pipes and Whistles)

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Flue Pipe Acoustics (The Physics Behind the Sound of Flutes, Organ Pipes and Whistles) Carousel Organ, Issue No. 7 — April, 2001 Flue Pipe Acoustics (The Physics behind the Sound of Flutes, Organ Pipes and Whistles) Richard J. Weisenberger etween 1974-1978 I was doing independent research on results. A basic knowledge of the physics involved in flue pipe the effects of cutup (the cutup is the height of a pipe's design is the basis for any further scientific investigation in the Bmouth—the distance between the lower and upper field of flue pipe acoustics necessary to relate cause with effect. lip).and scaling on flue organ pipes as to the effect on operating This was an important first step, as it enabled me to be able to pressure and acoustical output. accurately predict the operating pressure and acoustical output capability of virtually any pipe design using open toed voicing. Organ Pipes Of course, coning in the toes will increase the operating I found there were direct correlations among these parameters; pressure and reduce the output of ANY pipe at a given operat- the operating pressure being directly related to the square of the ing pressure. change in cutup ratio if the scaling is held constant and the operating Figure 1. Stopped Steam Calliope Whistles pressure likewise being directly pipes will require The next step was to use these for- related to the square of the change exactly 1/2 the work- mulas to design everything rang- ing length, using the in scaling if the cutup ratio is held ing from the softest flutes to whis- same cutups, to pro- constant. duce equal output to tles which resembled those on the Also, the acoustical output their open counter- old steam locomotives. The result power of any pipe, prior to parts at a given oper- was that it was possible to design overblowing, is directly related to ating pressure in whistles of high output which did the fourth power of the change in terms of both fre- not require the customary high cutup ratio with a pipe of a given quency and acousti- pressures found on steam locomo- scale and also directly related to cal power. Their dif- tives and steamboat calliopes. I the fourth power of the change in ferences lie in their was able to design whistles which lack of even order scale with a pipe of a given cutup resembled steam calliope whistles harmonic radiation ratio. which would produce outputs as Thus, doubling the cutup of a high as 110 dB at 100 ft (140 dB at pipe would result in one which would require four times the 1 meter) operating on as little as 15 PSI, rather than the usual operating pressure and produce 16 times the output (a 12 dB 150 PSI. increase), prior to the onset of overblowing (provided that the I found that the acoustical output of a whistle is much more mouth area did not exceed the pipe's cross-sectional area). The dependent upon the flow rate rather than the actual operating same holds true if doubling the scaling of a pipe with a given pressure, thus if you use a relatively large air slot width of 1/16" cutup ratio. and large diameter inlet, whose area exceeds the slot area, you I had thus discovered a kind of "Ohm's Law" for flue pipe could get the required flow rate at relatively low pressure. Thus, design, which produced easily verifiable and highly repeatable the operating efficiency of a whistle could be greatly increased over that of the traditional high pressure steam whistle. Also, Figure 2. The effect of the cutup on a pipe’s per- you gain nothing by making the mouth area larger than the formance is very dramatic. The operating pres- whistle's cross-sectional area other than allow high pressure sure will relate to the SQUARE of the change in the cutup and the acoustical power output will be operation without overblowing. You do not get more output. related to the 4th power of the change in the It makes sense! The whistles designed to be used on loco- cutup, all other factors being equal. motives and steamboats HAD to be designed to accommodate As an example, provided that the mouth area the high pressures, since the engines required high pressure in does not exceed the pipe’s cross-sectional area, order to be able to produce a useful amount of output. The whis- doubling the cutup will QUADRUPLE the pipe’s tles did not, but would overblow unless they were designed to operating pressure, prior to the onset of accommodate the high pressure. overblowing! The increase in output will be This led to the next stage. How would one go about 12dB, which is a full 16 times the output of the increasing the output capability of a whistle beyond that of tra- pipe of lower cutup! In addition, the air flow to the doubled cutup ditional steam whistle designs? It's true that an output of 110 dB pipe will also be doubled and the blower power at 100 ft. (140 dB at 1 meter) is nothing to sneeze at, but there required will eight times that of the lower cutup are mechanical sirens used for warning communities with out- pipe. Since the higher cutup pipe produces 16 puts as high as 135 dB at 100 ft. How would one design a whis- times the output using eight times the blower tle to compete with a siren in terms of overall output and effi- power, its efficiency is double that of the former. ciency? 10 Carousel Organ, Issue No. 7 — April, 2001 Figure 3. The dramatic effect of Still, this design was a full 10 dB short of that pipe scales have long ben known to of the loudest warning sirens. organ builders. Of course the larg- The next step was to design a Toroidal whistle er scales are capable of much specifically to operate in the manner of a compres- greater outputs when using the sion driver in a horn loaded speaker. With all of the same cutup RATIOS, as the larger output of a Toroidal whistle driving a suitable horn, scales permit much greater cutup an output to equal that of the loudest warning siren HEIGHTS, without the mouth area exceeding the pipe’s cross-sectional was no longer out of the question. area. This resulted in U.S. Patent #4,686,928, which With the cutup RATIO being can be searched by number on the IBM Patent constant (as is often the case) the Server website. acoustical power output will be In this design, an INVERTED Toroidal whis- related to the 4th power of the tle is used to drive a horn with a directivity index of change in the scale of the pipe. 13 dB or so. Since an inverted toroidal whistle is As an example, each time a blown from the INNER edge, rather than from the pipe’s scale (with a given cutup outer edge of the toroid, as is the case in the earlier ratio) is doubled, the pipe’s output will be increased by 12 dB or 16 patent, this design uses 25% less air flow and due times! To keep the smaller scales to horn loading, produces an extra 10 dB on axis from overblowing at a given pres- (135 dB at 100 ft). Thus a 420 Hz whistle of this sure, the toe hole areas are reduced type will use only 1,350 CFM at 15 PSI. Under to restrict the air flow. ideal conditions the 70 dB radius of a 420 Hz whis- As is always the case, the larg- tle of this type will extend up to 4 miles! er scales will produce the mellower Since the air can be furnished by a 100 HP sin- tones, regardless of the cutup. gle stage rotary screw compressor, this is more coverage/HP than the best siren available. Toroidal Whistle Except for the extreme This led to my designing the toroidal whistle. Think of a sound level, the sound is Toroidal whistle as a large phased array of about 30 high output very similar to that of a steam whistles all sounding the same frequency. It looked good standard cylindrical calliope in theory and when the prototype was tested I achieved an whistle, or even that of a incredible output of 125 dB at 100 ft. (155 dB at 1 meter)! The stopped flute. With this whistle was about the size and shape of a small automobile tire, accomplishment it is time required 1,800 CFM at a low 15 PSI and produced 430 Hz at an the Guinness record for the awesome level. The test was performed in a remote corner of world’s loudest musical per- the Greater Cincinnati International Airport in July of 1982. formance is taken away The tests were audible over parts of Erlanger, Florence, Hebron, from the rock concert circuit Figure 4. The patent drawing of the Elsmere and Ft. Mitchell, KY as well as in Delhi, OH. and restored to an all Toroidal whistle. The abstract reads: A I found that single-tone inverted toroidal whistle for acoustical instrument. producing a uni-directional output of because most of the My intention is not to about 135 decibels at 100 feet on axis at whistle's output was at deafen anyone, as I would a frequency of about 420 hertz. A hol- fundamental frequen- not advocate such an instru- low cylinder having a closed base end is cy, rather than in the combined with a toroidal body to pro- ment as my proposed vide an annular sound chamber the harmonics, there was Dynawhistle calliope in a working length of which determines the not as much loss due to stadium crowed with peo- wavelength of sound generated by pas- atmospheric absorp- ple, but in an inaccesable sage of air or steam under pressure tion as in a siren of through an annular slit formed in the spot such as atop a bridge interior of the cylinder and impinging equal near field dB rat- pier or similar structure, or against a spaced tapered lip on the inner ing.
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