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High-Resolution jpeg files - 300 dpi jpeg: Clicking on the High-Res link will bring the image up in a window. Low-Resolution jpeg files - 72 dpi jpeg: Clicking on the Low-Res link will bring the image up in a window. Soundproofing curtains are great for in front of windows, door frames and shared walls to absorb sound from the other parts of your apartment and from outside your home. An aerodynamic whistle (or call) is a simple aerophone, an instrument which produces sound from a stream of gas, most commonly air. Whistles have been around since early humans first carved out a gourd or branch and found they could make sound with it. The whistles described in this article are in a subclass where only the fluid is in motion and there is no significant dependent motion of the interacting solid.
In 1883 he began experimenting with pea-whistle designs that could produce an intense sound that could grab attention from over a mile away. Hudson demonstrated his whistle to Scotland Yard and was awarded his first contract in 1884.
This police whistle monopoly gradually made Hudson the largest whistle manufacturer in the world, supplying police forces and other general services everywhere. Wilson, et al.,[10] in their study of human whistling (see below), pointed out the importance of including the symmetry or asymmetry of the unstable flow in addition to the feedback classes listed below. Whistles that generate sound through fluctuations of mass flow across a boundary are called monopole-like sources. The variables U and L are considered characteristic of the source and their correct choice is important. Whistles that generate sound through fluctuations of momentum or a force exerted on the surrounding medium are called dipole-like sources. Aerodynamic whistles rely on the instability of flows and some mechanism downstream to send the disturbance back to the origin to continue the instability. The sound from a Category I whistle is primarily a byproduct of source motion.[11] In every case, there is a back reaction of the medium on the source (resistive and reactive impedance). The back reaction of the medium is an determinant of source motion.[11] In many important cases, linear thinking (small cause = small effect) is fallacious.
The feedback is compressible and depends on the speed of sound.[11] This action may be called intermediate field, quasi-compressible feedback. The feedback is compressible and depends on the speed of sound.[11] This may be called far field or acoustic feedback. There are feedback loops associated with many whistle operations and they are non-linear.[12] Because of the nonlinearity, there can be several possible conditions for a given flow speed or geometry.
Early studies have used the term stage to describe the possible states of feedback as shown schematically in the figure on the right. At any particular flow speed it is possible for one of several loops to be dominant, depending on how that speed was achieved.
Higher stages are associated with more vortices in that distance, hinting that this distance can be an important characteristic dimension.
An example is shown in the figure on the right with a water jet.[13] The laminar two-dimensional jet amplifies small disturbances at the orifice to generate a vortex street. One important source of instability in a fluid is the presence of a velocity gradient or shear layer with an inflection point. In a whistle, the instability starts at some point in the three dimensional region and then moves along some path in that region as the local variables change.
Whistles come in all shapes and sizes, but their operation can be unified through the concepts of dynamic and geometric similarity.
Similarity is best exposed by determining a speed, U, that is characteristic of the dynamics, and a dimension, L, that is characteristic of the geometry.
The first version is used for dynamic similarity of the fluid motion in whistles while the second version is used for dynamic similarity of the acoustical motion in whistles. This number describes the range between flows that can be considered incompressible and flows where compressibility is important. The number was named in honor of Osborne Reynolds,[16] an engineer who did pioneering studies on the transition of laminar to turbulent flow in pipes. Now the Reynolds number can be derived directly from the dimensionless form of the momentum equation.
The number was named in honor of Carl-Gustav Rossby,[17] a meteorologist who first described the large scale motions of the atmosphere in terms of fluid mechanics.
Now the Rossby number can be derived directly from the dimensionless form of the momentum equation in curvilinear coordinates. In these whistles, the flow instability is symmetric, often resulting in periodic ring vortices and the sound generation is associated with fluctuations of volumetric (mass) flow rates. The steady flow from a circular orifice can be converted to an oscillatory flow by adding a downstream plate with a circular hole aligned with the orifice. The disturbance in the jet is a symmetric vortex ring that moves at some speed slower than the mean jet speed until it encounters the hole and some fluid is forced through it, resulting in a monopole-like sound field in the half space outside. To invoke dynamic similarity,[18] the characteristic speed in a study was chosen to be the average speed of the jet at the orifice U (deduced from measured volumetric flow rate) and the characteristic length was chosen to be the orifice diameter I?.
The frequency of the tone determined by how often a vortex encountered the hole while moving at some speed u less than the initial jet speed. The uniformity of the measured sound field for this whistle confirmed its monopole-like nature.
There seems to be evidence that events similar to the hole tone occur on aircraft landing gear covers with circular holes.
The yellow plastic pipe is actually a childa€™s toy that sounds when the pipe is whirled around. The characteristic speed is the mean flow through the pipe U and the characteristic length must be a multiple of the spacing between corrugations, nL, where n is an integer number and L is the distance between corrugations. The unique feature of this whistle is that the tone sounds only with flow through the orifice from outside; it is an acoustical diode. These devices have been studied,[30] and reviewed by Raman.[31] Here we look primarily at the Hartmann whistle.
The sound field may be similar to that created by oscillatory flow from a pipe, except for presence of the supersonic jet structure which can strongly modify the directivity. The diameter of the orifice and cavity is d, the distance between orifice and cavity is h, and the orifice pressure P was given in kilograms per meter squared.
Comprehensive studies of this phenomenon[32][33] have shown that the position of the cavity is critical in creating sound. Since the characteristic speed U and sound speed are essentially the same, it can be rewritten as the second equation. Since it is highly likely that the oscillations are coherent around the periphery, there should be a fluctuating volumetric flow rate from the cavity with only a small net lateral force. Originally, the gauze was heated with a Bunsen burner; later, a wire grid was heated electrically. Another characteristic length associated with sound power is I±L, the position of the gauze. The Sondhauss Tube is one of the early thermal tone generators; it was discovered in the glass blowing industry. In analyzing this tube, Rayleigh noted that if heat had been added at the point of highest density in the sound wave, and subtracted at the point of lowest density, the vibration would be encouraged. The number and variety of whistles created by humans is quite large, yet very little has been done to examine the physics of the process. Wilson and his colleagues[38] have simulated the human whistle by creating a cylinder 2.04 inches in diameter with a rounded orifice at one end that supplied a jet and another rounded orifice at the other end of the same diameter and on the same axis. The Strouhal number was essentially constant over the limited speed range, suggesting hole tone operation with Class I or Class II feedback.
In these whistles, the flow instability is asymmetric, often resulting in rows of alternate vortices and the sound generation is associated with fluctuations of applied force.
The steady flow over a cylinder (or similar object) will generate vortex shedding and consequent sound.
Whistling telephone wires, automobile radio antennae, certain automobile front grilles, and smoke stacks are other examples of this tone.
Hydrodynamic feedback (Class I) influences the formation of new vortices and exerts a fluctuating force on the cylinder. It is surprising how often oscillatory flow phenomenon have Strouhal Numbers in this range. The second equation suggests that the Strouhal Number is a weak negative function of Reynolds number. An approximate way to relate the sound generated to the flow characteristics is to perturb the standard drag equation with velocity perturbations as shown in the upper equation below.(lift measurements for cylinders are generally not available).
Manipulation of the equation yields the lower two equations for the dipole sound power of both lift and drag. Phillips[41] found the lateral velocity fluctuations were two orders of magnitude greater than the longitudinal, so the lift dipole is 20 dB above the drag dipole. A particular shaped object is placed within a pipe and a pressure sensor is embedded either in the pipe wall or in the inserted object. It should be noted that three-dimensional (viscous) effects occur at low Reynolds numbers so dynamic similarity is not achieved there. Photographs taken from space have shown alternate arrangements of clouds around mountains; The figure on the right shows an example.

These whistles generate enough sound to be detected but at frequencies below 1 Hz they are inaudible. Choose from high resolution jpeg format graphics (for print use), or the low resolution jpg format (for web use). Later versions of QuickTime may need to disable tif file viewing first to complete downloads. With a high noise reduction rating (NRR) of 32 decibels, this high performance hearing protection can be used in environments where noise is just a nuisance up to environments with hazardous noise levels.
In prehistoric Egypt, small shells were used as whistles.[1] Many present day wind instruments are inheritors of these early whistles. There are many ways to create pure tones, but we restrict the descriptions here to what are called aerodynamic whistles.
The conversion of flow energy to sound comes from an interaction between a solid material and a fluid stream. Depending on the geometry there are two basic types of whistles, those that generate sound though oscillations of fluid mass flow and those that generate sound through oscillations of the force applied to the surrounding medium. His invention was discovered by accident, when he accidentally dropped his violin and it shattered on the floor.
Both Ratchet rattles and whistles were used to call for back-up in areas where neighborhood beats overlapped, and following their success in London, the whistle was adopted by most police in the United Kingdom.
They can be used for hunting, controlling dogs, as toys, for sports events, as musical instruments, for police or military use, as ship or lighthouse fog horns, as steam whistles on trains, for scheduling and emergency use in industrial settings such as mines, in fluidic circuits, in domestic settings such at the tea pot whistle, for reducing foam bubbles, and for human whistling.
Because of the close relationship of flow symmetry to the sound field generated, their concept was included here as part of the sound source description (monopole -symmetric and dipole - asymmetric). The figure on the right is example of a small rigid sphere that is moving back and forth in a given direction. Unstable fluid motion or the sound generated by it can feedback to the source and control it, much like audio feedback squeal. A well known example is the hole tone (described below) where the feedback distance of a compressible (sound) wave is very small as compared to the wavelength of the sound. Which of these is dominant is determined by the gain of the unstable flow at a particular frequency and whether the feedback is constructive or destructive. As the flow speed increases (Reynolds number - Re) the frequency slowly climbs (nearly constant Strouhal number -St) but then the frequency jumps up abruptly to a higher stage.
In a number of the whistles described here, Stage I is associated with the development of a single vortex in the distance between initiation of the flow instability and initiation of the feedback signal. For this case, the flow speed, in terms of Reynolds Number, was graphed against the disturbance frequency, in terms of the Strouhal Number for a variety of disturbance amplitudes to reveal the region of instability as shown in the figure on the left.
Transition to turbulence can occur over a rough surface or over an irregular shape, such as an aircraft spoiler. Thus, fluid instability can be described as a three dimensional region with flow speed on one axis, disturbance amplitude on the second, and velocity profile on the third.
This makes the comprehensive understanding of whistle instability mechanisms very difficult.
Nature knows nothing of the specific measurement systems we use; it cares only about ratios between the various forces, time scales, and the several dimensions. If these values are used in dimensionless numbers, such as those listed below, much understanding of the phenomenon can be achieved. The number was named in honor of Vincenz Strouhal[14] who first deduced the relationship between the vortex shedding frequency around a cylinder and the flow speed. Now the Strouhal Number can be derived directly from the dimensionless form of the mass continuity equation.
Many whistles, especially those with Class III feedback, require use of both numbers (see (Monopole-Dipole Whistles).
The number was named in honor of Ernst Mach[15] who first studied (among other things) supersonic flow and shock waves. Now the Mach number can be derived directly from the dimensionless form of the momentum equation.
He described the jet stream, and his number was first used to describe the motion associated with the Coriolis force in the atmosphere. The sound field is as close to the directivity of an actual monopole source as local geometry allows. Small perturbations in the flow feedback to the orifice to cause a variable volumetric flow rate through the downstream hole because of the symmetry of the feedback. The oscillatory volumetric flow in the hole sends a wave back to the orifice to complete the feedback loop and causing a nearly pure tone. Since the jet slowed as it proceeded toward the hole, the speed of the vortex slowed with it so the frequency and Strouhal number was greater at closer spacing. Measurements of speed dependence of the sound level showed it to be very close to , further confirming the monopole nature of the source. The hole tone has been rediscovered in the form of the tea pot whistle.[19] They found that above a Reynolds number of 2000, hole tone operation occurred with symmetric vortex evolution and a constant Strouhal Number with Reynolds number. In Australia, there is the Tenterfield Fox Whistle[21] and the Traditional Fox Whistle that appear to operate as hole tones. The metal pipe shown was used in the Concorde cockpit to provide cooling air to the pilots, but its loud tone got it canceled. At low speeds, the unstable interior flow needs to travel several corrugations to establish the feedback loop. The highest frequency (7554 Hz) was found in the a€?overblowna€? condition and n was presumed as one corrugation. A cylindrical cavity with a small circular, square-edged hole at one end and totally open at the other is known to generate a tone when air is passed through it.
Karthik[25] and Anderson[26][27][28] have studied this phenomenon and concluded that symmetric vortex shedding on the cavity side is the driving agency. When a subsonic jet impinges on a cavity, jet instability becomes part of the feedback loop as with the hole tone. The shock cells of the jet interact with the shock in front of the cavity (the flow in the cavity being subsonic). The process has hysteresis loops and the frequencies are related to multiples of the quarter wavelength resonance of the cavity.
Thus the source is yet another version of a monopole-like geometry; the volumetric flow rate is a cylindrical area between the jet and cavity. The temperature in a sound wave varies, but since it is so small normally it is common to neglect its effects. The heat transferred to the air in the tube sets it into near half-wave resonance if the gauze is placed below the midpoint of the tube as shown in the figure on the right.
Another thermal effect is called the Taconis oscillation.[36][37] If a stainless steel tube has one side at room temperature and the other side in contact with liquid helium, spontaneous acoustic oscillations are observed. There are three possible mechanisms: Helmholtz resonance, symmetric hole tone operation (monopole), or asymmetric edge tone operation (dipole). Their work indicated symmetric unstable vortex flow as would be expected but there was no mention of stages.
The early Greeks used this phenomenon to develop a harp and the sound was called an Aeolian tone after Aeolus, God of the Wind. At very low Reynolds numbers, the flow around a cylinder is stable, forming two fixed vortices behind it. The upper equation is the modified drag equation with both drag component u and lift component v and the cross sectional area dL where d is the cylinder diameter and w is the length.
Each time a vortex is shed, the drag velocity fluctuation u has the same sign, but the lateral velocity fluctuation v, has opposite signs, since the vortex is shed on alternate sides.
There are several accurate flow meters that are designed to take advantage of the constancy of the Strouhal Number with Reynolds Number to provide a linear relationship between flow rate and measured frequency.
Whistles vary in size from a small slide whistle or nose flute type to a large multi-piped church organ.
Strictly speaking, they are fluid mechanical whistles since they occur in gases, such as air or steam, as well as in liquids, such as water. This became the first referee whistle used at association football matches during the 1878a€“79 Football Association Cup match between Nottingham Forest and Sheffield. Observing how the discordant sound of the breaking strings travelled (trill effect), Hudson had the idea to put a pea in the whistle.[6] Prior to this, whistles were much quieter, and were only thought of as musical instruments or toys for children. They also occur as accidental byproducts of fluid flow such as supersonic jets, cavity resonances, whistling telephone wires, and idling circular saws. If the sphere is small with respect to the wavelength of the sound emitted, it can be called a point dipole. Although tuning forks are not whistles, they create sound fields that are very close to the idealized dipole model. The feedback that causes a stick in a water stream to vibrate, or a flag to wave, is due to hydrodynamic feedback. As the flow speed is later decreased the frequency slowly decreases but then jumps down abruptly to a lower stage.
By blowing hard in some musical wind instruments Stage I jumps to Stage II; it is called overblowing. The value of D in the figure represents the ratio of the lateral disturbance displacement to the nozzle width; the disturbances were minute.
All whistle mechanisms described here are created by temporal disturbances that are in one of the three classes. To compare them we need to take into account the established ratios that are relevant to whistle operation.

The characteristic variables were the cylinder diameter L1, and the speed of the flow over it U. This equation may be referred to as a fluid mechanical Strouhal number in comparison with the second version which may be referred to as the acoustical Strouhal number.
Two scaling laws were used; the Strouhal number was graphed as a function of Reynolds number. The Strouhal number data showed clearly the almost linear relation between frequency and initial jet speed. At these speeds and spacings, the feedback was normally Class II, but reflecting surfaces as far away as three meters and with proper phasing, controlled the tone, converting the feedback to Class III.
Comparison of their data with data in the figure suggests that the cylindrical enclosure between the two orifices raises the Strouhal number. Steady flow through the pipe at low Reynolds numbers results in a fluctuating volumetric flow rate that generates a monopole-like sound field at the pipe exit. This whistle is similar in many respects to the hole tone, in particular the teapot whistle. End corrections for radiation from the openings is needed to bring the two frequencies in consonance. When a supersonic jet impinges on a cavity, shock wave instability becomes part of the feedback loop.
Small symmetric disturbances in the jet stream are amplified as they proceed toward the cavity (similar in some respects to the hole tone) causing the shock in front of the cavity to oscillate.
In this case, the equation could have been reformatted in terms of the acoustical Strouhal Number as shown in the second equation above.
After reformatting Hartmanna€™s formula, and using the new formulation above, an equation for sound power can be written. Although the amplitude factor A replaces the dimensionless volumetric flow rate in these equations, the speed dependence strongly confirms the monopole-like characteristics of the Hartmann whistle. When amplification can occur a small variation can grow and have important influence on the sound field created.
There is no theoretically optimum position, as the wave speed upward is the sound speed plus u, the convection speed, while the wave speed downward is minus u. For detailed study of the whistle, see Matveev.[35] Since the first mode resonance is about half-wave, the sound field emitted from the tube is from two in-phase monopole-like sources, one at either end.
After a number of tests at various speeds, orifice diameters, and orifice thicknesses, they concluded that the whistle was created by a Helmholtz resonance in the cylinder volume.
In the study by Henrywood, it was noted that Helmholtz resonance could occur at low speeds.
As the speed increases, the flow, although laminar, becomes unstable and vortices are shed alternately. Theodor von Karman[39] identified and analyzed the flow behind objects like a cylinder and since then this special flow has been called the Karman vortex street. At low Reynolds numbers the Strouhal number rises as inertial effects begin to dominate and then decays slightly at higher numbers. The characteristic dimension is that of the object lateral to the flow and the characteristic speed is that of the impinging flow.
The fluctuating force exerted on the cylinder is a result of the flow circulation around it caused by the alternate vortex separation as suggested in the third figure. As a result, The drag dipole would be expected to be twice the frequency of the lift dipole. At higher speeds, the vortex separation may not be correlated over the entire length of the cylinder resulting in multiple essentially independent dipole sources and lower sound power.
The figure on the right shows data from a meter called the Deltameter.[42] The inserted shape was that of a trapezoid with the wider end facing upstream. The dependence of Strouhal Number on Reynolds Number for this confined geometry is slightly negative as was found also for the Aeolian tone. The NOAA laboratories in Boulder, Colorado, were tasked with detecting the extremely low frequency sound of nuclear tests. Using Strouhal's number, it might be possible to estimate the wind velocities; they appear to be quite high. Hudson & Co began facing greater competition, as other whistle manufacturing companies were established, including W. If the sphere is small enough relative to the sound wavelength it is emitting, it can be called a point monopole. Nevertheless, much can be learned about whistles with the useful form of the sound power equation for the dipole. The number would be more constant if the actual jet speed at the hole could have been used as the characteristic speed.
At intermediate flow rates, several non-harmonically related frequencies occurred simultaneously suggesting that several corrugations were involved in the sound generation.
To determine the end corrections, two additional dimensions are needed: the diameter of the orifice d1 and the diameter of the tube d2. The shock front acts much like a piston source of high energy resulting in a monopole-like sound field. The most well known thermal whistle is the Rijke Tube.[34] Peter Rijke placed a heated a gauze material inside a vertical tube. Without a convection flow, the midpoint and the lower tube end are the best locations for heat transfer.
There was enough data for one case in their study to calculate the Strouhal and Reynolds numbers. The flexibility of the mouth suggests that although a hole tone feedback mechanism is highly likely, the possibility of Helmholtz resonances in the mouth cavity and asymmetric edge tone actions with the teeth are considered possible.
Vincenz Strouhal was the first to scientifically investigate the sound emitted by flow around a rigid cylinder. The fact that the vortices are not directly behind the cylinder suggests that the force vector has both a lift and drag component resulting in lift and drag dipoles. The lower figure on the right shows the correlation coefficient as a function of distance along the cylinder and is from the Etkin, et al. The graph shows a nearly linear relationship with flow speed over nearly a 1000 to 1 range of Reynolds Numbers (12,530 to 1,181,000). For this type of source, the sound is emitted radially so the sound field is the same in every direction and decays with the inverse square of the distance. The surrounding medium in the direction of motion is compressed to radiate sound, but the medium at right angles slides past the sphere and is not compressed. In many cases, say turbulent jets, the sound created is random and it is convenient to consider the sound to be merely a byproduct of the flow.
They noted that at lower speeds, the cylindrical volume responded as a Helmholtz resonator. In the smaller metal tube, a predominant tone appeared at 6174 Hz and corresponded to n=2. The fundamental tone occurs near , so one characteristic dimension is L, the length of the tube.
A cylindrical cavity with one end open and facing the supersonic circular jet will result in extremely intense sound. It is interesting that the number is very close to that found by Strouhal for flow over a cylinder.
Here the cavity is excited by an annular jet which oscillates symmetrically around the sharp edges of the cavity. With convection, a compromise position halfway between the two points is normally chosen which depends on the amount of heat added. This device is not considered a true whistle since the oscillations decay as the temperatures equalize.
At low Reynolds numbers the tone was pure and the frequency was proportional to the steady flow speed U and inversely proportional to the cylinder diameter d. Orifice plates as flow meters typically have a 5 to 1 speed range, while turbine meters may have up to 100 to 1 range.
In this category the back reaction is insufficient to strongly control source motion, so whistles are not in this category. The hysteresis loops are clear indications of the complex nature of the jet instability gain structure.
A unique aspect of this whistle is that the internal flow carries both the unstable vortex downstream and the returning feedback signal upstream.
It appears to be a circular version of the edge tone (discussed below) in which the symmetry of the otherwise dipole source of the edge tone is converted to a monopole source. There are numerous satellite photos available on the web showing this phenomena in many places of the world. A related configuration, called the stem jet, has a central rod in the jet that extends to support and align the cavity. Nozzle diameter d characterizes the sound power while the separation distance h characterizes the frequency. Nevertheless, much can be learned about whistles with the useful form of the sound power equation for the monopole. In 1987, Ron Foxcroft released the Fox 40 pealess whistle, designed to replace the pea whistle and be more reliable.

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