A whistle is a device that makes sound from air blown from one end forced through a small opening at the opposite end. They are shaped in a way that allows air to oscillate inside of a chamber in an unstable way. The physical theory of the sound-making process is an example of the application of fluid dynamics or hydrodynamics and aerodynamics. The principles relevant to whistle operation also have applications in other areas, such as fluid flow measurement.
Types
Wilson, et al., 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. 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 (monopolesymmetric and dipoleasymmetric).
Monopole
Whistles that generate sound through fluctuations of mass flow across a boundary are called monopole-like sources. The figure on the right is an example of a small sphere whose volume is oscillating. 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 sound power can be expressed as:
The variables U and L are considered characteristic of the source, and their correct choice is important.
Dipole
Whistles that generate sound through fluctuations of momentum or stress and strain of a force exerted on the surrounding medium are called dipole-like sources. The figure on the right is an example of a small rigid sphere that is moving back and forth in a given direction. This results in a non-uniform sound field. The sound power can be expressed as:
Feedback categories
Aerodynamic whistles rely on the instability of flows and feedback that enhances the instability. There are several ways that feedback can occur.
Category I
The sound from a whistle in this category is primarily a byproduct of source motion. The back reaction is insufficient to strongly control source motion, therefore whistles are not in this category.
Category II
The back reaction of the medium is a determinant of source motion. Unstable fluid motion or the sound generated by it can feedback to the source and control it. What is required is: a source of steady power; an amplification mechanism that can convert the steady power to time-varying power; a disturbance, which supplies the oscillations to be amplified; a means of generating sound or other oscillatory fluid Brownian motion; a means for feedback of that oscillatory motion as a disturbance to the input of the amplifier. Whistles are in this category. There are several ways to describe the feedback process.
Class I
The feedback is essentially incompressible; the speed of sound, although finite, is sufficiently large that it can be considered infinite. This action may be called hydrodynamic feedback. There are a number of class I devices.
Class II
The feedback is compressible and does not depend on the speed of sound. This action may be called quasi-compressible feedback.
Class III
The feedback is compressible and depends on the speed of the sound. This may be called acoustic feedback.
The figure on the right shows a block diagram of these feedback mechanisms. All aerodynamic whistles operate under one of the classes.
Stages
Feedback in whistles is nonlinear mechanics or chaos. Because of the non linearity, it is possible to have more than one frequency at a given flow rate. The difference depends on whether the flow rate is achieved by increasing the flow or by decreasing the flow. The possibility of multiple states is called a stage and is shown schematically in the figure on the right. 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. As the flow speed is later decreased, the frequency slowly decreases but then jumps down abruptly to a lower stage. This pattern is called a hysteresis loop.
Higher stages are associated with more vortices in that distance, hinting that this distance can be an important characteristic dimension. In several whistles, three stages have been identified. Overblowing in some musical wind instruments causes stage I to jump to stage II.
Flow instability
Flow instability is the engine for whistles. It converts steady energy to time-dependent energy.