Jens Blauert

Magnetic-Field Transducers

While dealing with magnetic-field transducers in this chapter and electric-field transducers in the next, we will demonstrate that the force-law relationship between the mechanic force, F, and the coupled electric quantity, u or I, is either linear or quadratic. A linear force law, characterized by F ~u or F ~i, is observed when the energy content of the magnetic or electric field does not vary when the movable component changes position. A quadratic force law, characterized by F ~u2 or F ~i2, appears when the movable component meets the electric or magnetic field at a boundary, implying that the energy of the field varies when the movable component changes position. The force in the boundary area is given by the relationships described below that can be derived by imagining a small virtual shift of the border area. We have

Horns and Stepped Ducts

The wave equations derived in the preceding chapter allow for calculation of arbitrary sound fields with any possible, physically meaningful boundary conditions. We had restricted ourselves to one-dimensional waves so far. These can, for instance, be observed in tubes with a diameter being small compared to the wavelength, that is d ≪ λ. This condition guarantees that no other waveforms than axial ones can propagate in the tube. One-dimensional propagation also means that all wave planes perpendicular to the axial direction are planes of constant phase.

Spherical Sound Sources and Line Arrays

The wave equation, \(\nabla^2 p = \ddot{p} / c^2\) as derived in Sections 7.1 and 7.2 theoretically determines all possible sound fields in idealized fluids, that is, gases and liquids. The special task of computing sound fields for particular cases requires solutions of the wave equation for particular boundary conditions. In general, this task can be mathematically expensive, but there are helpful computer programs available, some of which are based on numerical methods like the finite-element method, FEM, or the boundary-element method, BEM. In praxi, approximations are often sufficient to understand the structure of a problem.

Isolation of Air- and Structure-Borne Sound

Sound isolation is the confinement of sound to a space in such a way that transmission to neighboring spaces is totally or partially prevented. Sound isolation is predominantly based on reflection caused by impedance discontinuities in possible transmission paths. Dissipation and absorption may also play a role in sound isolation, but it is usually minor. Another term for sound isolation is sound damming because the sound is, so-to-say, “dammed in”.

Noise Control – A Survey

So far we have dealt with sound sources that convert electric energy into mechanic/acoustic energy. These sound sources are mainly used to radiate desired sounds because the mechanic/acoustic signals are easily controlled by the electric ones. In addition to desired sound, there is undesired sound that one would reduce or even eliminate if possible. This kind of sound is called noise. A reasonable definition of noise in acoustics must cover various aspects, such as the following one.

The Wave Equation in Fluids

So far in this book we have dealt with vibrations. These are processes that vary as functions of time. We were able to describe relevant types of vibrations with common differential equations. This chapter now focuses on waves, which are processes that vary with both time and space. Their mathematical description requires partial differential equations.

Geometric Acoustics and Diffuse Sound Fields

So far in this book we dealt with sound propagation in terms of the wave equation. This procedure becomes very complicated, however, when treating sound fields inside rooms with complicated shapes like concert halls or churches. An approximate method called geometrical acoustics is often useful in these cases.

Electromechanic and Electroacoustic Transduction

In the preceding chapter, we dealt with simple linear, time-invariant mechanic and acoustic networks and their electric analogies. In general, these networks can be quite complicated and may assume any number of degrees of freedom. Yet, regardless of how sophisticated the networks are, the energy and power transported in these networks is either mechanic, acoustic, or electromagnetic. Acoustic power and energy are of mechanic nature. Thus the terminological distinction between mechanical, \(\underline{F}\), \(\underline{v}\), and acoustical coordinates, \(\underline{p}\), \(\underline{q}\), is purely operational. In this chapter, we shall present the possibility of coupling electrical and mechanical domains, which results in a coupling of electric and mechanic energy and power. This topic is extremely important for modern acoustics.

Electric-Field Transducers

In electric-field transducers mechanic forces are caused by electric fields or, in the reverse effect, electric polarization is influenced by mechanic forces. Even more than magnetic-field transducers, electric-field transducers exist in a wide variety of forms and shapes. There are transducers that are intrinsically linear and others that naturally have a quadratic force law and must be linearized. There are also irreversible controlled couplers. In this chapter we concentrate on the basic principles of electric-field transducers and discuss some illustrative examples.

Electromechanic and Electroacoustic Analogies

During the discussion of simple mechanic and acoustic oscillators in Chapter 2, readers with some electrical engineering experience may have realized that many mathematical formulae are similar to those that appear when dealing with electric oscillators. There is a general isomorphism of the equations in mechanic, acoustic and electric networks that can be exploited for describing mechanic and acoustic networks via analogous electric ones. Formulation in electrical coordinates is often to the advantage of those who are familiar with the theory of electric networks since analysis and synthesis methods from network theory can be easily and figuratively applied.