Purple is inner ear. The circuit diagram shows an impedance analogy model of the human ear. The ear canal section is followed by a transformer representing the eardrum. The eardrum is the transducer between the acoustic waves in air in the ear canal and the mechanical vibrations in the bones of the middle ear. At the cochlea there is another change of medium from mechanical vibrations to the fluid filling the cochlea. This example thus demonstrates the power of electrical analogies in bringing together three domains acoustic, mechanical and fluid flow into a single unified whole.

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Applications[ edit ] Mechanical—electrical analogies are used to represent the function of a mechanical system as an equivalent electrical system by drawing analogies between mechanical and electrical parameters. A mechanical system by itself can be so represented, but analogies are of greatest use in electromechanical systems where there is a connection between mechanical and electrical parts.

Analogies are especially useful in analysing mechanical filters. These are filters constructed of mechanical parts but designed to work in an electrical circuit through transducers. Circuit theory is well developed in the electrical domain in general and in particular there is a wealth of filter theory available. Mechanical systems can make use of this electrical theory in mechanical designs through a mechanical—electrical analogy.

This was of some importance in early phonographs where the audio is transmitted from the pickup needle to the horn through various mechanical components entirely without electrical amplification.

Early phonographs suffered badly from unwanted resonances in the mechanical parts. It was found that these could be eliminated by treating the mechanical parts as components of a low-pass filter which has the effect of flattening out the passband. In former times, up to about the early 20th century, it was more likely that the reverse analogy would be used; mechanical analogies were formed of the then little understood electrical phenomena.

These are network diagrams that describe the topology of the electrical system using a specialised graph notation. The circuit diagram does not try and represent the true physical dimensions of the electrical components or their actual spatial relationship to each other.

This is possible because the electrical components are represented as ideal lumped elements, that is, the element is treated as if it is occupying a single point lumped at that point. Non-ideal components can be accommodated in this model by using more than one element to represent the component. For instance, a coil intended for use as an inductor has resistance as well as inductance. This can be represented on the circuit diagram as a resistor in series with an inductor.

What the mechanical analogs of these elements are depends on what variables are chosen to be the fundamental variables. There is a wide choice of variables that can be used, but most commonly used are a power conjugate pair of variables described below and the pair of Hamiltonian variables derived from these. The model works well if the components are small enough that the time taken for a wave to cross them is insignificant, or equivalently, if there is no significant phase difference in the wave either side of the component.

What amounts to significant depends on how accurate the model is required to be, but a common rule of thumb is to require components to be smaller than one sixteenth of a wavelength.

This limit is much lower in the mechanical domain than the equivalent limit in the electrical domain. In the electrical domain, on the other hand, the transition from the lumped element model to the distributed element model occurs in the hundreds of megahertz region.

In the electrical domain, a transmission line , a basic distributed element component, can be included in the model with the introduction of the additional element of electrical length. Just such an approach was used in one paper to model the cochlea of the human ear.

In the electrical domain the power conjugate variables chosen are invariably voltage v and current i. Thus, the power conjugate variables in the mechanical domain are analogs. However, this is not enough to make the choice of mechanical fundamental variables unique. The usual choice for a translational mechanical system is force F and velocity u but it is not the only choice. A different pair may be more appropriate for a system with a different geometry, such as a rotational system.

There are two ways that the two pairs of power conjugate variables can be associated with each other in the analogy. For instance the associations F with v and u with i can be made. However, the alternative associations u with v and F with i are also possible.

This leads to two classes of analogies, the impedance analogies and the mobility analogies. The same mechanical network has analogs in two different electrical networks. These two electrical networks are the dual circuits of each other.

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## Mechanical–electrical analogies

We will also discuss the basic directional properties of cone loudspeakers under varying conditions of baffling. A number of assumptions will be made based on the physics of the acoustic wave equation, drawing on primary references in the literature as needed. In the way of terminology, a loudspeaker mechanism is generically a transducer, a device that changes power or energy in one form to another. More commonly, loudspeaker mechanisms are referred to as drivers, while the term loudspeaker is generally reserved for the complete system. This process is experimental and the keywords may be updated as the learning algorithm improves.

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## Impedance analogy

Measured Terfenol-D material properties under varied applied magnetic field levels by Marcelo J. Dapino, Frederick T. Calkins, Alison B. Flatau, David L. Hall , " An experimental approach is used to identify Terfenol-D material properties under magnetic bias and mechanical prestress conditions typical of transducer applications for the magnetostrictive material Terfenol-D.

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## Electroacoustics

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