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How Speakers Work
Sound is a sensation produced by mechanical waves traveling in air, when the wave frequencies are into the audible range, theoretically between 20 Hz and 20 kHz. In loudspeakers, such mechanical waves are produced by a vibrating diaphragm. This diaphragm can be made of a variety of materials, though paper, plastic, metal and cloth are the main materials used.
The size and shape of the diaphragm may vary depending upon the intended frequency range. Examples are: cones made of paper, plastic or metal for low to moderately high frequencies; domes of all of the above materials and also fabric, generally used for mid to high frequencies, even very thin films and/or strips that may be used for full range or very high frequencies, respectively.
To produce low frequency sounds, diaphragms of relatively large areas are required whilst high frequency sounds only require small diaphragms due in part to the smaller wavelengths.
Transducers transform one kind of energy to another. Loudspeakers are electro-mechano-acoustical transducers.
In dynamic loudspeakers, the electric power supplied by an amplifier is first transformed to mechanical movements of a diaphragm (the membrane already mentioned) and later to acoustic power. The transduction is made by means of the interaction of two magnetic fields, one dynamic (produced by a bobbin of wire called the voice coil) and other static (produced in a magnetic circuit having a magnet as the generator). The physical law that governs this interaction is known as the Lorentz Force Law.
In electrostatic speakers, the magnetic' fields interaction is substituted with the attraction and repulsion of static electric fields, one static powered by a DC source and another dynamic produced in an alternatively charged membrane by the voltage signals supplied by the amplifier.
The magnetic circuit of dynamic speakers has a gap where the voice coil is placed and immersed into the flux lines of the magnetic field. When a voltage signal is applied to the voice coil an alternating current circulates in the wire, generating a force that, in the best, should be proportional to the current.
This means that, if the current in the wire is:
i(t) = Imax*sen(wt)
the resulting force should be:
f(t) = Fmax*sen(wt)
If the force is produced as stated by the Lorentz Law for orthogonal vectors, the magnitude of such force will be:
F = ilB
where "i" is the current in the voice coil, "l" is the length of the wire that is effectively immersed into the magnetic field of the gap and "B" is the magnetic field strength. Then, ideally the resulting force should be:
f(t) = Bl*Imax*sin(wt)
Usually, in low frequency drivers (woofers), the voice coil width is bigger than the gap's height and some wire turns of the voice coil result placed in regions of diminished magnetic field strength, but efforts are done trying to keep the Bl product constant along all the voice coil travel. This could not happen with high frequency drivers (tweeters) due to the small displacements of the voice coil.
The voice coil is suspended to place it in a rest position (when no current flows in the wire) at the center of the magnetic field in the gap. The suspensions (surrounding the cone, or dome, and at the diameter where the cone, or dome, and voice coil join one to another) act as a spring that offers a force that opposes to that of Lorentz, to return the voice coil to the rest position.
The ratio of the membrane´s displacement to the suspensions' opposition force is called the suspensions' compliance.
Loudspeakers are spring-mass-damping forced oscillators having a natural resonant frequency as a consequence of the suspensions' compliance and the membrane mass. This frequency is calculated as:
fo = 1/(2*pi*SQRT(Mms*Cms))
where pi = 3.14159265358..., Mms is the "mechanical mass" of the membrane, Cms the "mechanical compliance" of the suspensions and "SQRT" means the "square root of...".
The adjective "mechanical" is necessary because in the analysis of the loudspeakers behavior, also "acoustical" mass and compliance as well as resistance, result.
Damping in loudspeakers is due to all elements that dissipate mechanical energy of the oscillations. In many texts is read that the soft materials in the suspensions are such dissipative elements, but changing the magnetic field strength in the magnetic circuit's gap will produce a change in the mechanical resistance of the system, and also a change in the membrane's mass or the introduction of a viscous fluid in the gap will do it.
The magnetic field strength can be changed by attaching an external magnet to the magnetic circuit, that can be in attraction or in repulsion with the circuit's magnetic field.
The mass of the membrane can be increased by attaching stickers to its surface or by adding modelling clay to it as when Mms, the membrane's mass, is determined.
Also, by covering with porous cloth the windows of the loudspeaker "basket", the mechanical resistance is increased. Such basket is the rigid frame where the magnetic circuit and the mobile components are supported.
The mechanical resistance Rms imposes a restriction to membrane's axial movements. When the electrical impedance is plotted as function of the frequency of the applied signals, a characteristic peak shows the main resonant frequency. Low mechanical resistance systems show higher resonance peaks than those having higher mechanical resistance, for same "Bl" product of the voice coil and the magnetic field in the gap.
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