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How does a speaker work?

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Basically the movement of the speaker is the cause of the stereo (mono speakers) making the noise via induction. The Induction is the result of controlled oscillation of electrical current.
A speaker is essentially an air pump. I like to say the bigger the pump the bigger the sound!!!
A driver is a device that reproduces sound. Drivers consist of woofers, subwoofers, tweeters, midranges, compression horns etc. A driver consists of a magnet assembly, a metal or composite basket/frame, coil and cone or dome.
A driver has a coil of wire that is electrically attached to your amplifier. The coil is the electro magnet not the magnet itself. The magnet is usually made of ceramic but used to be made of Alnico (Aluminum, Nickel, Cobalt; expensive compared to ceramic) and is more often now made of neodymium (a lighter stronger material than ceramic). The magnet has a permanent magnetic polarity that does not change. When the coil of wire is placed inside the magnet assembly "pole piece" and an alternating signal is placed thru the coil it will cause the coil to oscillate as the coil will now attract and repel within the magnet assembly as the polarity changes on the coil. The coil is attached to a cone (or dome in the case of tweeters and some midranges) which is capable of moving air more effectively.
Speakers consist of these drivers usually a woofer, a tweeter, and sometimes a midrange. A speaker will almost always also have a crossover network which is basically a filter network that effectively divides the signals to each driver so that the bass only goes to the woofers and the high freq only goes to the tweeters.
Typical speaker arrangements contain multiple speakers: two for a simple stereo system, or more for more recent systems. All multi-speaker systems need observing the polarity such that the coils in all speakers make the same, synchronized, movement: in a multi-speaker system, some sounds only come out of the left speaker, or the right speaker. That makes the stereo effect. The majority of the sound, however, is being emmitted through all speakers at the same time. The bass drum, for example, can typically be heard through the left and the right speaker at the same time.
Wiring all the speakers in such a system while observing their polarity allows the speakers to make a syncronized movement. For example, when the bass drum hits, all affected speaker coils would make a movememt towards you, then away from you, etc. If one of the speakers is wired with the reverse polarity, this speaker would start by moving away from you, then towards you. Air would simply be shifted back and forth between the speakers, instead of applying pressure on your ear drums.
To avoid that effect of lost sound energy, speakers should be wired up with the same polarity even though they are driven by an alternating current (AC) signal.


Additional
Another type of speaker is the electrostatic loudspeaker. Electrostatic loudspeakers are generally very much more expensive than the electromagnetic loudspeaker described above and, in most cases, far superior. Physically, they look completely different from conventional loudspeakers, usually taller and wider, but very much thinner (rather like a plasma television compared to a CRT television!).

Electrostatic loudspeakers work on the principle of attraction and repulsion between electric charges. The general principle is as follows. The diaphragm ('driver') , a large rectangular flexible sheet of material, such as mylar, is coated with a conducting layer and placed between two large metallic perforated sheets. A high DC voltage is placed between across this arrangement and the audio signal is impressed upon the voltage, causing the polarities to change in magnitude and direction in accordance with the musical signal. The result is that the flexible sheet will then move, acting in much the same way as the diaphragm described in the previous answer. Compared with electromagnetic loudspeakers, the diaphragm is much lighter and reacts far more rapidly to variations in signal. Furthermore, because the whole of the surface of the diaphragm is charged, the resulting forces are applied to the whole of the surface of the diaphragm rather than being 'pushed' or 'pulled' by a separate coil -as is the case with the magnetic loudspeaker.

Like electromagnetic loudspeakers, electrostatic loudspeakers also have 'woofers' and 'tweeters' -different-sized rectangular diaphragms.

Because electrostatic loudspeakers require a very high voltage (thousands of volts) to operate, they each have a heavy built-in transformer and rectification system and must, therefore, be connected to an electricity supply.

Electrostatic loudspeakers were developed, commercially, by a British hi-fi company called Quad, which has been manufacturing them since the 1950s.
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