Speaker Driver Response Impedance Frequency Equation

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I am looking for equations which would describe sound that a speaker produces.If I understood the principle how a speaker works correctly, there are a permanent magnet and an electromagnet.As alternate current flows trough a wire, the poles of electromagent constantly swich places. When current flows in one direction, the magnet repels the electromagnet, when the current flows in another direction, the magnet atttracts the electromagnet, so the electromagnet oscillates.The frequency at which it oscillates probably depends only on the frequency of the signal, but what the amplitude of the sound (loudness) depends on? Does anyone know any equations with explanations?(if I am wrong about anything here please tell me so). Yes, the frequency of the sound played by the speaker is exactly the frequency of the current that flows through the coil (electromagnet).The loudness of the speaker depends primarily on the intensity of the current through the coil and the strength of the permanent magnet.

But actually it is given by the volume of air displaced by the membrane when it oscillates. This means that the loudness also depends on the dimensions of the speaker.Another thing which increases the loudness of a speaker is it's enclosure. Because the sound waves produced by the back of the speaker are in antiphase with the waves produced by the front of the speaker, ther will be some destructive interference if the speaker is not enclosed.

There are some useful equations for buiding a speaker enclosure. I used them when I built my bass-reflex subwoofer enclosure. Could you give me any equations, with explanations?I tought that amplitude of the sound must vary with frequency, but some people told me its not true.therefore the factors that would affect the amplitude of the sound would be:1. Current through the coil and since its resitance does not vary, it only depends on the voltage?2.

B of the permanent magnet3. Size of the speakerEnclosure?Do you by any chance know where could I find equations as simple as possible with explanations as understandable as possible?When I typed Loudspeaker equations into google I got thisCan you explain those?Thanks a lot for your help.

I tought that amplitude of the sound must vary with frequency, but some people told me its not true.They were wrong and you were right. Of course it depends upon frequency. The response of the coil depends strongly on frequency, the response of the mechanical system (springiness of the air and the paper, mass of air, paper, coil, etc. Etc.) depends strongly on frequency, and so on.When speaker manufacturers build speakers, they try very hard to make the output level not depend too much on frequency. Speakers always have some frequency repsonse that isn't a straight line.

That's why some companies can charge you $10000 for a speaker, if it has a fairly flat response.Building and modeling speakers is a very complex science, and acoustic engineers can make huge money trying to do it well. I think what you need is to study acoustics a little (it's an extensive science), if you want to know about how loud the output will be for a certain shape of speaker and a certain frequency. I know you want something simple, but then you shouldn't be asking about speakersIf you are interested in modeling the speaker electrically (i.e., you want to know how the speaker will affect the circuit, but not necessarily how loud the sound will be), that's a lot easier.

A speaker is an inductor and a resistor in series. Of course, it's a little more than that if you want to model the effect of the mechanical system too. But for most electronics purposes, inductor + resistor is close enough. Do you by any chance know where could I find equations as simple as possible with explanations as understandable as possible?When I typed Loudspeaker equations into google I got thisBrokenI don't know of any equations made specifically for calculating the intensity of the sound played by a speaker. Instead you can use general physics equations (like those in the pdf you mentioned) to find, for example, the relation between the intensity of the input current and the distance travelled by the speaker's cone, and then relate this distance to the intensity of the sound.

Speaker Driver Response Impedance Frequency Equation Examples

Thanks for replies.Could you give me an example how would the shape of the speaker affect the amplitude of the sound? Thanks for replies.Could you give me an example how would the shape of the speaker affect the amplitude of the sound? Is it just the volume of the air displaced by the speaker or is there something more?There is a LOT more. The way air vibrates in 3 dimensions is pretty complicated, and any resonances of the system will dramatically affect the loudness of the sound at certain frequencies. That said, I guess if you have a good enclosure around your speaker, and you are listening from directly in front of it, and you're neglecting the effects of the room you're in, you could approximate it by just thinking about the area of air it displaces. But understand that is only a rough approximation. Yes, I see that the equations dont describe the loudness, as it depends on many other things including the properties of the air.I just want equations relating the current and the distance travelled by the cone.That depends on the acoustic impedance seen by the speaker, which involves every single bit of the complexity of the problem.

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These equations seem to be based on some very basic approximations, and don't involve acoustics at all. Though I think acoustics will be most of the work in the problem.May I ask why you want to know all this? I mean what are you trying to do?

There might be an easy way out. I think of a speaker as a servo device. It's commanded to position itself based on the +/- voltage received. The accuracy of it's response determines the quality. It's power handling capability detemines it's 'quantity'.Similar to a good servo, a good speaker system will need some sort of feedback to prevent overshoot and a means to dampen the overshoot tendency.

A drag inducing device or negative feedback circuitry will do this. The result is increased accuracy, but reduced loudness (efficiency in terms of sound power output versus input power is reduced).In terms of quality, true studio monitor systems are the most accrate, followed closely (sometime the same accuracy, but nicer looking) by 'reference' speaker systems targeted towards music listening. Home theater systems, are a big step down from this.

Thanks, you have all been very very helpful.Here is text I wrote, and I would like you to tell me did I understand everything correctly. If I misunderstood something or made a mistake somewhere, please tell me so that I can correct it.ThanksSpeakerSpeaker is an electromechanical device used to convert an electrical signal into sound.

There are several existing designs, but the speakers consisting of dynamic drivers are most commonly used today. Here we will primarily focus on explaining how this type of speaker works.A speaker can consist of one or more drivers. The main parts of a driver are a diaphragm, a basket (or frame), a voice coil and a permanent magnet. Diaphragm is on the wide end attached to the basket by a rim of flexible material called suspension or surround. On a narrow end it is connected to the voice coil.

The voice coil is attached to the basket by a ring of flexible material called spider, which holds it in position, but also allows the coil to move back and forth freely.A speaker produces the sound by vibration of the diaphragm, also called cone, which is usually made of paper, plastic or metal. The movement of the diaphragm is what sets the particles in air into motion, therefore creating a sound wave. The characteristics of the motion of the cone determine the characteristics of the sound produced.

The frequency of the sound depends on how fast the diaphragm moves back and forth (frequency of its oscillation). The amplitude of the sound wave (loudness of the sound) is on the other hand much more complex, but one of the factors (the one that can be changed by changing the electrical signal) on which it depends is how much the diaphragm moves from its initial position.As shown on the diagram, the cone is attached on one end to the voice coil and it is the movement of the voice coil what moves the cone.

The voice coil consists of the coil of wire wrapped around a piece of metal, usually iron. It is important that the material used has ferromagnetic properties, so as the current flows trough the metal wire the magnetic field is created around the wire and the metal wrapped in the wire becomes magnetized. The magnetic field created by the coil and the piece of magnet is thereforeB=B(applied) + μ0M(since magnetic field due to the current in the coil, Bappplied, alone and magnetic field due to the magnetised iron, μ0M, are in the same direction). Μ0M can be easily calculated if the relative permeability of the material, Km, is known usingμ0M= Km B(applied) –B(applied)As it will be explained further in the text, the direction of the magnetic field applied is being reversed constantly, so the metal used should be magnetically soft in order to avoid energy loss.The magnetic field applied, Bappplied, depends on the current in the wire.

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