One of the most important points when designing a circuit is the correct matching of one component or stage, to the next. It might be an electret microphone to the input of an amplifier or a pre-amplifier stage to an output stage.
When everything "matches-up," the circuit works perfectly. If they don't match-up, you will get poor transfer of waveforms and this is directly related to the transfer of energy. The result may be distortion or low output.
In many cases the matching will be done with a capacitor as it has the amazing feature of connecting two stages while keeping the voltage levels separate.
This is called AC COUPLING. 
Capacitors, however are not highly efficient at matching two stages and you can use resistive or direct matching if you need to transfer a large amount of energy.
Direct matching is called DIRECT COUPLING or DC COUPLING - meaning the DC voltages will pass from one stage to the other as well as AC waveforms. With AC coupling, only the varying signals (called the AC signals) will pass from one stage to the other.
Connecting two stage together is called IMPEDANCE MATCHING as we are connecting the "output "resistance" of one component (or "stage") to the input of another. We cannot use the term "resistance matching" as the resistance of both output and input consist of components other than just resistors and the value is changing according to the frequency being transferred.
This means you have to know how to match the two items to get the best results.
This is the skill of electronics.

Lots of decisions have to be made when designing a circuit. When an engineer decides on the value of a particular component, he generally has a reason for selecting the value. It may be to keep the overall current requirement as low as possible, it may be to create maximum gain, or one of a number of other reasons.
Most component values are obtained from his experience of how a circuit works, or from observing the effects. This can be called "intuition" or "knowledge." Rarely can you find component-values in a text-book.
This topic is enormous and some of our discussions may not seem to be correct. This is because the art of matching two items is not a "science." There are no "hard-and-fast" rules.
Sometimes, the worst mis-match produces the most amazing effect.
You may want to produce distortion or just detect the high frequencies such as the frequency of "glass-smashing" or the low frequency of  the change in air-pressure when a door opens. This type of requirement produces the most amazing circuits and that's why you have to sometimes think "outside the square" to get the results you want.
That's why "impedance matching" or "circuit designing" is such an art.

In most cases you need to build the circuit and experiment with different types of components, especially when you use items such as coils and transformers, as the size, shape and wire gauge can change the way it operates, enormously.
Sometimes the type of transistor is critical and sometimes the microphone or piezo diaphragm is important. These are all things you have to remember. Sometimes the exact-same device from a different supplier will completely fail to work.
I know it's complex but we have to start somewhere:

Let's start with a simple example of connecting two items together - a coil and a transistor.

CONNECTING AN INDUCTOR TO A TRANSISTOR
There are three ways to connect a coil to the input of a transistor. Fig 1 shows the connections:

Fig 1: Connecting a coil to a transistor.

The three circuits in Fig: 1 look similar, but their operation is completely different.

In circuit (A), the transistor is biased OFF. (Actually it is not-biased AT ALL).  No current flows through the transistor when at REST (called the QUIESCENT STATE) because the base is not supplied with a turn-on voltage of approx 0.7v. The voltage on the collector is equal to RAIL VOLTAGE.
The resistance of the coil does not matter. It can be 1 ohm , 100 ohms 1,000 ohms or more.
The only important thing is the voltage it produces when a magnet passes the end of the coil.
The voltage must be higher than 0.7v.
When a magnet approaches the coil, a voltage will be produced from the coil and the positive must emerge from the top of the coil. This will turn the transistor ON. The collector voltage will fall to about 0.5v
When the magnet moves away from the coil the voltage from the top of the coil will be negative and the transistor will not respond. If you want the transistor to respond to the magnet moving away from the coil, simply reverse the connections.
If the coil tries to produce a voltage higher than 0.7v, the extra voltage will be prevented from rising higher than 0.7v due to the characteristic of the transistor known as the base-emitter junction voltage.  However if the magnet passes the end of the coil at a faster rate, a higher current will be produced by the coil and this will be passed to the transistor to turn it on HARDER.
In this case the transistor will be able to drive a heavier load. In other words, the transistor will be able to activate a component such as a LED (in place of the 47k resistor). You will need to include a resistor of 100R to 220R to limit the current through the LED.
If you use a coil with more turns, the LED will turn on more brightly as the magnet is brought towards the coil. If you move the magnet past the coil FASTER, the LED will flash brighter.
The two features of the circuit are:
1. If a stronger magnet is used, or the magnet is moved faster or more turns are added, the energy from the coil (in the form of voltage and current) is passed to the base of the transistor to turn it on HARDER.
2. The transistor operates in two states. It is cut-off when no magnetic flux is detected and it is turned-ON when a magnet passes the coil.
These two states are called "OFF" and "ON." These two states do not happen instantaneously but are equivalent to digital states and we can say the transistor is operating DIGITALLY if we only talk about the completely-OFF state and completely-ON state.

Circuit (B) has different features.
The transistor is biased ON via the 2M2 resistor during the "rest" state. The collector voltage will be approximately half rail voltage.
Voltage from the coil will turn the transistor ON when the magnet is approaching the coil. When the magnet is moving away from the coil, the transistor will be turned OFF. The transistor will detect the slightest voltage from the coil as the base is partially turned-on via the 2M2 resistor.
The capacitor allows the base to be biased via the 2M2 without the low resistance of the coil affecting the voltage on the base.
This arrangement is very sensitive. The only problem is the transistor is drawing a small current when in the "rest" state.

Circuit (C) is a special design.
Resistor R_bias and the resistance of the coil must be selected so that the voltage on the base of the transistor is just below the point at which the transistor turns on- say 100mV. Any voltage above 100mV, produced by the coil, will turn the transistor ON. This circuit allows the bias resistor to deliver the first 550mV of "turn-on" voltage and the coil produces the remainder.
For this circuit to work, the resistance of the coil must be fairly high. The coil must allow 650mV to be developed across the winding due to the value of the bias resistor, and the bias resistor is selected to create this voltage.

DIFFERENT IMPEDANCE VALUES
In the three examples above, we have different values of "impedance-matching."
In the first example, a 1 ohm to 10k inductor (coil) will match perfectly to the input of the transistor.
In the second example the inductor can also be 1 ohm to 10,000 ohms or more.
The third example requires the resistance to be worked out so that 550mV is developed across the coil when it is in series with the bias resistor.
In the first two examples you can see the impedance of the coil can be almost any value.
This brings up an important point.
In the introduction, we mentioned the importance of matching stages. We have just shown that the impedance of the coil DOES NOT MATTER!
In this case, the important impedance-value is the "receiver" i.e: the impedance of the input circuit.
The input impedance of a transistor stage is a very complex value but we can explain it in simple terms.
You cannot simply say it is 1k or 10k or 5k at 7kHz. This may be true but the real value you need is the CURRENT required by the transistor for it to carry out its operation.
The current required by the base of a transistor is approx 1/100 of the current required by the load. (We are assuming the gain of the transistor is 100).
If the load current is 1mA, the base current will be 0.01mA = 10uA
If the load current is 10mA, the base current will be 100uA.
If the load current is 100mA, the base current will be 1mA.
If the load current is 1A, the base current will be 10mA.
If the load current is 10A, the base current will be 100mA.
In all cases, the coil is required to deliver this current.
To find out if the coil will deliver this current, you need to set up an experiment.
There is no way to mathematically determine if the coil will deliver the required current as the speed, strength and efficiency of the magnet are unknown factors. The diameter of the wire is also very important, as is the core material and how the coil is wound (in other words the length and diameter of the coil.  Jumble winding the coil will produce about the same results as layer-winding). 
To understand the capability of a coil, you need to perform some experiments. That's the purpose of performing "Physics Experiments" - the type of experiment you carried out in school.
A trained technician will be able to "see" if a particular coil will perform a particular function by drawing on his knowledge.
For example, if you put a 6v globe in the collector circuit and use a power transistor in the first circuit of figure 1, the globe will not illuminate. This is because you will not be able to swipe the magnet past the coil fast enough to deliver pulses of current equal to about 1/00th of the current needed by the globe.
If you place say 4 powerful magnets on a rotating shaft and increase the RPM, the pulses of energy produced by the coil will gradually increase and the globe will begin to glow (flicker).
If you want a coil to illuminate a globe, without a transistor, you will have to design a coil especially for the application. This is an entirely different application and can be quite easily done with a coil of about 100 turns of thick wire and a strong magnet.

CONCLUSION
We have shown a coil (inductor) will interface to a transistor because the transistor requires approx 0.7v and less than 1mA for circuits (A) and (B). Any coil able to deliver these values (when a magnet is passed across the end), can be used.
We have shown the impedance of the coil is not important.
We have shown the impedance of the transistor is not the relevant parameter.
We have shown the base-voltage (0.7v) must be supplied by the inductor.
We have shown the current requirement of the base must be supplied by the inductor.
This is how "impedance matching" is done in this case. If the coil will deliver the required values, it is suitable.
When connecting other devices to a transistor, we need to consider other parameters.

CONNECTING OTHER DEVICES
Many other devices can be connected to the input of a transistor.
The best method is "trial-and-error."
Simply connect the device and see if the circuit works as required.
This saves an enormous amount of mathematics, calculating the size of the waveform produced by the device from data sheets and trying to match it up to the input of transistor by reading a set of graphs for the transistor.
Not only is "trial-and-error" the quicker method but it produces GUARANTEED RESULTS.

The following diagram shows different devices connected to the input of a transistor.
You may not think some of them will work but if you build the circuits you will get some very interesting results.

Fig 2: Connecting devices to a transistor.

As we have said, connecting two items together involves "impedance matching." They must match fairly-well to prevent "signal attenuation" (signal degradation - reduction in size). Some attenuation always occurs as the receiving device uses some of the energy in the "reception process" and this reduces the amplitude of the delivering signal. The receiving device then amplifies the signal. The receiving item can be a transistor, chip or any other amplifying device.
The two items can be directly coupled or capacitor coupled. For the moment we will cover capacitor coupling.

HOW THE CAPACITOR WORKS
The capacitor is exactly like two people holding a shock absorber. The first person pushes the shock-absorber and the second receives some of the effect as the shock-absorber absorbs some of the shock.
Another example is to stand a mattress on its end and try to fight someone on the other side, thorough the mattress. They will get very little effect.
In the same way, one plate of a capacitor is raised and the other plate is pulled up, during the positive portion of a waveform.  But the capacitor is charging during this time and the second plate is not pulled up to the same voltage-level. In other words it absorbs some of the voltage. The size of the capacitor and the speed it is pulled up also has an effect on how much the other side is affected.
When the waveform is falling, the capacitor has to be discharged so that its "pulling-effect" will be available on the next cycle.
In the diagrams above, the base of the transistor does not perform any discharge and it is left to the very slight effect of the base-bias resistor.
This is one of the reasons why the capacitor cannot perform a very good transfer of signal.
In theory the capacitor does not work but in practice the circuits work fairly successfully.

HOW TO KEEP A CIRCUIT HIGH OR LOW IMPEDANCE:
When creating or modifying a circuit, it is important to keep it "high impedance" or "low impedance." 
In other words, you need to know if a circuit is high or low impedance and work out if it has a special reason for the way it has been designed.
We have already discussed the features that make a circuit high or low impedance and how to recognize these features.
Basically, these features have to be maintained if you want the circuit to perform as originally designed.
The easiest way to maintain the conditions is to measure the current taken by the circuit, view the waveforms and record any frequencies etc. Listen to the output if it is an audio stage.
These are the parameters that must be maintained.
If you want to change the frequency of the circuit or some other characteristic, change one component at a time and re-check the parameters - especially the current consumption.
If you have the luxury of keeping the old design while creating an improved version, you will be able to compare the old with the new.
This is extremely important with audio circuits or tone circuits as distortion can very easily creep in.

REACTANCE
There is also another term that defines the resistance of a circuit. It is called REACTANCE. It is used when a capacitor is present in the circuit.
When a signal passes through a capacitor it appears to the surrounding circuit as a resistor with a particular value. The value is called REACTANCE.
As the frequency increases, the REACTANCE decreases.
The terminology is called CAPACITIVE REACTANCE.
The diagram below shows a low input frequency, medium input frequency and high input frequency and the capacitor appears as a high, medium and low value resistor: