A speaker's impedance and power rating are two main parameters you should understand to choose a speaker that's electrically optimised for your amp.
This guide explains them in simple terms to get you started quickly.
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A speaker's nominal impedance indicates the intended amplifier output impedance that it was designed to work with.
There are two main rules to observe:
1) The overall impedance of your combined speakers should match your amplifier's output impedance as closely as possible.
2) When loading multiple speakers into a single combo / cab (eg. 2 x 12 or 4 x 12), ensure that all speakers have the same impedance rating.
(15ohm and 16ohm speakers can be considered as having the same impedance for this purpose)
If your amp's output impedance is given as a range (eg. 4 - 16ohm), then any speaker impedance within that will be safe. Some say a higher impedance speaker sounds slightly brighter, but this isn't verified.
Theoretically, matched pairs of speaker-amp impedance sound identical. Eg. 8 and 16ohm versions of the same speaker will sound identical, when connected to the 8 or 16ohm outputs respectively of the same amp.
However in practice, its common for amps to have varying tonalities across their different outputs, resulting in differences in sound with impedance-matched speakers. Some Freidman models are known to exhibit this, for example.
Some players intentionally use mismatched speaker-amp pairs. As the mismatch widens, the speaker's sound changes from its original design, which could be desirable for some. Too wide however, could damage your equipment. If you want to experiment with this, read Hugh & Kettner's guide first!
Power Handling (Watts)
The speaker's wattage rating indicates the maximum amplifer power output that it was designed to work with.
The rule is simple:
Choose a speaker with a power rating that exceeds the power rating of your amp.
If you connect multiple speakers in a cab, then the combined power handling is a multiple of the lowest rated. Eg. 50W + 30W speakers has a combined handling of 2 x 30W = 60W.
Running speakers beyond their rated power handling can cause speaker distortion, which may or may not be a sound you like! Too much power and they'll be damaged.