What happens when you don't match the speaker resistance with the amp output resistance?
My amp kit has an 8 ohm output and it came with an 8 ohm speaker. I pulled a couple of speakers out of an old boom box that are rated 3.2 ohms. Wiring them in series gives me 6.4 ohms. They sound better than the 8 ohm speaker that came with the kit.
What are the consequences for not matching resistances and how close should you be?
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That should be fine. We have used this amp circuit with 4 ohm speakers with good results in the past.
Non-matched impedance isn't an issue if an amplifier calls for an 8 ohm load and your speaker(s) read 6.4 ohms. Many older speakers will have readings that are not exact to the impedance marked on the frame (i.e. an older 4 ohm speaker might give a reading of 3.2 on an ohm meter, but it is considered 4 ohms).
The big issue related to matching load impedance comes when dealing with AC powered tube or solid state amplifiers. In this situation, if the speaker load doesn't match the circuit requirements, it can cause damage to the power output end of the amplifier. In a tube amp, it can lead to early failure of the power output tube(s), along with the output stage operating outside of optimum performance levels.
So while it is entirely possible to use a 4 ohm speaker on an 8 ohm cigar box amp circuit (as mentioned by Ben), in the long term, this imbalance may cause stress on the circuit's output stage, cause overheating, and maybe failure over time.
So would putting a 4 ohm resistor in series with the 4 ohm speaker eliminate that problem?
I can't say yes, since impedance (the speaker rating) is not resistance.
Try reading this article for a bit of insight, and maybe it will help.
not to restate what everyone else has said, but
it depends on the amp board. more specifically, it depends on how much output amperage it can take. Most can take a speaker load of either 4 or 8 ohms, and the spec sheet will say how much output power in watts it will deliver for each, and you can interpolate for a speaker ohm rating in-between.
If the speaker has way way way more ohms than the amp board can drive, it will sound very very very quiet. If the speaker has way way way too few ohms then the speaker will draw more juice than the board can deliver and the board will cook like a bit of steel wool across the terminals of a 9v battery.
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