For best performance and sound, speakers need to be mounted in an enclosure. Arcade cabinets generally make poor speaker enclosures.
Speaker enclosure design isn't a simple thing, the internal dimensions (internal air volume) and design (ported, bandpass etc..) of any given speaker cabinet has as much to do with the sound quality as the speaker itself.
Mounting any speaker in any old box (such as an arcade cab) usually leaves less than optimum results. Generally, bass suffers.
You can try the hit or miss approach. Enlclose the back of each speaker in some manner of sealed, solid box. This should improve bass response, but will likely still be less than optimum.
For a proper design, you would need some specifications on the speakers and you'll need to do some calculations to determine proper internal cabinet air volume for the speaker you are using and the enclosure type you would like to use. RadioShack used to sell a little book on speaker cab design and included good information on how to figure this all out, I don't know if they still carry this book or not. I'm sure you can google and come up with the same information as well.
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