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Hi Jerry Welcome to the site.
Most likely due to the pre historic age of the unit I am guessing it would use 8 ohm impedance speaker ribbon cable
Due to its pre historic age it is very hard to find a manual or specifications on the internet most probably because it was made before computers were invented.
If the speakers have an impedance value on them you would use what ever the ohms value stated on the speakers.
Here is a guide on wire length versus impedance https://www.cambridgeaudio.com/en/blog/speaker-cables
and how to get the most efficient power transfer https://www.amplifiedparts.com/tech-articles/speaker-impedance-power-handling-and-wiring
if you google 8 ohm speaker wire retail
you should find a local retailer
Wattage is not the total solution to the problem. The amount of wattage an amp supplies is related to how loud you listen to the music AND how much power is left over so the amp can deliver when needed and not clip the available output signal and cause distortion.
Manuals Lib has the manual here: https://www.manualslib.com/products/Aiwa-Sx-Wna555-159268.html . You can download it or read it online. The speaker system has the model number SX-WNA555. The main part of the stereo system has the model number CX-NMA545.
You should be able to use any decent pair of speakers with an impedance between 8 Ohms and 16 Ohms and maximum power capability of at least 33 Watts. The link provided is for the specifications page of the owner's manual. http://audio.manualsonline.com/manuals/mfg/aiwa/cxnhmt75.html?p=31
Your Aiwa speakers are passive units and need considerable power to drive them to a reasonable volume level, comparative to the output of a PC.
The sound card of a PC produces a reasonable quality output but in the terms of power is a very modest output which is why the usual speakers used with a PC are active types - i.e. have a self contained power amplifier, usually driven by a remote power supply.
This type of active speaker is designed to connect via the headphone/speaker socket and still produce a good quality sound. This is possible as the speaker's internal amplifier is built with a particularly low impedance input that matches the low output impedance of the PC headphone output that would be unsuited to be connected to the average hifi amplifier.
Many PC sound cards have a Line Out socket that would be suitable for connection to many hifi amplifiers.
This Protection activates if you hook up Unmatched Speakers i.e less or over impedance as required by Aiwa Amp. 2nd reason can be extra speakers attachment.
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