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Because your wired computers go through a switch (connected to your broadband router), and because your access point is basically a switch (or bridge) between your wired and wireless networks, it will not put wired-to-wired traffic over wireless.
The switch(es) will learn which systems are on which ports, and filter that traffic from other ports.
There will be some broadcast traffic that does propogate to the wireless network (ARP, SAP, BPDU, etc).
Even so, you still want to put wireless security controls in place (WEP, MAC filtering, no SSID broadcasts, etc).
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