Why do you need both a cable modem AND a router for wireless internet?

In brief – Your cable provider might sell a model in which has wireless capabilities built into it. My Ambit for example has, wireless, and a 4 port switch in it.

http://www.ubeeinteractive.com/index.php/products/product-overview/wireless_cable_router2/

As far as why you would need the different devices, your cable modem that you have can be split into two logical sides down the middle. You have the public WAN (Wide Area Network) side (with the Coax connected to it possibly on the left) and the private LAN (Local Area Network) side of it, connected with the RJ-45 connectors (possibly on your right). With these two different physical types of cabling, your cable modem also acts as translator in a sense, and takes the digital signals sent from your computer, and modulates them into RF signals which are sent on the coax cable side of the modem.

Your Cable ISP gives you 1 public IP address to cruise around on the internet (just assume its just signed to the coax cable side).

So for your multiple computers at home to surf the web with their private addresses, your cable router needs a way to translate your private IP addresses to that single public IP the cable company gives you.

This is accomplished using a feature called NAT (Network Address Translation-Which is beyond the scope of this answer).

To add the wireless functionality to your home network if you couldn’t get a modem from the cable company with wireless built in; You would want to buy a wireless access point, and connect it with a straight through Cat5 cable to your cable modem RG45 ports – and configure its wireless settings.

You can think of this wireless access point similarly as the modem, if you split it in half, say the left half would have the Cat5 cable, and the right half would have the wireless antenna.

So if you were on the wireless with your notebook, the traffic comes from your notebook in through the antenna, and it switches the RF signals to digital and sends them to your cable modem, and vice versa.

Doing this will add wireless functionality to your network. And aside from the WEP/WPA security you set up on the access point, its passive in the sense that your wirelessly connecting computers will still pull their private addresses from your Cable modems DHCP server.

Which is what each device does.