Which LAN hardware component is used to amplify the signal travelling on the cable?

Any active network device will do that. If this is a test question, answer "A repeater", as that is the only function of such device.

In truth, any device that takes a signal from one end and transmits it through another end will "boost" (amplify) the signal

• or, rather, it will send out a "new" signal carrying the same

information. Such devices include all types of hubs, switches and routers. Also, as mentioned above, repeaters.

If you meant "cable" as in "cable tv" - then it's the modem/router, usually the first device hooked up into the cable. As I've mentioned above, however, these devices take the signal in and put out a new signal on the other end, so they don't really "amplify it" as such (usually processing of the signal is involved).