Attenuation and bandwidth
As mentioned before, the attenuation of twisted pair is proportional in the thickness of the wire and in the square root of the frequency.
Twisted pair cables of different categories allow different bandwidths ranging from 1Mhz to 600Mhz.
The transfer rate on a twisted pair is different for different category cables, it varies from 10Mbps up to 10Gbps.
Because of its nature a twisted pair must have a repeater every few kilometers, if used to transfer analog data (like voice for phone network) it's enough to place a repeater every 5km, but if used to transfer digital data it requires a repeater every 2km. That is why twisted pair is mostly used for LAN, where it isn't used to cover great distance.
Applications
Telephone – Usually the cable that run between the user (your home or office for example) to the phone company closest station are twisted pair cables, because voice data requires very little bandwidth and the twisted pair cables are very cheap to install (you need to wire every house to the telephone exchange). Usually in office buildings and residential buildings, a network of twisted pair cables connects each of the houses/offices to the nearest phone station. The phone station is in turn connected to the next phone station by fiber optic cables.
LAN – Nearly every wired LAN in the world uses twisted pair media. Not just because it very easy to install and use but also because it's very cheap compared to any other media. These days most LANs consist of several hosts (PCs) connected to one router using a 1Gbps or 100 Mbps transfer rate.
Because LANs are short ranged networks, usually in a building or a complex, there is never a big distance between one network device to another. It's therefore possible to transfer a high frequency signal on top of the twisted pair with very little noise.
When twisted pair is used for LAN, multiple twisted pairs contained in a single cable are used to connect between network devices. This enables us to to achieve higher bit rate over inferior twisted pair categories, for example Cat 5 can go up to 1Gbps using 4 twisted pairs and Cat 3 can achieve up to 100Mbps with 3 twisted pairs.