I found that the distance that data transmission can be done in Ethernet has to be reduced when the transmission speed increases, which in turn leads to the use of Carrier Extension, Frame bursting, etc. Is noise a fact that determines this distance? Then how does noise affect this transmission distance?
If I'm understanding your question correctly, its probably not noise (interference from external EM/Power sources), but Signal Attenuation (degradation of the signal traveling through the wires, caused by the imperfect nature of transmitting signal on copper). this would lead to more corrupted or lost frames, which in the case of TCP data, would trigger resends.
in the old days of bus networks, collisions were an issue, and CSMA/CD was employed to avoid otherwise mitigate collissions caused by two machines starting to transmit at approximately the same time, such that for the cable length, the sending machines had to pause for the length of time it took a 64k signal to traverse the max cable length at wirespeed, causing a relationship between transmission rate and cable length based on the logical operation of the network (not the physical).
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Both 10-baseT and 100-baseTX have a 100 meter specification. However, to reliably get 100m out of 100-baseTX, the cable has to conform to ANSI(TIA/EIA-568) specifications, particularly the use of either the T568A or T5678B (see previous hyperlink) wiring pinout standards. Each unshielded twisted pair of wires in cat5 have differing rates of twists per meter, to reduce crosstalk and interference. 10-baseT, however, only requires cat3 cable, which has a less rigourous specification, so in the case where a 100m cable is not terminated to spec, has been bent too sharply (less than 4x the outside diameter of the cable), or is otherwise degraded, it may no longer be fit to run 100-baseTX, but still adequate to run 10-baseT. However, when cables conform to the specifications above, both 100-baseTX and 10-baseT are good to 100 m.