Question: Let's say I have a short copper wire that I wish to transfer bits through.
I can push a bit on one end of the wire, and in no time (almost the speed of light) the bit will reach to the other end, and then I wait a second until I push the next bit.

As I understand, the transmission rate in this example is 1bit/sec and the propagation speed is nearly the speed of light.

Since the bit reached the other end so quickly, why should I wait a whole second before transmitting the next? So let's speed up the transmission rate to 1,000 bit/sec. Again, each bit will reach the other end in almost no time and wait about a thousandth of a second. **Is there any limit to transmission rate? Why do Ethernet cables have a limited transmission rate?**

As I read, the length of the wire should not change the transmission rate, but if I were to lengthen the copper wire to a large distance, it would take longer for bits to reach the other end, thus less bits will get to the destination in a second - lower transmission rate. where am I wrong? `:(`

Answer: 
The problem with the length and bitrate is closely related to the way how bits are represented.

The following description is valid for basic amplitude modulation that applies to your proposal of "sending bits through a cable". As @sawdust points out in the comment below, modern networks do things rather differently [1].

Ones and zeros are expressed by different voltage levels. In the digital domain, you can think of it as the perfect squares from the first plot in the picture below.

Now, if you transfer this signal over a cable, it will become distorted (see 2nd plot). There are a lot of factors like capacity and resistance of the cable, electromagnetic interference, ... Some electrical engineer might give you more details. The point is, that the distortion becomes worse in longer cables. That means the amplitude of the signal will decrease and the shape can change quite a bit.

At the end of the cable, the receiver will use the distorted signal to re-create the perfect square plot (see 3rd plot below). If the cable was too long and the distortion too strong (especially the smaller amplitude), the receiver might not be able to tell how the original signal looked like.
So that's the factor of cable length. 

The other problem is the increased bit-rate, since it will reduce the distance between the squares. The distortion might make it impossible to tell if there were 1 or 2 squares hidden in the now distorted signal. That's why you can't put the bits infinitely close together.

In the end, you can choose: high distance between the bits (low bitrate) and a long cable. Or a high bitrate and a short, high quality cable (that will introduce less distortion and dampening).

The figure below should help to illustrate how a square signal will deteroriate during a transmission. It's not the best example, so if anyone finds a better one, feel free to edit.

![enter image description here](https://i.stack.imgur.com/aHjCN.gif)

[1]: Modern transmission technologies use a high-frequent carrier-wave (a sine-wave signal) and that doesn't contain any information in itself and modulate it. This modulation (the changes to the original sine-wave) are what holds the actual information. In theory, all parameters of the sine-wave can be used to transfer information (frequency, amplitude, phase) and also combinations are possible.

However, some tradeoffs are still valid:

For example, in multi-amplitude modulation, where you have more then 2 different amplitude levels. You can use `2^n` amplitudes to encode up to `n` bits within each transmitted symbol. A higher value of `n` improves bitrate, but makes it more difficult to distinguish the `2^n` different amplitude levels.
There certainly is a maximum transfer of information rate for any given wire. I seem to remember there used to be a well respected formula for calculating it but I suspect is has been overtaken by newer information theories because I can't find it.

The factors though are many so it isn't at all easy - probably not possible - certainly not for me!! To work out (well not easily anyway).

In addition there are many practical limits to transmission rates.

Ethernet has set limits that are internationally agreed standards. This is so that they can be embedded into buildings (costly) with a known performance. The rated value of the cable is NOT the maximum transmission rate but rather the maximum *guaranteed* rate - IF it is installed correctly!!

Limits such as external noise, plug and socket mechanical wear, transmission noise from either end, cable bends, pressure on the cable, the electrical resistance in the cable and other components. All these things and probably more, take their toll on the ability of the cable to take a transmission that can reliably be put back together at the other end. They also limit the **length** of the cable. Exceeding the parameters or installing badly will result in unreliable transmissions. Of course, modern networks are designed to cope with transmission noise but the more they have to deal with, the slower and less reliable things get.