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Assume that there are two computers which are connected with a copper cable, e.g. Ethernet. Also, there is a radio connection between them, e.g. AM radio, in order to exchange data. When we try to send data from one to the other, which one would be faster? Assume they are the same distance away.

As far as I know, the propagation speed of electromagnetic signals in the air is better than the copper. On the other hand, frequency of the AM signal is smaller. Is there any other factors which affects the speed?

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    $\begingroup$ For sufficiently large one-way-bulk transfers the speed of the medium (latency) doesn't matter. As long as you have an outstanding transmission size of the bandwidth * delay (typically called the bandwidth-delay-product) all that matters is the bandwidth. This is why a truck full of hard drives is still the fastest way to get huge amounts of data across large distances. $\endgroup$ – Brandon Enright Dec 21 '13 at 19:19
  • $\begingroup$ Let's assume that we are transferring only 1 bit (theoretically). $\endgroup$ – Ricardo Cristian Ramirez Dec 21 '13 at 19:25
  • $\begingroup$ Then the answer is trivial. Whichever has the lowest delay (radio) wins. EM waves through air are way faster than electrical pulses through wire. $\endgroup$ – Brandon Enright Dec 21 '13 at 19:26
  • $\begingroup$ I should add that your question about which is faster directly relates to a latency arms-race among high-frequency traders. In HFT latency is the primary factor in profits and there is a ton of money being spent to get the lowest latency, closest to the stock-exchange links possible. This includes a point-to-point microwave link from Chicago to New York: cnbc.com/id/100695563 $\endgroup$ – Brandon Enright Dec 21 '13 at 19:33
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    $\begingroup$ Obligatory xkcd "What if" on bandwidth: what-if.xkcd.com/31 $\endgroup$ – Kyle Kanos Dec 21 '13 at 20:27
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Your question is pretty severely under-defined and you've really touched on the tip of the iceberg for a huge subject of information theory and network engineering. The bulk of this isn't physics so I will keep my answer brief.

This is how I've interpreted your question:

If I want to transmit data from point A to point B, is it better to have:

1) A very fast but long-delay link (like coper cables)

2) A very slow but very short-delay link (like radio transmission)?

The answer in the general case is "it depends" but for all transfers above some total amount of data, option 1 is better choice.

The speed at which you can transmit is called the bit rate (sometimes baud rate or symbol rate) and the link delay is usually called the latency. The bit rate is very closely related to the bandwidth.

If all you want to do is transmit a single bit, then (within reason) the bit rate doesn't matter. All that matters is which link will get the bit there sooner and that's entirely dependent on latency.

But, if you have a lot of data to transfer, you can keep on writing data to the link before the data you started writing has even arrived. The measure of how much data the link can holed (link capacity) is usually measured with the bandwidth-delay-product.

The total time it takes to transfer data is:

$$\mathrm{Time} = \frac{\mathrm{Number\ of\ bits}}{\mathrm{bit\ rate}} + \mathrm{Latency}$$

As you can see, the latency is a constant factor and only really matters when the total amount of data is low.

One good example of this is satellite TV providers. The transmission latency is very high to reach and then send from a geostationary satellite in orbit but they're able to send huge amounts of data in many television channels all at the same time because of the high bit rate.

So to answer your original question, coper wins when you have a lot of data to transfer.

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  • $\begingroup$ Latency for wireless is often dreadful. A key factor here is signal quality: wireless SNR is way inferior. So a wireless system can and does easily collapse under significant load owing to requests to resend when data become corrupted in sending. $\endgroup$ – Selene Routley Dec 22 '13 at 2:34
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For 1 bit information, what you care is the latency between two computers.

Since the EM signal is essentially travelling at the speed of light in the atmosphere, so it is expected to be faster than copper wire which transmit signal only at around 60% speed. For short distance communication, radio signal can be directly transmitted between two towers (say, ~10km if the tower is high enough and not blocked). However, Earth surface is curved and radio signal cannot transmit directly for long distance, which requires the reflection from the upper atmosphere (the ionosphere at around ~100km). Therefore, it is only fast at least this long distance.

That said, the latency of copper wire is low for the intermediate distance between ~10km to ~100km. But outside this range, radio wave win.

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One of the factors that the other, excellent answers don't address is signal to noise, although I agree that latency is often the main factor.

Wireless often has a dreadful signal to noise ratio. This weighs on the spectral efficiency $\eta$: how many bits one can send per symbol. For additive Gaussian noise, the number of bits per symbol that can be sent is, through the Shannon-Hartley form of the Noisy channel coding theorem (see also here):

$$\eta = \frac{1}{2}\log_2(1 + SNR)$$

(see also my answer here where I calculate in detail the capacity of fibre optic links). If a copper pair achieves a signal to noise of $10^4$ whilst a wireless network (often realistically) an SNR of 10, then this is roughly a factor of four gain in speed of the copper relative to wireless. The Shannon theorem assumes our coding is "perfect", which means that there is enough redundancy (checksums of parity bits and so forth) that the probability of error is vanishing. Real codes are not as good as this, and wireless networks often corrupt data; when this happens there needs to be a retransmission. If retransmissions are often, this devastates the spectral efficiency as what should take one transmission often takes two or three tries.

Lastly, copper pairs are not hugely slower in transmission than freespace. Although the drift velocity of electrons through wires is tiny, the wires only guide the signal energy, which mainly propagates in the freespace (or insulator) around the wires. So the signal velocity is an appreciable fraction of $c$. TEM modes in minimally insulated pairs propagate at just under $c$, the only deviation is from:

  1. The skin effect, i.e. that the EM field penetrates the conductor slightly; and
  2. the permitivity of the small amount of insulation you will need. Two bare wires running parallel in space support modes that propagate a fraction of a percent below $c$. A good working figure would be more likely to be $0.5 c$ or something like that. The old co-axial cables with the braided outer conductor and polymer in between the conductors get about $0.7 c$ if you measure the delay of a square pulse through one of these on an oscilloscope. It's an easy experiment to do if you can get hold of a roll of 10 metres or so of cable and even a modest, 100MHz scope. Try it; you'll be surprised! Indeed it would be good if you reported the answer for Ethernet cable back to this question as your own answer!

What you find is that most networks have a speed $\times$ bandwidth product and the underlying physics for this is a signal to noise ratio that worsens with length of transmission. To understand this, you need to so roughly the same calculations as I have done in my estimate of the capacity of fibre optic links: the principle is the same for copper and for freespace, assuming that retransmissions are not needed.

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