Is there any concept of speed in analog transmission? In digital data transmission, the speed is measured in bits per second. 1) Is there any concept of speed in analog data transmission? 2) Shannon Hartley theorem limits the speed achieved in digital data communications. Is there any equivalent of the theorem in the analog data communication?
Additional information:

The Shannon–Hartley theorem states the channel capacity C, meaning the theoretical tightest upper bound on the information rate of data that can be communicated at an arbitrarily low error rate using an average received signal power S through an analog communication channel subject to additive white Gaussian noise of power N: C=Blog2(1+S/N), where C is the channel capacity in bits per second, a theoretical upper bound on the net bit rate (information rate, sometimes denoted I) excluding error-correction codes; B is the bandwidth of the channel in hertz (passband bandwidth in case of a bandpass signal); S is the average received signal power over the bandwidth (in case of a carrier-modulated passband transmission, often denoted C), measured in watts (or volts squared); N is the average power of the noise and interference over the bandwidth, measured in watts (or volts squared); and S/N is the signal-to-noise ratio (SNR) or the carrier-to-noise ratio (CNR) of the communication signal to the noise and interference at the receiver (expressed as a linear power ratio, not as logarithmic decibels).

Source https://en.wikipedia.org/wiki/Shannon%E2%80%93Hartley_theorem
 A: There is no mathematical distinction between digital data and analog
data.   Shannon's theorem applies to 'analog' data transmission.
We're accustomed to  having massively redundant data in voice (you
can distinguish words, stress, and the identity of the speaker, all
at the same time), but if you constrict the bandwidth and signal/noise
you lose the data accordingly.  It won't be easy, though, to MEASURE
the loss.
A: I have not seen theorems but people have learned how to work with what they can measure. 
For quality it has been basically subjective opinions,ma erased out over groups of people. That's how ATT decided what was good enough for toll quality voice, about 3.3 KHz, and I can't remember the SNR. It led to an arbitrary scale which was made methodical with the group surveys. 
For FM cellular radio (the first generation of cellular with the ATT AMPS system it was an SNR of 18 dB they settled on, it was FM with the voice source I think the same 3.3 or so KHz (maybe it was more I forget), and of course it had the FM index they selected to get both the SNR and qualitative methodical quality. Of course there was also voice commanding. 
For many other radio comms including microwave they came up with SSB, and many variations. Because it so what they could control they controlled the RF parameters, the harmonics and dynamic ranges, the power and the noise factor, and so on, through analog engineering - no theorems, but plenty of RF engineering. For radar the series of books by the Radiation Lab and then the Radar Handbook put it all together, before much digital.   
I know less about video transmission, like analog TV but the BW was around 4 MHz baseband. I suspect the methodology was similar, but maybe they got it to be more methodical and better.  
There's been some great telecom handbooks, I had one but cannot remember the author or title. Lots of details for all of those, and many more on the details of,the modulation so, performance factors and measures, and much more. They usually have covered radio, TV, satellites and microwaves. 
It really got much more numerical and scientific with digital signals because you could duplicate results. More of a lab art form before, but they learned how to make very robust equipment - not much of that nowadays. 
A: There can be no direct equivalent, because an analog signal cannot be measured in bits.  However, the concepts of Bandwidth and Signal to Noise Ratio may cover what you are looking for.  In addition, there are many cases where bandwith-gain products are a major limiting factor in the circuitry that makes up the analog signal path.
A: The measure analogous to 'bits per second' that people care about for (electrical) analog signals are signal-to-noise ratio and bandwidth. The Shannon-Hartley theorem tells you how to calculate bits per second from S/N ratio and bandwidth.
Some examples: 
Human hearing has a bandwidth of about 20 kHz. A narrower bandwidth will result in perceptible changes, a wider bandwidth won't improve the sound. If you have a wider bandwidth available you can use some of the bandwidth to send a different signal. 
A Hi-Fi sound system requires a signal bandwidth of 20 kHz (or twice that for stereo) and a S/N ratio that is high enough so that the noise will be imperceptible. Vinyl records provide the 20kHz bandwidth (and more), but have a low S/N level. Magnetic tape has a higher S/N level, which also depends on the kind of tape. For magnetic tape in general the bandwidth depends on the speed at which the tape moves past the recording head. The 'tape hiss' component of the noise depends in a large part of the physical width of the track on a tape. Stereo sound on compact cassettes divides the mono track into two, each with half the width, resulting in more noise.
Analog television signals have a bandwidth of several MHz. Developing the technology to record such signals on magnetic tape or on disks was a challenge for a long time. Standard VHS tapes only have a signal bandwidth of 3 MHz for the B/W portion, and 400 kHz for the chroma. That is much less than the broadcast tv signal, which explains why video recordings look more smeared out than broadcast tv. Video long play modes will move the tape slower, reducing the available bandwidth or increasing the noise (if the individual tracks on the tape get written closer together).

Some of the other answers here mention phenomena that are specific to specific forms of analog signal such as wow/flutter (tape), reflections/multipath (coax and broadcast), etc, but in my opinion those are just specific cases of noise, albeit they are not white noise. Specific modes of digital signals also have their particular idiosyncrasies. An internet connection can suffer from packet loss, packet reordering, corruption, collisions, congestion, latency and jitter, routing changes, etc. As a user, you don't notice these directly, but they all translate into slower internet. The universal terms that apply to any kind of electrical analog signal are bandwidth and signal-to-noise ratio.
