A cable does not have any inherent bit transmission rate, whereas bandwidth is a measurable property. The cable can be thought of as a low pass filter. All cables can pass DC (f = 0Hz), but some cables have signal loss in the megaHertz range, while coaxial cable can go up to the gigaHertz range.
A cable can carry signal voltage, which is a continuous (i.e. analog) form of electrical energy. Voltage cannot be quantized, so the cable cannot carry digital data unless that digital information is modulated (or converted) to a waveform for transmission. The simplest modulation used for digital data is amplitude modulation, and is commonly known as digital or logic levels. Logic levels are okay for on-board circuitry and cables of very short length. Logic level is not used for longer transmission cables because, although trival and cheap to implement, it uses bandwidth inefficiently and is not energy balanced (consider the worst case of a long string of logical ones or zeroes).
The choice of modulation is a compromise based on the cable's bandwidth and attenuation properties and the complexity of the transmit/receiver electronics. Modulation for digital information can employ phase as well as amplitude. The modulation will determine the number of bits transmitted per symbol. For instance QAM256 can transmit 8 data bits per one symbol, but requires sophisticated transceiver electronics.
what exactly are these cycles if not the rate of bits?
Cycles of a pure sine wave (i.e. a single frequency, just the fundamental, no harmonics).
A digital data signal (using high/low logic levels) would have frequency components 10x to 100x the basic clock rate. If you're acquainted with Fourier series, then you're aware that a square wave is equivalent to an infinite summation of sine waves of related frequencies.
Bandwidth is measured in Hertz or cycles per second. For typical cables the bottom frequency of the band is DC or 0HZ, and the upper frequency would be the frequency of a pure sine wave of a given voltage that does not significantly attenuate (e.g. -3dB) over a given length of cable. Signal attenuation is an intrinsic property of cable; it is usually tabulated in the cable's spec sheet as a function of frequency (pure sine wave) and length.
The transfer rate (e.g. bits per sec) is established by design specification, and is a function of (at least):
- cable type and length,
- the capability & cost of transceiver electronics,
- connector design,
- the chosen modulation, and
- the protocol (e.g. Ethernet chooses powers of 10 (& then doubles it for full duplex), SATA chooses multiples of 1500).
For operational reliability the transfer rate actually chosen may be below the theoretical maximum rate.
A cable does not have any inherent bit transmission rate, whereas bandwidth is a measurable property. Therefore there is no conversion formula between the two numbers.