A Cable Fault Location Estimator

My final project is as mentioned above in my Title - but not in time domain measurement but by amplitude measurement (positive half sine wave).

I would like to know what actual relationship between bandwidth and frequency in measurement ? How does the frequency differ in increase in length of coaxial 50 ohms cable ?

I am using VCO, precision rectifier (op-amp) which operates above 1 Mhz (please guide me this circuit of precision rectifier) and microcontroller (Arduino).

Kindly explain me in details and also show me its relationship in equation like -
(beta2 x length) - (beta1 x length) = pie
....
.... in terms of frequency

Cable fault location is the
process of locating periodic faults, such as insulation faults in underground
cables, and is an application of electrical measurement systems. This is used
to find cable faults, which can’t be seen. Cable faults are Damage in the
cable, due to which resistance in the cable is affected.  If this damage
or fault in the cable is allowed to go unchecked, it can lead to a voltage
breakdown. In case of damage in the wire, could result in risk of wire damage,
short circuit and fire. To identify the fault in cable is high or low could be
measured by Surge generator, Time domain reflectometer.

Cable Fault Location

Syed,I'm a bit confused as to what you intend to measure to locate the faults. Is it your intention to output a signal and vary the frequency and measure the amplitude at each frequency? If so, how do you intend to separate the input signal from the output?
The relationship between wavelength and frequency is L = V/F where V is the velocity of the wave. I'm not aware that the velocity changes in 50 Ohm coax with frequency. Depending on the coax and the frequencies used, the attenuation in the coax will change which could affect your result.

Coaxial underground electrical power cables can have very different characteristics than RF coaxial cables. In particular, RF losses and surge impedance do not matter in power cables, which are built for 50/60 Hz service, but high-voltage insulation strength matters a lot. Power cables can be so lossy at RF that microwave TDR pulsers will refuse to pulse into the power cable.The wave velocity V in 50-ohm RF coax does vary somewhat with frequency (This is called dispersion.), as the dielectric constant of the dielectric is frequency-dependent. This is not a problem in narrowband RF applications, but can be a problem in wideband data-transmission applications, where dispersion can cause intersymbol interference.