Akinbo,
"Given, c = f*lambda during transformation between frames, supposing what changes is only frequency, f and speed, c."
They are indeed what change, in a particular circumstance. You forget I derived that some time ago for you. But always discern between the physical entity and the mathematical derivative. Wavelength, amplitude and ellipticity are physical. 'frequency' is a derivative, a 'number' found by applying 'time' at the processor (brain). However the effects of observer relative motion can change 'apparent' as well as real phenomena. As the human brain isn't good at remembering concepts perhaps, rationalise this scenario, write it down and memorise it.
On a transform between inertial systems there are FOUR observer cases;
1. At rest in first system; A.
2. At rest in second system; B.
3. At rest in A then accelerates to be at rest in B.
4. Reverse to 3, - but we'll ignore that one (and both may speed up or slow down).
To make it easy picture yourself in the cockpit of a fast jet circling earth. The thin air outside is rest frame 'A'. The denser air inside is rest frame B. The media have almost the same refractive index but a relative speed v. The mechanism is the same as sound; When at rest in the plane two light pulses (or sound signals) in the plane propagate LOCALLY at c (s). When at rest outside, clearly they propagate at c (s) there too.
As you float in your balloon watching the plane pass (case 1) you see the pulses hit the cockpit window one at a time, then propagate inside the plane. What apparently happens to them? (answer (a)) below). But will their apparent 'frequency' (past you) change? Watch them carefully; they 'slow down', but are also closer together, so will 'pass by you' at exactly the SAME 'rate' (frequency f).
Now as you sit in the cockpit (case 2) the two pulses come towards you, let's say at 'closing speed' c+v but far apart, so at frequency f. The moment they reach the electrons outside the glass they're scattered down to c in the electron frame. What will appear to happen to them? (answer (a)) below). And again, though now slowed to c as they reach you they're closer together (Blue shifted) so still at 'frequency' f.
Now case 3. You find the frequency in the balloon as the pulses pass at c, say 10/sec. But the plane hooks up the balloon, you accelerate rapidly, and somehow get inside. Now you STILL find the pulse doing c, BUT now they're closer together, so at a higher frequency. Only if YOU accelerate from the old into the new propagating medium rest frame to do find a frequency change!
(a) The pulses close together (Doppler shift/ WAVElength contraction) and 'appear' to slow down, always propagating at c.
Space is merely a very diffuse version of air. The electrons (plasma) do the job. The mechanism doesn't "depend" on wavelength change, it logically derives it in the (normal) fixed observer case. Astronomy relies on spectroscopy. Calling it 'frequency' change produces nonsense. Redshift can ONLY be a lambda/lambda transformation. Now try to find a Doppler shift equation that recognises that and uses wavelength! It's not 'joined up' science. No wonder theory ends in paradox! (That is a VERY VERY important missed fact; see my prev. essay).
You'll need to read twice slowly and visualise, then once more to memorise, unless you're a genius! Best wishes
Peter
