I find it incredible that you don't know Doppler's equation f' = f.(c+v)/(c+u)
and imagine nobody else does.

If the equation c = wavelength * frequency holds good, then the speed
is directly proportional to the wavelength.

I also find it incredible that so many people actually believe
"Wavelengths vary but not the speed of light", which is quite preposterous.

Do you imagine the frequency magically changes then?

AD.