"Vo is the velocity of an observer moving towards the source. This velocity is independent of the motion of the source. Hence, the velocity of waves relative to the observer is c + Vo. [...] The motion of an observer does not alter the wavelength. The
increase in frequency is a result of the observer encountering more wavelengths in a given time." http://a-levelphysicstutor.com/wav-doppler.php
So the speed of light relative to the observer does change, in accordance with the formula (frequency)=(speed of light)/(wavelength) and in violation of Einstein's relativity.
Here Einsteinians usually remain silent, but if they decide to advance an objection, it may be something like this:
"That the wavelength changes is not what Kip Thorne says. What he does say is that the moving observer SEES the wavelength shortened. Different observers at different speeds see different wavelengths."
So the wavelength is not shortened but the moving observer sees it shortened? And if he moves in the opposite direction he sees the wavelength stretched? And the observer sees both shortening and stretching in such a way as to keep the speed of light
gloriously constant? Einsteinian myths are immeasurably more idiotic than flat-earth myths.
It is easy to see that the wavelength varies with the speed of the source only if the speed of light is constant (independent of the speed of the source). However the speed of light is variable (c'=c+v), so the wavelength is constant in the moving-source
case (I have tried to prove these claims elsewhere).
(frequency) = (speed of light)/(wavelength)
tolerates two axioms:
Axiom 1: The speed of light is constant.
Axiom 2: For a given emitter, the wavelength of light is constant.
Axiom 1 killed physics.
Axiom 2 will resurrect it (if it's not too late). Corollaries (established truths in future, Einstein-free physics):
Corollary 1: Any frequency shift entails (is caused by) a proportional speed-of-light shift.
Corollary 2: If the emitter and the observer (receiver) travel towards each other with relative speed v, the speed of light as measured by the observer is c' = c+v, as per Newton's theory.
Corollary 3: Spacetime and gravitational waves (ripples in spacetime) don't exist. LIGO's "discoveries" are fake.
Corollary 4: Light falls in a gravitational field with the same acceleration as ordinary falling bodies - near Earth's surface the accelerations of falling photons is g = 9.8 m/s^2. Accordingly, there is no gravitational time dilation: Einstein's general
relativity is absurd.
Corollary 5: The Hubble redshift is due to light slowing down as it travels through vacuum. The universe is not expanding.