Roger Barlow: "In time t, ct/(lambda) waves pass a fixed point."
That is, the speed of the waves relative to the fixed point is c.
Roger Barlow: "A moving point adds another vt/(lambda)."
That is, the speed of the waves relative to the moving point (moving observer) is c+v.
See also:
http://a-levelphysicstutor.com/wav-doppler.php
"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://researcher.nsc.gov.tw/public/fangyuhlo/Attachment/031016202571.pdf
Fang-Yuh Lo, Department of Physics, National Taiwan Normal University: "Observer moves toward source: frequency becomes higher. Observer moves away from source: frequency becomes lower. How much higher (lower)? Wavelength does not change. Change in velocity: Vnew=Vwave±Vobs."
http://www.einstein-online.info/spotlights/doppler
Albert Einstein Institute: "The frequency of a wave-like signal - such as sound or light - depends on the movement of the sender and of the receiver. This is known as the Doppler effect. (...) In the above paragraphs, we have only considered moving sources. In fact, a closer look at cases where it is the receiver that is in motion will show that this kind of motion leads to a very similar kind of Doppler effect. Here is an animation of the receiver moving towards the source: (...) By observing the two indicator lights, you can see for yourself that, once more, there is a blue-shift - the pulse frequency measured at the receiver is somewhat higher than the frequency with which the pulses are sent out. THIS TIME, THE DISTANCES BETWEEN SUBSEQUENT PULSES ARE NOT AFFECTED, but still there is a frequency shift: As the receiver moves towards each pulse, the time until pulse and receiver meet up is shortened."
Pentcho Valev pvalev@yahoo.com