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The observer walks along the fence. Relative to him, the posts have speed c, and the frequency he measures is f=c/λ, where λ is the distance between the posts. Now the observer starts running along the fence and his speed increases by v. Relative to him, the speed of the posts shifts from c to
c' = c+v This shift in the speed of the posts (relative to the observer) causes the frequency he measures to shift from f=c/λ to f' = c'/λ = (c+v)/λ = f(1+v/c) The same argument is used to calculate the Doppler frequency shift for light: http://rockpile.phys.virginia.edu/mod04/mod34.pdf "Now let's see what this does to the frequency of the light. We know that even without special relativity, observers moving at different velocities measure different frequencies. (This is the reason the pitch of an ambulance changes as it passes you it doesn't change if you're on the ambulance). This is called the Doppler shift, and for small relative velocity v it is easy to show that the frequency shifts from f to f(1+v/c) (it goes up heading toward you, down away from you). There are relativistic corrections, but these are negligible here." http://www.hep.man.ac.uk/u/roger/PHY.../lecture18.pdf "The Doppler effect - changes in frequencies when sources or observers are in motion - is familiar to anyone who has stood at the roadside and watched (and listened) to the cars go by. It applies to all types of wave, not just sound. [...] Moving Observer. Now suppose the source is fixed but the observer is moving towards the source, with speed v. In time t, ct/λ waves pass a fixed point. A moving point adds another vt/λ. So f'=(c+v)/λ." Note that the frequency shift f' = c'/λ = (c+v)/λ = f(1+v/c) is a consequence of the fact that the speed of light (relative to the observer) varies with the speed of the observer, in accordance with the equation c' = c+v and in violation of Einstein's relativity. Pentcho Valev |
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Consider a light source emitting a series of pulses the distance between which is d (e.g. d=300000 km). A stationary observer (receiver) measures the frequency of the pulses to be f=c/d:
http://www.einstein-online.info/imag...ler_static.gif The observer starts moving with speed v towards the light source - the measured frequency shifts from f=c/d to f'=(c+v)/d (Doppler effect): http://www.einstein-online.info/imag...ector_blue.gif The speed of the pulses relative to the observer is c' = df' = c+v, in violation of Einstein's relativity: http://a-levelphysicstutor.com/wav-doppler.php "vO is the velocity of an observer moving towards the source. [...] Hence, the velocity of waves relative to the observer is c + vO." http://physics.bu.edu/~redner/211-sp...9_doppler.html "Let's say you, the observer, now move toward the source with velocity vO. You encounter more waves per unit time than you did before. Relative to you, the waves travel at a higher speed: v'=v+vO." Pentcho Valev |
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