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Why do you think the speed of the source is relevant?duri said:Let me put this way,
1. Observer moving with velocity v and source of signal from the front and rear are stationary from stationary reference. Observer is stationary with his own reference and source of signal is moving at velocity -v. These two are identical. This doesn't talks about speed of signal so invariance of c is not required.
Make it simple. Set it up like this: There are giant flash bulbs at each end of the train. Now the source of each flash moves with the train, so the speed of the source is zero with respect to the train observer.
The setup is the same: The bulbs flash at the same time according to the track observer.
Now what?