Frequency shifts for accelerated sources and observers: an illustration of non-locality in frequency measurement

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Abstract
We study the Doppler shift in the frequency of an acoustic or light wave emitted by a source at rest with respect to an inertial reference frame and received by an accelerated observer, and the same problem for a light wave emitted by an accelerated source and received by an inertial observer. The non-locality in the frequency measurement by an accelerating observer is taken into account, noting that two successive zeros of the wave are received at two different points in space, where the velocities of the receiver or source are different.