Final answer:
The question pertains to Physics and the scenarios described involve the principles of relativity, the Doppler effect, and parallax. It demonstrates how observers in different frames of reference can perceive the frequency of waves, the simultaneity of events, and measurements of distances differently. To properly answer the initial path difference question, additional specific details about the positions would be required.
Step-by-step explanation:
The question seems to revolve around concepts from the domain of Physics, particularly involving the principles of relativity, wave propagation, and parallax. The scenario provided for the path difference calculation is incomplete as there are key details missing (such as the actual locations of the sources and the observer). However, the rest of the supplied information discusses relativity in relation to time and the observation of events, the Doppler effect on observed frequency, and the use of parallax in surveying. These concepts are tied to how observers moving relative to a source or event may perceive time, distance, and direction differently due to the finite speed of light and relative motion.
To explore these concepts with an example, if an observer notes a moving source emitting a wavelength λ, according to the Doppler effect, the observed frequency fobs could be fobs = fs ± (vs/c)fs, where fs is the source frequency, vs is the velocity of the source relative to the observer, and c is the speed of light.
In the context of relativity and simultaneous events, we understand that simultaneity is relative and depends on the observer's frame of reference. The concept of parallax demonstrates how a change in observer's position can affect the measurement of angles and therefore the calculated distances. These fundamental principles of Physics highlight how measurements in physics are affected by the relative motion between observers and the events/sources they are observing.