The two situations that might cause Observer A and Observer B to measure different frequencies for the same vibrating object are:
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Observer A and Observer B are stationary but at different distances from the vibrating object. - While the frequency of the sound produced by the object itself doesn't change, the intensity and the Doppler effect (if they move) can affect what they perceive, potentially leading to differences in perceived frequencies due to distance effects.
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Observer A is stationary and Observer B is moving. - The Doppler effect causes the frequency of sound to change depending on the relative motion of the source and the observer. If Observer B is moving towards or away from the vibrating object, the frequency measured by B will differ from that measured by A, who is stationary.
The first and fourth options are correct.