The two situations that might cause observers A and B to measure different frequencies for the same vibrating object are:
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Observer A is stationary and Observer B is moving. - This scenario can cause a difference in the frequency measured due to the Doppler effect, where the frequency observed changes based on the relative motion of the observer to the source of the sound.
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Observer A and Observer B are moving at different speeds relative to each other. - This also leads to different frequency measurements due to the relative motion affecting how the sound waves reach each observer, again relating to the Doppler effect.
The situations involving both observers being stationary at different distances or both being stationary and at the same distance would not lead to different frequency measurements; they would measure the same frequency in those instances.