The two correct 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 situation can lead to a difference in perceived frequency due to the Doppler effect, where the frequency changes based on the relative motion of the observer and the source of sound.
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Observer A and Observer B are moving at different speeds relative to each other. - This can also lead to a difference in perceived frequency due to the Doppler effect, as the frequency observed will depend on the relative velocities of the observers with respect to the vibrating object.
The other two options would not result in different frequency measurements since both observers would be stationary and/or at the same distance from the source of sound.