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. - If Observer B is moving towards or away from the object, they will experience a change in frequency due to the Doppler effect.
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Observer A and Observer B are moving at different speeds relative to each other. - This scenario can also lead to different frequency measurements for the same reason (Doppler effect), as the relative motion will affect how the frequency is perceived by each observer.
The other options would not lead to different frequency measurements because if both observers are stationary at different distances or both are at the same distance, they will perceive the same frequency.