The situations in which observers a and b might measure different frequencies for the same vibrating object would typically involve differences in their relative motions with respect to the source of the vibrations (like sound waves). Here are the two correct answers based on standard physical principles:
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Observer a is stationary, and observer b is moving: In this scenario, if observer b is moving toward the source of the vibrations (sound), they will measure a higher frequency (blue shift due to the Doppler effect) compared to observer a, who is stationary and measures the original frequency. Conversely, if observer b is moving away from the source, they will measure a lower frequency (red shift).
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Observers a and b are both stationary at the same distance from the object: This situation would not typically result in different frequency measurements since they both are stationary and at the same distance, meaning they would experience the same frequency from the vibrating object. Thus, this option is incorrect for the situation in question.
Therefore, the correct answer to your question would be focused on the first option regarding the different states of motion of observers relative to the source.