Yes, a speaker with a higher sensitivity rating, such as 92 dB, will generally play louder than a speaker with a lower sensitivity rating, such as 89 dB, when driven with the same amount of power.
Sensitivity, usually measured in decibels (dB), indicates how effectively a speaker converts electrical power into sound output. It represents the loudness of the sound the speaker can produce with a given input power level. The higher the sensitivity rating, the louder the speaker will be at a given power level.
The sensitivity rating of a speaker tells you how many decibels (dB) of sound pressure level (SPL) the speaker will produce when measured at a distance of 1 meter with an input power of 1 watt. For example, a speaker with a sensitivity of 92 dB will produce a higher SPL than a speaker with a sensitivity of 89 dB when both are driven with 1 watt of power.
The relationship between sensitivity and loudness is logarithmic. Roughly speaking, every 3 dB increase in sensitivity corresponds to a doubling of the perceived loudness. So, a speaker with a sensitivity of 92 dB will be noticeably louder than a speaker with a sensitivity of 89 dB. However, the difference of 3 dB may not be perceived as a "lot" louder to the human ear, but it will be discernible.
It's important to note that sensitivity is just one factor that determines a speaker's overall performance. Other factors, such as frequency response, power handling, and speaker design, also influence the sound quality and loudness. So, while sensitivity is an essential consideration, it is not the sole determinant of a speaker's performance.