I have been doing research into blood pressure monitors, and I was wondering when the cuff tightens, how do the transducers actually measure the systolic/diastolic pressure in the arteries.
This is actually a really neat question, and it involves a few engineering and anatomical concepts.
Here's what happens when an automatic blood pressure cuff measures your blood pressure:
The cuff inflates until it reaches a pressure just above systolic pressure (the maximum pressure your blood reaches during a heartbeat). When it reaches this pressure, the main artery in your arm gets closed off because its pressure is not enough to resist the compression of the cuff.
The cuff then starts to deflate slowly. There is a pressure sensor that measures pressure fluctuations in the cuff. Once the cuff reaches your systolic pressure, the artery opens up just enough to let some blood through. Since the artery is mostly closed, this causes tiny vibrations as the blood squeezes through (this is because the blood flow is "turbulent"). These vibrations are transmitted through your skin and into the air in the cuff. The pressure sensor is sensitive enough detect these tiny vibrations in the air of the cuff once they start, and it records the current pressure of the cuff as the "systolic pressure".
The pressure in the cuff keeps decreasing, until the tiny vibrations stop (the blood flow becomes "laminar" instead of turbulent). This is the "diastolic pressure", i.e. the minimum pressure during your heartbeat.
It turns out that doctors do the exact same thing with a manual cuff and a stethoscope: they pump up the cuff until they can't hear any gurgling noises in the stethoscope, then they slowly release until they hear the first gurgling noise (systolic pressure reached). They keep releasing pressure until they can't hear the noise any more, at which point they've found the diastolic pressure.
I've actually performed these measurements myself in a Biomechanical Engineering Measurements course. Cool stuff!