I would bet US SONAR picks them up as soon as they power up.
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I’m sure it would depend on distance, depth, and speed. I have no idea from what these subs are constructed, but it’s possible that they have sound-absorbent materials on the hull. When you don’t have to put a crew onboard, they can be made pretty small too. I’d be interested in how much one of these costs to produce.
Sure, desert dwellers are really good at designing submarines with sound absorbing materials. Probably the experience of riding camels gives them some insight into aquatic acoustics. At least they probably spend a lot of time thinking about such things since there isn’t much else to do between bowing and praying towards Mecca 5 times a day.
The Houthis aren’t building that stuff — drones 7 subs — so would it be Iran, or China?
Electric subs can be extremely quiet. Nuke subs have steam plants and are much harder to silence.
Small electric powered subs could be a serious threat.