What is this hose?

I'm trying to track down a whining noise I've been hearing for years now that comes from behind the dash when getting speeds up to 45 to maybe 60 mph. It sounds like a bad speedometer cable, but it comes from the passenger side, and also seems to have some sensitivity to the accelerator, as apposed to simply the speed. It's not some vibration behind the glove box because I've removed the glove box and the noise is still there. Soooo, looking on the other side I'm wondering what the heck is this circled hose for? I doubt it's the heater, but in any event can it cause a whine???

 

Bumping. I still have this hum when over 45 coming from behind the passenger's dash. Surprised I'm the only one..