What the heck is causing this noise?

My 2009 Touring edition has been intermittently making this noise:

(see two posts further down as every time I refresh the page, the youtube link vanishes)
I hear it while driving as well as at stoplights. It comes and goes; sometimes I will drive it for over an hour before it starts. Sometimes I hear it as soon as the car starts even after sitting for hours. It doesn't appear related to my use/non-use of the fan or A/C. I've heard it when the ambient temperature is hot or cool, at start-up and after driving for a while, brakes on or off, First noted four or five months ago after an oil change, but may have stated earlier as I often have the radio up.

Any assistance would be welcomed. I'd like some idea of what it is before I take it in, as I will be charged for diagnostics.

 

Here is the recording from my car:

Sometimes I hear it at rest, sometimes in motion. I drove 12.5 miles each way to work and back(30 minutes there and 48 minutes back at speeds from 5mph to 45mph) today without hearing it once. Yesterday it started after I had driven about 25 miles(variable speeds), stopped for a half hour, then started up again. It started while in motion, and continued in Park. Sometimes the noise starts after the car has been sitting overnight.

 

I changed the recording to one actually from my car. It is a bit different.

The battery was replaced two years ago. The sound does not continue after the car has been shut off (that's a different noise). I couldn't tell if it was coming from the driver's side or the passenger side when I went under the hood. I have heard the noise start long after the car started. I went looking for a recording of the coolant thermos pump, but have not been able to locate one. Might you know of one? Isn't it supposed to sound like a water bubbler?

 

I reposted the recording of MY car - the one I had up before was one someone else had recorded three years ago of his non-Touring car making a similar noises. The recording was made of the car at rest, but I've also heard it while the car was in motion.

 

Thanks Patrick, I was hoping you'd respond. The coolant was replaced at the beginning of the summer, before the noise started. Could there be any relationship, like did they forget to tighten something, or did replacing the coolant loosen up debris? (The car was out of commission for about seven weeks in the summer, so I haven't been driving it with the noise as ling as one might surmise; a motorcycle tried to pass my car on the left while my daughter was turning left in a no-passing zone)(no one was injured enough to warrant hospitalization, amazingly)

 

Thanks for responding. Now I have to google the whereabouts of the inverter tank...

 

I looked at the post by Stomper88 from Jan 2012 on how to replace the valve: http://priuschat.com/threads/p1121-co... Sounds like it might be related to the coolant change or perhaps just the age of the car and the need for a coolant change? I have about 134K miles on the car.