My 05 Tundra started making a whining noise on Sunday when accelerating. It only makes it while pressing on the accelerator and stops when I let off the gas. I don't hear it while idling, and I can't tell if I'm hearing it when in neutral or park and giving it some gas. It sounds faster and a little louder as speed increases, but it's easiest to hear between 30-40 MPH (less road noise).

I also hear a similar sound as if it is winding down when slowing down. It consistently happens at around 18 MPH, 13 MPH, and 8 MPH.

Saturday & Sunday were the first really cool days (highs in low 50s). It looks like I'm a little low on power steering fluid as well although what is in there is pretty clear. I don't hear a difference when turning my wheel or making turns though. Could it still be related to low fluid?

If you sit in the drive way and rev it, does the noise increase?

That's how my issues started. Get it checked out. Like 1ags said, if it only does it "under load" while driving and not in park or neutral, it's not something to ignore. Trust me.
https://texags.com/forums/46/topics/2818182

Even if it isn't when moving it shouldn't be ignored.

Could be the idler or tensioner failing.

If it's a pulley with bearing failure, take a piece of dowel rod (cut an old broom stick) and place one end of it on the nut securing the pulley. Place your ear to the other end. It'll serve as a home made stethoscope and you'll be able to isolate each pulley if one of them is going bad.

You want to see your dash light up like a Christmas parade... Have your tensioner pulley let go.

1agswitchin4lanes said:

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If you sit in the drive way and rev it, does the noise increase?

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Not that I can tell (although doing that makes it harder to hear because of the engine noise).

Has the truck had the timing belt changed?