Hyundai Sonata 2002 whining at 55mph

General situation: Almost systematically, after about 40 min of driving at higher speed, car starts whining at speeds ranging from 45 mph to about 60 mph. The noise appears ONLY when my steering wheel is straight, or slightly turned turned to the right (say pointing at 1 o’clock).
Whining: first it slowly progresses from a timid whining, to eventually a whining that can be felt through the steering wheel.The whining is close to the frequency of the note F (about 700hz) , and seems to be coming almost from the steering wheel, or the engine bay. PLUS (…) when I let go of the gas, whining continues, but when I touch the breaks, whining stops immediately.
Condition of car: the car is obviously older, has around 120k miles, all fluids changed just past month. Everything is running fine otherwise.

I’ve been trying to figure out what the problem is but haven’t had much luck, so I’m trying my luck here. I tried to be as specific as possible but if I have left something out, def please ask, and if you could help me diagnose what the issue is, please let me know.

trying to figure it out? by having a shop look at it?
or asking folks what they think, sight unseen?

I had a very similar issue. If light braking makes the noise go away then it’s braking related. I brought my car to shops with the noise complaint. Most shops will check brake lining thickness and for grooves in the rotor. i.e. the easy stuff.

It turned out to be a slightly bent caliper slide pin. Brakes would operate fine to stop the car but would not fully retract so one of the pads would very lightly touch the rotor and heat up and hum, especially on the freeway. Braking would recenter and momentarily stop the noise.

The other suspect was the brake booster, but that was fine.

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When was the last time you changed brake pads?

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Might be a wheel bearing. The sound they make when they are going bad varies depending on variation of the the sideways forces (going straight/turning) they are undergoing. Touching the brakes squeezes the rotors, and that changes the dynamics, and the sound.

If there is any play in the wheel bearing, or any notchiness or grittiness it is rotated, or excessive force required to turn it, it needs to be replaced. Good luck and please let us know how it goes.

Took it to shop, seems like there’s a high chance that the cause were break pads after all. Getting them changed right now, if I don’t update this post further, you can assume that the problem was resolved (and that the solution was getting new breaks). Thank you all for the insight and help, very excited to have discovered this helpful community.