No, the noise is the all the time . A sort of grinding and winding noise:bang:
Tyre you say and not wheel/hub?
Do you have oversized tyres, or a tyre of a low quality brand?
The only noise I have experienced like that was when I was running 225 X 15 road tyres on a series 1 Citroen XM. This is what the previous owner had on, and was as I bought the car.
My series 2 XM with 215 tyres is fine, and should take 225's. However the ones on the car were a cheap brand. (I never go for cheap brand tyres for many reasons, mostly my life in the wet!)
The *cheap* brand tyres had a weak sidewall that flared out too much and rubbed on the car body. Luckily it was a hydraulic Citroen and set itself to the correct height whatever the weight, and kept the tyre in the clear.
But if I drove off too quickly after staring it, it gave a terrible grinding noise as it fouled the body.
Ironically I had to drive the tyres on a *lower* pressurebecause of this, to stop the sidewall flaring out more. This resulted in a few back end drifts from time to time. Luckily the XM always swung out to 45 degrees, then tucked in nicely in one go only (phew). (Totally unlike the Citroen 2CV when that let goon oversteer that always needed 3 corrections!, one way an then the other).
However if it is not the tyre, it could be broken ball/roller bearings in the wheel bearing.
Also check the wheel nuts are tight! When I was a lad my wheel nuts slowly came undone over time. Leaving a horrible clacking noise, intially on braking and acceleration (as it took up the play), and then all the time as they worked looser.
Those are my lifetime of driving experiences of "funny noise in the wheels!".
It also can be stones trapped under the wheel trim on classic Citroens (DS/GS/2CV) after driving on beaches; have you been driving down many dirt roads? ( I lived for a while in SA too))