Wobble happens around 30mph. can be stable at times as well. doesnt excist on curves or turns. seems to go from bad to worse at higher speeds and then settles down out of the blue. noticed when breaking in higher speeds it exaggerates the problem.

As your description of the symptom is rather vague it would be a good idea to ask an experienced person to take a drive prior to examining the underside and checking for wear, etc. in the steering, suspension and braking system.

The faults that could cause the car to wobble are many and various from a bad tyre mix through worn shock absorbers to semi-seized brake calipers.

The most common fault relating to brakes is caused by the bad fitting of brake rotors that after several thousand miles become unevenly worn so when applying the brake a judder can be felt; through the brake pedal, through the steering and sometimes through the seat (depending on which brake(s) and how many are affected). After 45 years repairing vehicles I have never known the fault to cause the vehicle to wobble.

Go to an Alignment Only Shop & have them road test
while you ride along

Then have them inspect for worn parts

have a wheel alignment as it indicates castor wobble from negative castor

If it wobbles at higher speeds like 55-60 mph or so probabley just worn and out of balance tires,If it wobbles at like 25-30mph or so at a lower speed it probabley mean you have a tire seperating and it could blow out at anytime and you would definitely need new tires,at least more than likely the front two.

try changing the tires . you may have a broken bead in a tire, which flattens when you hit higher speed.

missing would show itself at low engine speeds.bad starting.or heavy load (going up steep hills)a miss at high speed would not be felt (normally)without other symptoms(lack of power etc)have you tried using higher octane fuel......mazda rec 92+ octane...

It is now sorted somehow the window had become slightly open and caused the wind noise.

Rim may have a dent or a weel balance weight may have fallen off.

Have the balance checked before your tires develop abnormal wear.

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Steering dampner (thing that looks like a shock absorber mounted sideways) can cause this. Most good alignment shops will check front end components for wear (shame on them if they didn't) but sometimes what seems like "acceptable play" if added to other components in similar condition can add up to a total of unacceptable...If dampner does not help, I'd start eliminating anything with any wear. A side-note to this is about caster angle...I never like factory camber settings...it does make steering easier but I prefer setting caster at least one full degree (+) past factory settings. This makes the vehicle more stable at higher speeds and often eliminates tendency of wheels to wobble. (won't go into full details, but it's why you can ride a bicycle with "no hands" if you turn the fork around and try that you will land on your ****!) If adjustable, it involves placing equal thickness shims on both sides, behind rear of front lower control arms. Changing this may alter toe in, so that should be re-set.

If it seems to happen more when rounding a curve than on the straight, it may be your CV joint. I'm not sure but I think you can replace the half shaft that connects the wheel to the engine. Otherwise, you may have to find a press to press out the old one. It's kinda like a U-joint on rear wheel drive cars. Or it could be the tire out of balance, bad tire, bad stabalizer bar. Gonna have to jack it up and get under it and start shaking stuff to find out what's loose. GOod luck and have fun....