Adding something to your roof will always have some impact on wind noise, but depending on your car, the roof bars you go for and also the load you are carrying it can be fairly negligible - nothing that you'll notice too much with the radio on. Some loads will be more noisy than others, eg, a roof box will be much more aerodynamic than a load of bikes. An empty roof box tends to make more noise than a full roof box.
There are some things you can consider which may help if you are experiencing noise from your roof bars.
Cross bar profile
The profile of your roof bars will make a difference - rectangular profile bars are less aerodynamic than aero bars, particularly wing-shaped bars (Cruz Airo, Atera aero-profile, Thule WingBar and Yakima Whispbars and Streamline bars). Wind deflectors (e..g. the Yakima Windshield) are available and can be useful if you need to reduce noise, particularly if you have box-section roof bars.
Correct fitting
Are your roof bars fitted the correct way around? We see a lot of wing-shaped roof bars that have been fitted the wrong way around. The trailing edge of the bar goes towards the rear of the car, like an aircraft wing.
Have you fitted all the rubber strips (especially the ones on the underside of the bar)? Lots of roof bars come with rubber or plastic strips to fill in the small slot on the underside of the bar. Make sure the rubber strips are all installed, and if they are, check for gaps. Also make sure that the end caps are fitted to all the bars.
Position on the roof
The shape of roof will make a difference to airflow and can have an impact on roof bar noise. If you able to, moving the bars forwards or backwards can improve wind noise. This is usually only possible if you have roof rails or T-track channels on your roof. Even if your roof bars are fixed in position, you may be able to alter the position of the load you are carrying. E.g. almost all roof boxes now come with some sort of sliding fitting, so you'll be able to slide your roof box forwards and backwards. In terms of wind noise, further back does tend to be better but it is really trail-and-error as the roof line varies so much between cars.
Do you have an opening sunroof?
We really don't recommend you open a sunroof with roof bars fitted, on some cars it won't be possible because the glass will clash with the roof bars, box etc. If you do open the roof with your roof bars fitted it can make things quite noisy, depending on the shape of the roof and the positioning of the roof bars.