If you have a sliding barn door that looks like the one in the picture below then you will probably need a bit more than a small weather strip to stop the noise.
Soundproofing sliding barn doors.
During installation the plywood or mdf panel you intend to use should be cut to the precise measurements of the door.
You can buy what s called a soundproof foam corner block amazon link.
Else you are planning for an ugly scene.
Fiberglass panels and foam panels.
First off the wood you are using should be heavy and thick that s the principle behind noise blocking.
Foam panels are superb for reducing the amount of echo while fiberglass panels are much more efficient at blocking noise.
Soundproofing barn door using this method is a bit of a risk.
Attaching acoustic panels to your barn doors is another effective option.
Get a barn door style sliding door a thick door made of solid wood is better than glass or hollow wooden doors for blocking noise.
To soundproof a sliding barn door make sure there are no gaps or cracks that noise can travel through.
Make sure the doors are made from solid wood meaning a solid and not a hollow core.
Sliding barn doors are the easiest sliding doors to soundproof in my opinion which means that you have plenty of options to do this.
Therefore investing in a solid core wood door can definitely help.
However the down side to this option is the price.
A door sweep and weatherstripping tape can be used to cover gaps.