I don't think you "need" any degree. Many speaker designers don't. Actually some of the most brilliant electronics engineers i have ever had the pleasure to work with seem to be self taught.I would try to hook up with a designer you respect and see if you can do some sort of apprenticeship.
But if you want a degree to get you started, Physics would certainly give you some helpful fundamental info.
Eat Mo' Hot Sauce,
crazychile