I kind of know what happens when you act with a centrifugal force upon a material object, but what about sound? For example, grabbing a phone who has music turned on and spinning it in the air? Thank you!
The centrifugal force has nothing to do here. The term is also misused. We do not act with a centrifugal force about anything. Instead, it is correct to say that in our reference frame at rest we see rotating objects which experience a centripetal force, which can be friction, tension of a rope etc..
Sound is not an object, is a mechanical wave, a perturbation that propagates in a medium. In air, a vibrating object moves the nearby air molecules back and forth. They do the same job on the other adjacent molecules and so on. In this way, a pattern of compression and rarefaction is created. This is sound. So there is no centripetal force acting on it.
The phone rotates with a certain speed. It will produce a sound whose frequency is shifted according to the frequency it would produce if it was still. This is called Doppler effect. So you would just simply hear your music with a very slight Doppler shift, since the speed of the phone is small.