  When a dynamic system undergoes a cyclic evolution, a geometric phase that
depends only on the path traversed in parameter space can arise in addition to
the normal dynamical phase. These geometric phases have profound impacts in
both quantum and classical physics. In addition to the geometric phase
associated with band structures in reciprocal space that has led to the
discovery of topological insulators, the spin-redirection geometric phase
induced by the $SO$(3) rotation of states in real space can also give rise to
intriguing phenomena such as the photonic analog of the spin Hall effect. By
exploiting the orbital angular momentum of sound vortices, we theoretically and
experimentally demonstrate the spin-redirection geometric phase effects in
airborne sound, which is a scalar wave without spin. We show that these
effects, associated with the helical transport of sound, can be used to control
the flow of sound. This finding opens new possibilities for the manipulation of
scalar wave propagation by exploiting spin-redirection geometric phases.
