Acoustic radiation force due to a diverging wave: Demonstration and theory

Abstract

A radiation force is the time-averaged force exerted by any kind of wave on a body. In the case of a divergent traveling acoustic wave, it is known that a relatively small rigid body can experience a radiation force that is directed toward the source. We show that this effect can be readily demonstrated with a styrofoam sphere pendulum near a horizontally directed loudspeaker that is emitting sound of sufficiently high amplitude and low frequency. The attraction is surprising because repulsive forces are exerted by a traveling plane wave and by an outward jetting or “wind” from the loudspeaker. We argue that the attractive force near a source that is small compared to the wavelength can be roughly understood and calculated as a time-averaged Bernoulli effect, if scattering is ignored. The result is within a factor of two of rigorous published results based on scattering calculations, when these results are specialized to the case of a rigid body whose average density is much greater than the density of the fluid. However, repulsion occurs when the average density of the body is less than the density of the fluid, in which case our Bernoulli result completely fails.