An acoustic spanner and its associated rotational Doppler shift

Abstract

Light carries a spin angular momentum associated with its polarization and an orbital angular momentum arising from its phase cross-section. Sound, being a longitudinal wave, carries no spin component but can carry an orbital component of angular momentum when endowed with an appropriate phase structure. Here, we use a circular array of loudspeakers driven at a common angular frequency ωs but with an azimuthally changing phase delay to create a sound wave with helical phase fronts described by exp (iℓθ). Such waves are predicted to have an orbital angular momentum to energy ratio of ℓ/ωs. We confirm this angular momentum content by measuring its transfer to a suspended 60 cm diameter acoustic absorbing tile. The resulting torque on the tile (∼6.1×10−6 Nm) is measured from observation of the motion for various torsional pendulums. Furthermore, we confirm the helical nature of the acoustic beam by observing the rotational Doppler shift, which results from a rotation between source and observer of angular velocity ωr. We measure Doppler shifted frequencies of ωs±ℓωr depending on the direction of relative rotation.