Acoustic Levitation: How a Standing Sound Wave Holds Objects in Mid-Air

Sound has momentum, and momentum can hold an object up

A sound wave carries not just energy but a small, steady push in its direction of travel — acoustic radiation force. For an everyday speaker the effect is far too small to notice, but concentrate enough ultrasonic intensity into a standing wave and that force becomes strong enough to cancel gravity on a small object, holding it suspended in mid-air with no physical contact at all.

The trick is the standing wave. Two opposing transducer arrays emit ultrasound at the same frequency toward each other; the outgoing and reflected (or oppositely emitted) waves interfere to produce a stationary pattern of pressure nodes (zero oscillation amplitude) and antinodes (maximum amplitude), spaced half a wavelength apart. A small, light object dropped into this field does not feel a uniform average of the field — nonlinear acoustics gives it a small time-averaged net force that pulls it toward the nearest pressure node, where it settles and stays.

The Gor'kov potential

The rigorous treatment for a particle much smaller than the acoustic wavelength was worked out by Lev Gor'kov in 1962. He showed that the time-averaged radiation force on such a particle is the negative gradient of a scalar potential U, built from the local acoustic pressure and velocity fields:

U = 2*pi*r^3 * [ f1/3 * kappa_0 * <p^2>  -  f2 * 3/2 * rho_0 * <v^2> ]
f1 = 1 - kappa_p/kappa_0                       (compressibility contrast)
f2 = 2*(rho_p - rho_0) / (2*rho_p + rho_0)     (density contrast)
F = -grad(U)                                    // the radiation force itself

Here r is the particle radius, kappa the compressibility and rho the density, with subscript 0 for the surrounding fluid (air) and p for the particle. The angle brackets denote a time average over one acoustic period. For a solid or liquid bead in air, both contrast factors are positive, which makes the potential minimum — and therefore the stable trap — sit exactly at the pressure nodes of the standing wave. This is why levitated beads in a demonstration line up in neat, evenly spaced rows: one bead per node, half a wavelength apart.

Why this specifically needs ultrasound

The radiation force scales with particle volume but with the gradient of acoustic intensity, so you want a high acoustic pressure amplitude packed into a short wavelength — meaning a high frequency. Audible sound loud enough to levitate anything would be both impractical to generate at that intensity and unbearable to stand near; ultrasonic transducers around 40 kHz (a wavelength of about 8.6 mm in air) give fine-grained node spacing, silent operation, and, using piezoelectric transducer arrays now cheap enough to be hobbyist-accessible, enough acoustic pressure to levitate polystyrene beads, water droplets, small insects and even small electronic components.

Two practical levitator geometries exist. The classical setup is a single-axis standing wave between an emitter and a passive or active reflector, trapping particles along a line of nodes. More recent phased-array levitators use dozens to hundreds of small transducers whose individual phases are computed to synthesise an arbitrary focal pressure field, including traps in free space with no reflector needed, letting the trap itself be moved smoothly in 3D by recomputing the phase pattern — which is how modern acoustic-levitation demonstrations move objects along paths rather than just holding them fixed at a grid of nodes.

Real applications beyond the demo

Acoustic levitation is used for containerless processing: melting and studying materials that would react with or be contaminated by any physical crucible, handling reactive or ultra-pure chemical samples, and studying droplet evaporation and crystallisation without a supporting surface that could seed unwanted nucleation. Pharmaceutical research uses it to observe how single drug-formulation droplets dry, and, at a bio-scale, researchers have used phased-array levitation to manipulate small biological samples without touching them — a genuinely contact-free tool for situations where contact itself would corrupt the measurement.

Frequently asked questions

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