Acoustic levitation
Two transducers face each other, generating a standing wave. Pressure piles up at antinodes, vanishes at nodes. Small particles drift toward the nodes and hover there, suspended by sound alone. Click to drop particles into the field.
U(x) ∝ −⟨p²⟩ · F = −dU/dx
Sound that holds things up
When two speakers face each other and emit sound at the same frequency, the waves travelling in opposite directions superpose to form a standing wave. At certain points — the nodes — the pressure oscillation is always zero. Between them lie the antinodes, where pressure swings wildly between compression and rarefaction. A small, lightweight object placed in this field doesn't experience a net time-averaged force at an antinode. But near a pressure node, the acoustic radiation force nudges it toward the node and holds it there. The object levitates.
The standing wave
The pressure field between the two transducers follows p(x,t) = P₀ sin(kx) cos(ωt),
where k = 2π/λ is the wavenumber, ω = 2πf is the angular frequency, and
P₀ is the pressure amplitude. The spatial part sin(kx) determines where the nodes
and antinodes live. Nodes occur at kx = nπ, i.e., every half-wavelength. This is the skeleton
of the trap: the geometry of silence inside a field of sound.
The Gor'kov potential
In 1962, L. P. Gor'kov derived the potential energy landscape that a small spherical particle experiences
in an acoustic field. For a 1D standing wave, the Gor'kov potential simplifies to
U(x) ∝ −sin²(kx) (for particles denser than the medium). The minima of this
potential — where U is most negative — coincide with the pressure nodes. The acoustic radiation
force is F = −dU/dx, always pointing toward the nearest node. It acts like a spring:
the farther a particle drifts from a node, the stronger the restoring force that pulls it back.
The potential plot below the simulation shows this landscape in real time. The gold curve traces U(x) across the chamber. Each dip is a trap. Each peak is unstable. Particles accumulate in the valleys, exactly where the pressure vanishes.
Gravity versus sound
Toggle gravity in the simulation to see the competition. With gravity off, particles drift cleanly to the
nearest pressure node regardless of vertical position. With gravity on, a particle will only levitate if
the acoustic force exceeds its weight. Increase the amplitude to strengthen the field. At low amplitudes,
particles fall through the nodes; at high amplitudes, the traps are strong enough to catch them mid-air.
The critical amplitude depends on particle size, density, and the acoustic frequency — a balance
between mg pulling down and −dU/dx pushing toward the node.
Real acoustic levitation
Acoustic levitation is not a thought experiment. Laboratories routinely levitate droplets of water, beads of polystyrene, even small biological samples using arrays of ultrasonic transducers operating at 25–40 kHz. The same principle scales: NASA has used acoustic positioning to study materials in microgravity, and recent work with phased arrays of speakers can move levitated objects along programmable 3D paths. The physics you see in this simulation is the same physics at work in those systems — standing waves creating potential wells, radiation force herding particles into the quiet places in a field of sound.
What the simulation computes
The main canvas renders the instantaneous pressure field p(x,y,t) as a color map. Red and blue
mark positive and negative pressure; the neutral band between them is the node. Particles obey Newton's
second law with three forces: the acoustic radiation force derived from the Gor'kov potential gradient,
a viscous damping term (air drag), and optionally gravity. Integration uses the Verlet method for stability.
The lower plot shows the time-averaged Gor'kov potential U(x) as a 1D cross-section along the
horizontal axis at the vertical midpoint — the landscape of traps that the particles feel.