Levitah: Held by Sound
Optics, Waves & Sound arc, page 117 of 193. Back to The Pixelated Physics Universe
Who they are
Levitah holds a row of pearls still in mid-air, caught in a column of sound no one can see.
Levitah is a character of the Optics, Waves & Sound arc: drawn in pixels, ruled by one piece of real physics, and never allowed to break it.
The physics
Sound carries momentum, and a strong standing wave exerts a steady average force, the acoustic radiation force, on small objects. King computed it for spheres in 1934. Gor'kov (1962) wrote it, for a sphere much smaller than the wavelength in an ideal fluid, as the gradient of a potential U, with a compressibility factor f₁ and a density factor f₂. For a small bead much denser and much less compressible than air (ρ_p ≫ ρ₀, κ_p ≪ κ₀), both factors are close to 1. U is then lowest where the pressure amplitude vanishes and the velocity amplitude peaks, so the bead collects near the pressure nodes, which are the velocity antinodes, half a wavelength apart. At 40 kHz in air the wavelength is about 8.6 mm, so the trapping sites are about 4.3 mm apart.
$$ \begin{gathered} U = \frac{4\pi}{3}a^{3}\left[f_1\,\tfrac{1}{2}\kappa_0\langle p^{2}\rangle - f_2\,\tfrac{3}{4}\rho_0\langle v^{2}\rangle\right] \\ \mathbf{F} = -\nabla U \qquad (a \ll \lambda) \\ 40\ \mathrm{kHz\ in\ air:}\ \lambda \approx 8.6\ \mathrm{mm},\ \text{nodes } 4.3\ \mathrm{mm}\ \text{apart} \end{gathered} $$
| Symbol | Meaning | SI unit |
|---|---|---|
| $U$ | acoustic radiation potential (Gor'kov) | J |
| $a$ | sphere radius | m |
| $f_1,\ f_2$ | monopole and dipole scattering coefficients | 1 |
| $\kappa_0$ | compressibility of the air | 1/Pa |
| $\langle p^{2}\rangle$ | time-averaged squared acoustic pressure | Pa² |
| $\rho_0$ | density of the air | kg/m³ |
| $\langle v^{2}\rangle$ | time-averaged squared acoustic velocity | m²/s² |
| $\mathbf{F}$ | radiation force on the sphere | N |
| $\lambda$ | wavelength | m |
Honest caveat: It is not anti-gravity, and it does not work on any object: size and density limits apply. Dense, rigid beads collect near pressure nodes (velocity antinodes), not at velocity nodes; in a vertical levitator gravity holds each bead slightly below its node.
Sources
- King (1934) On the acoustic radiation pressure on spheres, Proc. R. Soc. Lond. A 147, 212
- Bruus (2012) Acoustofluidics 7: The acoustic radiation force on small particles, Lab Chip 12, 1014
Crossovers
Levitah meets Sonara (Sonoluminescence). Levitah holds a bubble or droplet in a standing sound wave. Sonara does the same, then drives the bubble so hard that it collapses and flashes. How the light is made is still debated.
Levitah meets Chimella (Hot Chocolate Effect). Levitah uses the force of sound to hold objects. Chimella uses bubbles to change the speed of sound itself. Both are acoustics in the everyday kitchen and lab.
Levitah meets Sabina (Echo Has a Clock). Sabina's echo returns after the sound travels to a wall and back, about 343 m/s at room temperature. Levitah uses reflected sound too: an emitter and a reflector set up a standing wave whose pressure nodes can hold a small bead in air.
Wear the lore
- Levitah – Held by Sound Physics T-Shirt
- Related infographic poster: Kundt's Tube – Plate 086 Physics Poster
Concept keywords: Held by Sound, Levitah, Optics, Waves & Sound, physics lore, Pixelated Physics