Acoustic Levitation Node Calculator

Overview: Acoustic Standing-Wave Levitation Nodes

Acoustic levitation suspends small objects near pressure nodes in a standing sound wave. When opposing ultrasonic emitters face one another, their waves can form stationary regions of minimal pressure fluctuation (nodes) separated by regions of maximum fluctuation (antinodes). A particle can be held near a node when the modelled acoustic radiation force exceeds its gravitational weight.

This acoustic levitation calculator estimates the geometry and force quantities needed for a simple one-dimensional standing-wave arrangement:

• Wavelength of sound in the selected medium
• Spacing between consecutive pressure nodes
• Number of interior node positions between opposing emitters
• Approximate acoustic radiation force on a small spherical particle
• Particle weight and the resulting acoustic force margin

Use these results for conceptual planning, demonstrations, and quick checks of a standing-wave arrangement rather than final design of safety-critical equipment.

Acoustic Levitation Node Formulas and Definitions

This calculator models a one-dimensional standing wave between emitters separated by L, using medium sound speed c, acoustic frequency f, and pressure amplitude P at the levitation region.

Its reported quantities describe the acoustic field and the selected particle:

• Wavelength λ in the medium
• Node spacing between adjacent pressure nodes
• Wavenumber k
• Acoustic energy density used by the force estimate
• Radiation force on the sphere
• Particle weight and the force margin, F − W

Frequency is entered in kilohertz and separation in centimetres, so the calculator converts both before evaluating the standing-wave relationships:

• Frequency in Hz: f = fkHz × 1000
• Wavelength: λ = c / f
• Node spacing: dnodes = λ / 2
• Interior-node count: N = max(0, floor(L / dnodes) − 1), with L converted from cm to m
• Wavenumber: k = 2π / λ

Acoustic Levitation MathML Reference

The MathML below records the wavelength, spacing, wavenumber, energy-density, and force-scaling relationships used for this acoustic levitation estimate:

The calculator evaluates its stated small-sphere force approximation from your pressure, wavelength, and radius inputs, then subtracts particle weight from that force to report the force margin.

Interpreting Acoustic Levitation Outputs

After you enter frequency, sound speed, emitter separation, acoustic pressure, particle radius, and particle density, the acoustic levitation results show:

• Wavelength in the medium – the spatial scale of the sound wave. Raising frequency or lowering sound speed shortens it.
• Node spacing – one half of the wavelength, representing the ideal axial separation of adjacent pressure-node planes.
• Interior nodes – the number of complete node positions calculated between the emitter faces; end positions are excluded by the calculator’s count.
• Radiation force – the approximate force from the calculator’s standing-wave small-sphere model.
• Particle weight – the downward gravitational force computed from particle radius and density.
• Force margin – Facoustic − W, expressed in µN. A positive value means the calculated acoustic force is greater than the particle’s weight; a negative value means it is not.

A positive force margin is only an initial axial check. It does not establish stable trapping because lateral forces, field shape, phase error, and emitter alignment can reduce real-world performance.

Worked Example: 40 kHz Air Levitation Node Spacing

For a representative air-based ultrasonic levitation setup, enter 40 kHz, a sound speed of 343 m/s, and 4 cm between the emitters. These field inputs set the node geometry independently of the particle choice.

1. Convert the drive frequency
   f = 40 × 1000 = 40,000 Hz.
2. Find the wavelength in air
   λ = c / f = 343 / 40,000 = 0.008575 m, or 8.575 mm.
3. Find the pressure-node spacing
   dnodes = λ / 2 = 4.2875 mm.
4. Count interior nodes over the 4 cm gap
   With L = 0.04 m, the calculator applies floor(0.04 / 0.0042875) − 1, giving 8 interior nodes.
5. Check particle weight separately from field geometry
   Particle radius and density determine the spherical particle’s mass and weight. Increasing either raises the required upward force, while neither changes wavelength or node spacing.
6. Compare calculated force with weight
   The result panel reports radiation force, particle weight, and their difference in µN. The sign of that difference is the relevant simplified support check.

For this acoustic levitation example, pressure amplitude changes the force estimate without moving the nodes, while frequency changes both the node spacing and the wavenumber. Recalculate after changing an input rather than treating a node layout as fixed across media or frequencies.

Practical Acoustic Levitation Design Guidance

Use the following considerations when turning the acoustic node calculation into a physical transducer layout:

• Frequency range: Ultrasonic levitation commonly uses frequencies from 20 kHz to 100 kHz. Higher frequency produces shorter wavelengths and more closely spaced node planes, but may require more specialised hardware.
• Emitter separation: Select a gap that is compatible with the desired number of half-wavelength intervals. A near-integer standing-wave fit can help support a repeatable node pattern.
• Acoustic pressure amplitude: Enter a pressure amplitude that your transducers and driver can actually deliver at the trapping region. Confirm limits from the relevant hardware documentation and measurements.
• Particle properties: In this model, larger or denser particles have greater weight. Shape, liquid surface tension, and material response can make actual behaviour depart from the spherical-particle estimate.
• Medium conditions: Temperature, humidity, and composition affect sound speed and attenuation. Supply a sound speed appropriate to the medium rather than assuming an air value for every setup.

Acoustic Node Parameter Comparison

This table summarises how the calculator’s standing-wave inputs change node geometry and the simplified force check.

Acoustic Levitation Assumptions and Limitations

This acoustic node calculator uses a deliberately simplified model, so its results need to be interpreted within the following limits:

• One-dimensional standing wave: The calculation assumes opposing emitters on one axis. Actual levitators have three-dimensional fields, off-axis forces, and geometry-dependent modes.
• Small, rigid, spherical particles: The radiation-force estimate is intended for a small sphere. Non-spherical, deformable, or wavelength-scale objects may respond differently.
• Homogeneous, lossless medium: The model uses a uniform medium with fixed density and sound speed. Absorption, scattering, air flow, and spatial temperature changes are omitted.
• Linear acoustics: It does not model nonlinear propagation, shocks, heating, or cavitation that can occur at high acoustic intensities.
• Approximate force expression: The reported radiation force is the calculator’s simplified estimate, not a full treatment of contrast factors, viscous effects, boundaries, or near-field transducer behaviour.
• No lateral stability analysis: The force comparison concerns an axial support estimate only; it does not predict lateral confinement or rotational dynamics.
• Ideal alignment: Emitter phase, placement, and facing alignment are presumed ideal. Small errors can shift nodes or reduce field strength.
• No safety or regulatory checks: The calculator does not assess exposure limits, electrical hazards, transducer ratings, or regulatory compliance.

Accordingly, treat the calculated spacing, node count, and force margin as indicative values. Measurements and more detailed simulations remain necessary for a precise acoustic levitation design.

Safety and Responsible Acoustic Levitation Use

Acoustic levitation experiments can combine ultrasonic sound pressure, high transducer drive voltages, and components that are sensitive to heat or vibration. Keep these practical safety points in view:

• High-intensity ultrasound can create hearing risks and can damage sensitive components.
• Liquids and biological specimens may warm or cavitate in strong acoustic fields.
• Follow laboratory procedures, transducer documentation, and applicable regulations before energising a setup.
• Use this calculation as a planning aid, not as a replacement for engineering review or a safety assessment.

Using the Acoustic Levitation Node Calculator Effectively

For a useful standing-wave levitation check, start with values that describe the actual medium, gap, and particle you intend to test:

• Use an appropriate sound speed for the medium; 343 m/s is a common starting point for room-temperature air.
• Adjust one input at a time to distinguish changes in node geometry from changes in the force estimate.
• Inspect force margin in µN by comparing the reported radiation force and particle weight, rather than assuming that a positive result guarantees stable trapping.
• Use the calculated node spacing when planning an emitter gap, then confirm the resulting field with experimental measurements.
• Refine promising configurations with detailed modelling or published experimental data before building a high-power system.

Understanding how frequency, medium sound speed, pressure amplitude, and particle properties enter this simplified model makes the calculator useful for exploring acoustic levitation concepts and planning early standing-wave experiments.