Parametric Speaker Frequency Calculator

1. Enter the ultrasonic carrier you plan to drive the array at (40 kHz is the default because the most common low-cost transducers resonate there).
2. Enter the highest audio frequency you want to reproduce. The tool returns the AM and DSB-SC sideband frequencies the array must actually radiate — the modulator and amplifier have to be flat over that whole band.
3. Enter the array aperture diameter directly, or tick the box and build it from an N×N grid and element pitch.
4. Adjust the speed of sound if you are not at ~20 °C in air. The carrier wavelength λ = c/f_c and every beam-width result follow from it.
5. Read the sideband plan, the carrier wavelength, and the beam-width estimate, and watch the directivity sketch update. Treat the beam numbers as a far-field upper bound, not a guarantee.

Carrier & sidebands. To send audio on an ultrasonic carrier you modulate it. With classic AM (DSB with carrier) the array radiates the carrier f_c plus an upper sideband at f_c + f_a and a lower sideband at f_c − f_a; the total occupied bandwidth is 2·f_a. With DSB-SC (suppressed carrier) the same two sidebands are present but the carrier is removed, which changes the demodulated distortion. In air’s nonlinear self-demodulation the difference-frequency term is what becomes your audible f_a, so the array genuinely has to reproduce the carrier and both sidebands cleanly — the example above shows where they all land.

Carrier wavelength. λ = c/f_c. At 40 kHz in air this is about 8.6 mm. Because the beam is set by this very short ultrasonic wavelength rather than by the audio wavelength (metres long), a palm-sized array can produce a tightly focused beam that an ordinary loudspeaker of the same size never could at audio frequencies — this is the whole point of the technique.

Beam width. For a uniformly-driven circular aperture of diameter D, simple diffraction gives a first diffraction null at a half-angle θ₀ where sinθ₀ = 1.22·λ/D (the Rayleigh / Airy-disc relation, with 1.22 being the first zero of the J₁ Bessel function). The half-power (−3 dB) full beamwidth is roughly 58.4°·λ/D for the same aperture. Larger D or shorter λ (higher carrier) → narrower beam. Honest caveat: these are idealised far-field approximations for the carrier; a real parametric array has a long collimated near field, the self-demodulated audio beam follows its own physics, and in practice the audible beam is usually narrower than the half-power figure here — so use these as an orientation, not a spec.

A parametric (or parametric-array) loudspeaker exploits the fact that air is a slightly nonlinear medium. The principle was set out by Westervelt in 1963 (“Parametric Acoustic Array,” J. Acoust. Soc. Am. 35, 535), who showed that a high-amplitude beam of ultrasound generates new sum- and difference-frequency components as it propagates — the medium itself acts as a distributed mixer, a process called nonlinear self-demodulation. Yoneyama and colleagues in 1983 turned this into the “audio spotlight” directional loudspeaker (J. Acoust. Soc. Am. 73, 1532), modulating an ultrasonic carrier with audio so that the difference frequency that demodulates in air is the audible signal — arriving as a narrow beam you can aim like a torch.

The signal chain is: a baseband audio signal (up to f_a) modulates an ultrasonic carrier f_c; a class-D ultrasonic amplifier drives a transducer array with that modulated carrier; the array launches a high-intensity ultrasonic beam; and as the beam travels, air’s nonlinearity demodulates it back to audio along the beam path. Because the beam’s directivity is governed by the very short carrier wavelength (millimetres) rather than the audio wavelength (metres), the audible sound stays collimated in a tight column — only listeners in the beam hear it.

This tool computes the parts of that plan that are pure, exact arithmetic — the sideband frequencies (f_c, f_c±f_a) and the carrier wavelength λ = c/f_c — and adds an approximate beam-width estimate from standard circular-aperture diffraction. It does not model the self-demodulation efficiency, the achievable SPL, harmonic distortion, or the near-field length, all of which depend on drive level, modulation scheme (AM vs DSB-SC vs single-sideband, and pre-processing such as square-root distortion correction) and transducer behaviour. For those you need the full Westervelt/KZK propagation models and real measurements.

Two honesty points specific to this category. First, nothing on this page makes ultrasound — a web browser, laptop or phone outputs ordinary audio (typically capped near 20 kHz), and consumer speakers and headphones cannot cleanly reproduce 25–80 kHz; emitting a real carrier requires dedicated ultrasonic transducers. Second, the beam-width formulas are idealised: they assume a uniformly-illuminated circular aperture radiating into the far field, ignore the long collimated near field of a real array, and treat the carrier rather than the demodulated audio — so read them as a sanity-check on geometry, not a measured beam.

• Museum & exhibit audio spotlights — deliver a narration only to the visitor standing in front of an exhibit, with near silence a step to either side.
• Directional signage & retail — aim a message at a single display, kiosk or aisle without flooding the whole space with sound.
• Personal sound zones — give one seat in a car, office or living room its own audio without headphones, leaving neighbours undisturbed.
• Targeted alerts & assistive announcements — reach a specific listener or location rather than broadcasting everywhere.

In every case the appeal is the same property this calculator estimates: a beam set by the ultrasonic carrier wavelength, far narrower than any ordinary speaker of the same size. Real-world performance (loudness, fidelity, beam shape) depends heavily on the drive electronics and transducer array — build and measure before you design around a specific figure.