The Acoustic Levitation Ceiling: Air Itself Sets the Largest Object Sound Can Hold Up

The radiation force on a small sphere in a standing wave in air is evaluated from the Gor'kov expression. The contrast factor is Phi = 0.832 for water, 0.833 for glass and 0.833 for steel: in air essentially every condensed material has Phi close to 5/6. Balancing force against gravity, the radius cancels, so for objects much smaller than the wavelength the levitation condition is on density and field alone: at 40 kHz the minimum level is 152.8 dB for a water-density object, 156.8 dB for glass and 161.7 dB for steel. Air caps the field itself: a sine whose peak exceeds one atmosphere cannot exist, and the conventional waveform-distortion limit is about 194 dB re 20 uPa on a peak-pressure basis (191.1 dB rms for the largest undistorted sine). At realistic device levels of 150-165 dB the energy density is 2.82-89.3 J/m3 and the radiation pressure is of the same order in pascals. For objects near or above the wavelength the force is bounded by radiation pressure times projected area while weight grows with volume: at 160 dB the largest holdable sphere has radius 2.16 mm for water and 0.28 mm for steel, the maximum slab thickness is 2.88 mm for water, and a 40 kHz trap (wavelength 8.6 mm) holds at most 0.042 g of water per site. These bounds agree with the record: millimetre droplets, centimetre foam, gram-scale small animals, nothing dense and large. The negative result is stated at full size: levitating a person, a car or a building stone with sound in air fails by factors of 11 to 434 at the strongest realistic fields, and amplifier power cannot repair this, because above the distortion limit extra energy leaves as harmonics and heat instead of force. The ceiling is set by the pressure of air itself. All derived numbers are produced by the deposited compute.py. This is a calculation, not a measurement. AI use is disclosed: this paper was produced by Dave, an AI system, which carried out the derivation, computation and drafting under the direction of the named author. The author, William Alexander Aldred, is sole author of record.