We investigate acoustic levitation in a vertical standing wave in an attempt to understand the basic physical mechanism responsible for this phenomenon. We find that a description in terms of a simple pressure force leads to the prediction of stable equilibria that occur slightly below the anti-nodes of the standing pressure wave. We then demonstrate that such a prediction is at odds with experimental data, which show that levitating particles come to rest slightly below the nodes of the standing pressure wave. Finally, we outline a theoretical approach based on fluid dynamics that correctly predicts the locations of the levitating particles, which leads to a simple qualitative description for this fascinating phenomenon.

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,”
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2018
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For a practical acoustic levitation setup, see
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Because we are mainly interested in the height of the levitating particles, we assume a perfect one-dimensional standing wave in the z-direction in our analysis. Experimentally, the transducer has cylindrical symmetry with a
small dimple in the center that leads to inward lateral forces and results in a stable lateral position for the particles.
7.
Using a small angle approximation for kz, the ponderomotive potential can be written U pond = κ z 2 / 2, where κ is an effective spring constant. With the help of Eq. (5), the oscillation frequency can then be written in terms of the acoustic frequency as ω pond = κ / m = A ω / 8 π 2. For the numerical simulations shown in Fig. 3, in which A = 1, we find a frequency ratio of ω / ω pond = 8 π 2 8.90, in excellent agreement with Fig. 3.
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9.
In some of our experiments, we incorporated a home-made transformer (as described in Ref. 1 
) between the amplifier and the transducer and, depending on the ratio of windings, this leads to different resonance frequencies.
10.
Some readers may find it surprising that the transducer surface results in a displacement node and a pressure anti
-
node
;
after all
,
the transducer is in oscillatory motion. This situation is analogous to producing standing waves on a string with nodes at the two ends even though one end is being driven. Although energy is being added to the system at the
“fixed” end of the string, the amplitude of the oscillation is very small; the large amplitude at an anti-node is a resonance phenomenon that results from multiple reflections from the ends.
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Langevin transducer analysis and acoustic levitation
,” Senior thesis, Lake Forest University <https://publications.lakeforest.edu/cgi/viewcontent.cgi?article=1133&context=seniortheses> (
2018
).
12.
Our mirror was made by AstroReflect (<astroreflect.com/en>) and cost approximately $3,000, including shipping and insurance. It can take 4–6 months for such a mirror to be constructed, so appropriate planning is important.
13.
In Fig. 7, our schlieren system has been set up to show only vertical gradients by orienting the wire light block horizontally. One can also orient the wire vertically to show horizontal gradients, or diagonally to show both vertical and horizontal gradients (but with a reduced sensitivity).
14.
We drive our LED using a universal LED controller (Metaphase ULC-2), which can be externally triggered.
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For a comprehensive discussion of studies on the effects of ultrasonic noise on humans, see
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