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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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
, 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
. For the numerical simulations shown in Fig. 3, in which A = 1, we find a frequency ratio of
, in excellent agreement with Fig. 3.
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-node
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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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).© 2021 American Association of Physics Teachers.
2021
American Association of Physics Teachers
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