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• Andrei Markin

# Simple acoustic levitation

Updated: Mar 18, 2019

Float things with sound!

This might sound like science fiction or something that only physics labs can afford but this is not true, as I found out you can make your own for just a few pounds.

The physics gets a little complicated but the general idea is that if you take a sound wave and reflect it back into itself, this will setup a stationary wave. Somewhere along that wave there will be a condition (or several of them) where the forces are directed towards a single point, and if the acoustic power is high enough, this can overcome gravity and we get stable levitation.

The frequency of this wave must be high enough so that the object does not drop out of the pressure node ("levitation zone") during a single cycle.

These frequencies are therefore usually in the ultrasonic range (< 20 kHz) so we need a special speaker to generate the wave. Luckily these can be found pretty cheap if you take the transmitter side of these cheap HC-SR04 range finder modules.

These speakers are quartz crystals which usually resonates at 40 kHz. The easiest way I found of driving them is using an arduino to generate a 5V 40 kHz square wave and then buffering it with a TC4427 mosfet driver. The driver is powered from a boost converter which puts out 18 V from the arduino's 5V supply.

Finally to double the available power I decided to use 2 opposed speakers rather than one reflected into itself. I figured this would mean that the speakers have to be a set distance apart to mix in phase. So I designed this 3-piece jig to hold the speakers and change their separation by turning the center screw. It turns out that this has very little effect but it did make for some nice results. The jig can be 3D printed and transducers glued on with hot glue.

The wavelength of the sound can be calculated by λ = c / ν, which is ~0.9 cm for a 40 kHz wave travelling at 340 m/s. This means that the levitation zones are spaced out by roughly 5 mm.

This can be tested, because these speakers can also act as microphones. A signal can be fed into the bottom transducer and read out from the top:

The yellow trace is the signal sent out on the bottom transducer and the purple is the signal received on the top transducer.

Firstly you can see that only the fundamental frequency of the 40 kHz square wave gets transmitted, and secondly changing the distance essentially "steps through" the stationary wave. The height screw has a pitch of 1 mm therefore it takes around 4 turns to cause a 180 degree phase shift.

Now we are ready to levitate things! I lined up the transducers so that the received signal is in-phase with the transmitted signal, and re-wired the top transducer to act as a transmitter again. Now anything small and light, like polystyrene beads, gets pulled into the pressure nodes and floats. Wizardry!

We can also look at the pressure nodes directly; if you put a piece of dry ice next to the wave, the cold air is drawn into the low pressure nodes and water vapour is condensed out:

## Now the not quite so simple acoustic levitation

Using two of these rigs its actually possible to make a speaker in which the air itself is the diaphragm. Imagine taking a pressure node from one rig and moving it back and forth using a second pair of transducers. The pressure node can now act as the diaphragm in a speaker. This is my setup to try this:

Its a little crude but what I have here is a set of traducers driven at a constant resonant frequency (yellow), and perpendicular to that is another set (white) which can be driven at any frequency from a DIY signal generator. There is also a microphone to record the sound coming out of the setup.

Using an oscilloscope, the frequency of the yellow pair is exactly 40,006.8 Hz. My signal generator has a resolution of 1 Hz so I set it to output three different frequencies to try and generate three different tones.

The frequencies are :40,007 Hz, 40,010 Hz and 40,030 Hz. The top trace is the signal feeding the yellow transducers and the bottom trace is the signal feeding the white transducers:

I should mention here that the transducers on their own do not make any sound that you can hear, but have a listen to what the microphone picks up when the three offset frequencies are fed in on the white transducers:

There is sound!! It looks like the microphone picks up: a sub 1 Hz, ~ 3 Hz and ~ 23 Hz sounds

The physics here is actually pretty simple, when two waves of different frequencies (f1 & f2) interfere their superposition looks like:

We end up with 2 new frequency components: one at the average frequency ([f1 + f2] / 2), and one at half of the difference in frequencies between the original waves ([f1 - f2] / 2). Since our ears are not sensitive to phase it simplifies to just the difference between the original frequencies (f1 - f2), called the beat frequency.

Which is exactly what the microphone picks up:

40,007 Hz - 40,006.8 Hz = 0.2 Hz

40,010 Hz - 40,006.8 Hz = 3.2 Hz

40,030 Hz - 40,006.8 Hz = 23.2 Hz

So as long as the frequencies stay close to the resonance frequency of the quartz transducers, what we have here is a speaker made out of thin air.

Update:

Because anything worth doing is worth overdoing

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