Acoustic Levitation: A Theoretical Exploration Sarah Fontana Irina Liu [email protected] [email protected] Devin Moeller Kimberly Robins [email protected] [email protected] New Jersey Governor’s School of Engineering and Technology 22 July 2016 Abstract 1 Introduction For many years, scientists and other have investigated technology that can be used to defy gravity. Thanks to research that be- No longer confined to science fiction, gan decades ago, pressure produced by sound acoustic levitation - the use of high and low waves can now provide a way to levitate ob- pressure zones in standing sound waves to sta- jects and to stabilize them against gravitational bilize objects against the pull of gravity - is and other forces. a real technological advancement that can be applied to various areas of science, medicine, Though the principle of acoustic levi- and industry. It can be used to solve a broad tation arose in the 1940s, the technology of range of problems and to optimize and sup- standing waves had been explored long be- plement many technologies that already exist, fore then. German physicist August Adolph such as human cell research. The authors con- Eduard Kundt experimented with the manip- ducted extensive research and concluded that ulation of sound waves to form nodes and with the current technology, acoustic levita- antinodes in the mid nineteenth century. His tion works best in a lab setting, and is not yet “Kundt’s Tube” is a basic model that tests feasible for commercial or industrial use. With for nodes in standing waves using a closed more research, however, it can be perfected glass tube[1]. Several decades after Kundt’s and made exceedingly practical. The follow- research, American physicist Charles Albert ing paper explores in depth a theoretical ex- Rey was credited with the first successful use periment that could be conducted in order to of an acoustic levitator. acquire data about the potential and limits of acoustic levitation. Today, scientists all over the globe in- 1 vestigate and utilize acoustic levitation in the relationship of the velocity of a particular kind fields of medicine and technology. Physicists of wave through the medium, the frequency, at Utah Valley University, for example, have and the wavelength. This equation allows for used acoustic levitation for advanced cancer physicists to calculate basic characteristics of diagnostics by using the pressure differences waves in order to apply them to their research. within the wave to test the density of human cells[2]. With more research and experimen- tation, acoustic levitation will also come to v = fλ (1) revolutionize the packaging and transporta- tion industries by making it easier to handle Equation 1: The Wave Equation small, fragile objects and corrosive materials. *The Greek letter lambda (λ) represents wave- Acoustic levitation is a field of great length. The denotation (v) stands for velocity opportunity, as there are many potential im- and frequency is denoted as (f). provements to be made to the already devel- oped technology. A functioning acoustic levi- The fact that sound is a wave is im- tator will counteract the force of gravity acting portant for many reasons. As a wave, sound upon an object, but it is also important to see can be reflected. Depending on the surface, how forces can be balanced in other directions waves can be reflected back upon themselves as well. The experiment detailed below was or even directed in different directions. Sound designed to research these ideas by testing the waves through gas are longitudinal, with fronts strength of acoustic levitation when the stand- that move parallel to the direction of motion. ing wave was disturbed by an outside force. There are areas of compression, where the par- ticles in the medium are closer, and areas of 2 Background rarefraction, where the particles in the medium are more spread out. Most sound waves are de- 2.1 Sound Waves picted as transverse for convenience because the crests and troughs of transverse waves Sound is a type of disturbance created are easier to visualize than the compressions by vibrations. As an object vibrates quickly, and rarefactions of longitudinal waves. Even it disrupts the the particles around it and pro- though the image of a transverse wave is use- duces a wave of pressure, carrying this dis- ful because the pressure variations of sound turbance across space[3]. The propagation of waves are sinusoidal, it is still important to sound relies on the movement of surround- remember that sound waves are actually lon- ing particles and thus, sound waves can only gitudinal pressure waves. travel in a medium. In most cases that humans are concerned with, the medium is air. The sound waves push and pull the air molecules, which then push and pull the particles near them. Some energy is lost in this transfer so, like all waves, sound waves will not travel in- definitely. As long as people are close enough to the source, the vibrations will pass through their eardrums and produce what humans per- Figure 1: This diagram shows the basic ceive as sound. Below, Equation 1 shows the components of a longitudinal wave. The 2 compressions and rarefractions show the wave pressure differences cause the wave to propagate through the air.[11] Figure 2: Transverse waves clearly show where the maximums and minimums are located, especially since they can be modeled Figure 3: Longitudal Standing Waves[13] by a sinusoidal function. Where the graph or wave crosses the x-axis is where one would place an object to levitate. These spots are the nodes of the transverse wave. [12] λ L = n n (2) 2 2.2 Levitation Equation 2: Relationship Between Lambda Acoustic levitation centers around the and Length ability to create standing waves. Standing waves are formed when two waves of the same frequency interfere while traveling in exactly The symbol (n) will refer to the degree of the opposite directions. An acoustic levitator re- harmonic. (L) represents the distance of the flects a wave upon itself, so the resulting fre- medium. quencies are the same while the directions are exactly opposite. The points of destructive in- Objects tend to move from areas of high terference along the reflected wave are called pressure to low pressure, so objects placed in nodes. Equation 2 provides insight about the the standing wave will move to the nearest location of the nodes and distance between the node. The movement from high to low pres- transducer and the reflection needed to create a sure is explained by the second law of thermo- particular wavelength. At the nodes of a stand- dynamics, which explains how energy tends to ing wave, there is essentially no wave move- flow from areas of high concentration to low ment so the pressure is very low. Directly be- concentration. Thus, the low pressure and low tween nodes, the standing wave reaches points energy nodes are ideal places for objects in a of maximum displacement called antinodes. standing wave to rest. In space, where there is The greater the distance from the node, the negligible gravity, the objects will stay exactly greater the pressure, so these antinodes have at those nodes. On Earth, however, the objects maximum pressure[4]. This pressure is also will sit slightly below the nodes because equi- explained because the antinodes are points of librium is established where the upward force constructive interference and the wave has a from the wave is equal to the downward force lot of resonance in those areas. from gravity. 3 2.3 Constraints Upon the Levitator When building an acoustic levitator, a transducer is needed to convert electrical en- Several factors limit the real-world use- ergy to sound. The energy starts in a func- fulness of acoustic levitation technology. tion generator. The function generator runs an Firstly, since low pressure zones exist be- electric signal to generate waveforms, which tween the nodes of standing sound waves, it then sends to an amplifier. The amplifier these zones can only measure half of the wave- is used because the transducer alone usually length of the standing wave. Therefore, an cannot generate a sound strong enough.The acoustic levitator can only levitate objects with amplifier increases the volume and thus inten- diameters smaller than that. An additional, re- sity and amplitude of the sound waves. The lated constraint is that only sound waves with amplified waves are then sent to the trans- frequencies above 20 kHz can be used to lev- ducer. In some setups, the transducer is simply itate macroscopic objects, so the equipment a speaker. After the sound waves are amplified used to generate the frequency must be pre- and travel out of the transducer, they hit the re- cise[5]. Additionally, since the pressure pro- flector. The reflector bounces the waves back duced by the wave must counteract the force of upon themselves and thus creates a standing gravity upon the levitated object, the levitator wave by causing interference between iden- can only support objects that weigh less than tical waves in opposite directions. Different the wave’s maximum pressure. More mas- shapes are used to create the reflector depend- sive objects can only be levitated by extremely ing on how researchers plan redirect the sound loud sounds produced with immense amounts waves and create a standing wave. Curved re- of power. flectors tend to be used because they provide a more focused pressure on the levitated object. 2.4 Levitator Design To make sure that the sound waves properly reflect back upon themselves, the reflector in the apparatus sits upon a lab jack. Adjust- ment of the height of the lab jack changes the distance between the reflector and the trans- ducer.This change in separation is important because the reflector must be positioned so that it is at a distance that is a multiple of half the wavelength of the sound wave.