Today's refrigerators use a compressor that condenses some refrigerant (likely HFCs, or hydrofluorocarbons), increasing its pressure and temperature. A fan then blows air over pipes (condenser coils) holding this warm high-pressure gas, and as heat transfers to the outside air the refrigerant condenses into a liquid (and becomes somewhat cooler). The cooler liquid then travels through an expansion valve that allows the liquid to expand and evaporate (as its pressure decreases). During this process of evaporation, the refrigerant absorbs heat from the air inside the refrigerator, cooling it. The refrigerant, now in a low-pressure gas state and somewhat warmer, completes the cycle by flowing back to the compressor.
So how can you cool a refrigerator using sound waves? First, you have to know what sounds waves really are. They're pressure waves. In other words, they are variations in pressure in some medium (like air), over some distance (really, volume). They are alternating "bands" of high and low pressure, with lots of air molecules packed together in the high pressure "bands" and relatively few molecules of air in the low pressure "bands". They move through the air like a shock wave moves through a horizontal Slinky. When a sound wave passes through a room, it passes energy along to some air molecules, which then forward the energy to nearby air molecules, which do the same thing, and on and on. (Again, like the Slinky.) Each individual air molecule oscillates over a very short distance and does NOT follow along with the wave. Sound is not a way to transfer individual air molecules from one place to another. It IS a way to transfer a pressure variation (in the medium) from one place to another.
When you hit a drum, the membrane vibrates up and down. It moves up, pushing air molecules forward and out of its way, forcing them closer to the air molecules that were just above them, creating a thin high pressure zone that then propagates forward at some speed characteristic of the medium (in this case, air). Then the membrane moves down, creating a semi-vacuum, opening up a space with few air molecules in it, creating a low pressure zone. Then it moves back up and produces another high pressure zone. This cycle continues as long as the drum's membrane vibrates, and these alternating high and low pressure zones continue to move outwards in basically all directions at a speed of about 760 mph.
Now, when gas is compressed, not only does its pressure rise, but also its temperature. For air compressions associated with normal human speech, the temperature change is miniscule, only about one ten-thousandth of a degree Celsius. The temperature change in something like the HFCs, mentioned earlier, as they move through the refrigerator's compressor, is much greater. (The compressor is obviously much more powerful than our vocal cords.) To make the sound wave useful for transferring a significant amount of heat, it needs to be able to handle a larger temperature span. This can be accomplished in two ways. The first way is to use more intense pressure waves (i.e. crank up the volume). The second way is by putting it (i.e. the air molecules) in contact with a solid material. If a gas carrying a sound wave is placed near a solid surface, the solid will tend to absorb the heat of compression (i.e. the heat associated with the temperature increase, brought about by the pressure increase), keeping the temperature stable. The opposite is also true: The solid releases heat into the gas when the gas expands, preventing it from cooling down as much as it otherwise would.
OK, so picture a long rectangular plate (perhaps metal, perhaps plastic) with an intense sound wave traveling along its surface. (Picture the wave as traveling from left to right.) When the sound wave first reaches the plate, the phase is, say, coming off a high pressure zone. The air molecules floating near that end of the plate start to expand, forming a low pressure zone. As the gas now expands, it extracts heat from the solid with which it is in contact. This heat (energy) is then passed forward by the sound wave. The wave then enters a period of high pressure, a bit farther down the plate, and as the air molecules in that region are compressed, they pass on their heat to the solid surface. The wave has now relocated a bit of heat from one end of the plate to the other end (or at least a point a bit farther down the plate).
You should now be asking yourself, won't a high pressure zone follow the initial low pressure zone, at the front of the plate, passing on heat to that end of the plate, offsetting the transfer of heat just accomplished. You'd be right if the structure wasn't designed to alleviate this problem. Take a look at the following picture:
Even though it doesn't look like it, let's pretend that the left end of the tube is open and the right end is sealed shut. Now when a sound wave enters the tube from the left, it travels to the closed end and, having nowhere else to go, is reflected back towards the left end. The red line here is a graph of sorts. It marks the magnitude of the pressure above or below the "normal" or atmospheric pressure, which is indicated by the dashed line. The wave, entering the tube, follows the upper red line, and pressure grows until it reaches a maximum at the right end of the tube. The air is piled up at the right end of the tube, hence the high pressure zone. When the air pushes into the wall at the tube's end, the wall pushes back, and the air starts moving back towards the left. It now rushes away, creating a low pressure zone at the tube's end. We now follow the lower red line back towards the left of the tube, as the pressure difference between the wave and the "normal" pressure is reduced until they equal one another at the "node" at the left end of the tube. When successive waves are timed just right so that they always follow this pattern, we obtain a "standing wave." That is, waves reinforce one another and don't cancel out. We say the standing wave is resonant or has a resonant frequency. This property of the system allows our sound-based refrigerator to work. We can alter the frequency of the sound waves in our device until we find one that supports a standing wave, and this way we can control where along a closed tube, as well as our plate, we have a high pressure zone and where we have a low pressure zone. We can ensure that we always have an expanding pressure zone (primed for compression) at the front of the plate. And we can ensure that we always have a fully compressed zone at the end of the plate. The fact that we can change the length and position of the plate, within the tube, makes this task easier. (Im simplifying a bit here, for brevity.)
Lets restrict our focus to a single parcel of gas, situated in an enclosed tube with a plate running along some portion of the tube. Remember, each parcel of gas moves over a very small range, back and forth; parcels do not move along with the wave. As a wave [of energy] approaches, it forces a parcel of gas to expand, lowering the temperature of the gas parcel to something less than the temperature of the plate. Heat then flows into the parcel, in an attempt to equalize the temperature, and this causes further expansion of the parcel. This heat is then carried by the parcel a short distance forwards (perhaps a centimeter) and is passed along to another gas parcel. Like a bucket brigade, heat is passed along until it reaches a point in the standing wave that corresponds to high pressure, where the parcel is compressed, raising its temperature to something above the temperature of the plate at that point. Heat then moves from the gas parcel into the plate, in an attempt to equalize the temperature. This happens again and again, during each cycle of the acoustic wave, creating a cold end of the plate and a hot end of the plate. Heat exchangers can then be placed at each end of the plate. These may be pipes filled with something like antifreeze, which transfer heat into or out of the plate. At the cold end of the plate, the antifreeze is in a pipe that runs through the walls of the refrigerator box, pulling heat from the air in the refrigerator and dumping it into the plate, from which the heat is extracted and carried away by the sound wave. The hot end of the plate is placed alongside a separate pipe (also containing some fluid, such as antifreeze). The fluid here absorbs heat from the plate and carries it away, to a section of pipe that is in contact with the outside air, and over which a fan blows. Heat then flows out of the fluid-filled pipe and into the air in the room, leaving the fluid cooler and ready to return to the plate for another round of heat transfer.
Though somewhat complicated, this design allows for the construction of a refrigerator that has few moving parts and that, perhaps most importantly, doesn't rely on HFCs, which are greenhouse gases (that have the potential to find their way out of the refrigerator's pipes and into the atmosphere). Furthermore, a sound-based refrigerator is unlike a conventional compressor-based refrigerator, in that it can run at full force or less. That is, it can be adjusted in real-time to run at precisely the appropriate level for the desired temperature and heat load. A conventional refrigerator's cooling system is either on (at full-force) or off. The current drawback to thermoacoustic refrigerators (as they're called): they're not very efficient. They use lots of electricity versus conventional models. If they can be made more efficient, we may start to see them in the market place. (But don't hold your breath.)
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