Welcome to another installment of The World Through Sound. Previously we learned about the acoustic medium, and how sound can even move through the seeming vacuum of space, and shape entire galactic structures in the process. Today’s article is a direct follow-up to that article since we will be talking about one of the most important features of any acoustic medium: acoustic impedance. In the process, we will learn how an acoustic horn works, and the answer may surprise you!
It is likely that you have heard the term impedance (or the related term, resistance) when describing electronics. Impedance holds a special place in electronics, as it is the value that ties together the two most important quantities in an electrical system: voltage and current. Circuit diagrams are ultimately just maps of impedance, and by knowing what those impedances are, an engineer can understand the behavior of even a complicated system of resistors, capacitors, inductors, and even more complex components.
Acoustic impedance is quite similar to its electrical cousin, but instead of describing how electrons flow when exposed to the voltage of an electric field, it describes how the acoustic medium flows when exposed to the pressure of a sound wave. And while acoustical engineers may not work with circuit diagrams as often as electrical engineers, understanding the impedance of all of the elements in acoustic network can help us understand otherwise complex problems much more simply.
In a previous article we discussed the acoustic medium, and its importance in how sound travels. Every acoustic medium has what is known as a “characteristic specific acoustic impedance,” which essentially describes the impedance of the material for a generalized sound wave. This acoustic impedance is simply the product of the medium’s sound speed and density. Thus, a medium with a low sound speed and density (like air) will have a much lower impedance than a medium with a comparatively high sound speed and density (like water). As a direct result of this, if you wanted to compare two sound waves with the same pressure in both water and air, the wave in air would be considerably more intense than the wave moving through water.
At this point it would be natural to ask the question “Which is better, a higher or lower impedance?” The answer, though, is “neither.” This is because of a practice known as “impedance matching,” which takes advantage of when the impedance of two different parts are made as close as possible.
Impedance matching is derived from a simplified version of an acoustical (or electrical system) where there are two parts: a source and a load. The source generates sound ultimately destined for the load, with the goal usually being to maximize the power delivered to that load. A simple example of this sort of system would be a speaker sending sound out into the air. In this case, the speaker is the source and the outside air is the load. Without going into too much math, the answer to this problem is to make the impedance of the source match the impedance of the load, but reaching that goal can be difficult.
This brings us to the concept of a transformer. Electrical transformers are a common enough sight, either cylindrical canisters on the top of a power pole or large boxes humming on the ground. These transformers are designed to change a high voltage and low current on one side into a low voltage and high current on the other side. Notably, for an ideal transformer, the power on both sides of the transformer is the same. A common use for a transformer is impedance matching because a transformer connected to a load changes the apparent impedance of the load.
The concept of a transformer goes beyond electricity, however, and chances are that you have used a common transformer throughout your life without even realizing it: the lever. The lever, it turns out, is the mechanical equivalent of a transformer. On one side of a fulcrum, you apply a small force over a long distance, and the other side experiences a large force over a small distance. Levers make many otherwise difficult tasks nearly effortless. A bottle opener, for example, allows a person to bend a piece of metal using only the strength of their hand, and other tools, like crowbars and cranes, also make use of levers to make work easier. Levers even exist throughout our bodies, with practically every joint in our body acting as a fulcrum. Our middle ears even have levers, which match the acoustic impedance of the air at our ear drums to the fluids of the inner ear!
And this brings us to one of the most misunderstood tools in acoustics: the horn. Much like how transformers are ubiquitous in electricity, and levers are used throughout mechanics, horns are some of the most commonly used tools in acoustics. They have been used for centuries for passively amplifying sounds. No doubt, you have an image in your mind of a common horn, like the bullhorns used by cheerleaders at football games or the long conical horns attached that were part of the first record players, long before electrical amplification became the norm. Horns even occur in nature, with the open mouth of a person shouting being an obvious example.
Horns, however, are as misunderstood as they are ubiquitous. I have heard physicists describe a horn as a tool that increases directionality (a topic we will cover more in a later article). The horn, by this description, supposedly works by focusing the acoustic energy in one direction, keeping it from spreading out all over. By this description, the total sound power generated with the horn is the same as without it, but the sound is distributed less evenly. This explanation seems natural, especially given the nature of the horn as a passive device, and to some extent this explanation is true. But there is more to story that gets left out with this explanation, the horn’s role as a transformer, and how it can make sound sources more efficient.
Earlier we discussed the idea of a source and load, and how matching the impedance of those two parts of a system can increase the power delivered by the source. If we look at the specifics of most acoustics problems, we find that air in a free environment has a surprisingly low impedance compared to the sources we want to use with it. To match the source to the load, in this case, we need to make the source impedance as low as possible, which is a difficult task to say the least! Alternatively, we can try to increase the apparent load impedance…exactly the sort of job that a transformer is made for!
So, how does a horn achieve that goal? Simply put, the less room that air has to move around, the higher the impedance it presents. A small amount of air enclosed on all sides is much stiffer than a large volume of air. An open space, like we usually send sound into, has the lowest impedance that you can get for air. By starting with a small space (the small end of the horn), and gradually working up to a larger space (the big end of the horn), you can slowly transition from a high impedance to a low impedance, and ultimately couple to the outside air. This is much like how a long rod being used as a lever provides more and more mechanical advantage, the further you get from the fulcrum.
Using this transformer analogy of the horn, we can see how a horn makes a source louder. Rather than wasting acoustic energy when coupling the source to the air, more of that energy makes it to the listener. A horn not only focuses sound, but also increases the total amount of sound there is to focus!
Now that you understand the true value of a horn, hopefully you will start to see how horns are all around us. Our ears are horns, coupling our eardrums to the outside air. Crickets try to find tight corners to stand in when making their songs, the walls acting like a horn to amplify it (and burrowing crickets even dig their own highly advanced horns). Subwoofers in living rooms are often placed in corners or against walls, turning the room itself into a horn to improve the listening experience. The list goes on!
Next time we will learn about resonance, and how unexpected resonances can have consequences ranging from annoying to utterly catastrophic.
Andrew “Pi” Pyzdek is a PhD candidate in the Penn State Graduate Program in Acoustics. Andrew’s research interests include array signal processing and underwater acoustics, with a focus on sparse sensor arrays and the coprime array geometry. Andrew also volunteers his time doing acoustics outreach and education as a panelist and moderator on the popular AskScience subreddit and by curating interesting acoustics news for a general audience at ListenToThisNoise.com.
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