The speed of light is 186,282 miles per second. The speed of sound is 761.2 miles per hour. That takes care of vision and hearing, but what about our other senses? Shouldn't there be a speed of smell?
At first glance, it seems like there really ought to be. After all, smell isn't like taste or touch, where you need to be in physical contact in order to experience a sensation. You can smell a pretty flower or some diesel exhaust at a distance, which implies those odors traveled some distance to get to you and, by extension, they must have traveled at some speed. And, in a way, there is a speed of smell - it just depends on what smell you're talking about.
Getting up to Speeds
To understand why there isn't a set speed of smell, we need to first look at why there is a speed of light and a speed of sound. Really, these two speeds don't have much at all in common, other than the fact that they're both associated with our senses, so we should probably do a quick review of what they actually are.
The speed of light is a fundamental constant of the universe, the maximum speed at which all energy, matter, and information can travel. The reason why light travels faster than anything else is that light is carried by massless particles called photons, and only particles without mass are capable of attaining this maximum speed. Anything with mass will travel lower than light speed. Also, this maximum speed only refers to the speed of light in a vacuum - light slows down as it travels through materials, although most of the time we're talking about only very tiny decreases in velocity.
The speed of sound also varies depending on where you are, and the 761.2 miles per hour refers to how fast sound travels through air at sea level. But that speed can vary depending on altitude and temperature, and it can really vary depending on what the sound is traveling through. The speed of sound is four times faster in water, and 15 times faster through iron.
While light is carried by photon particles, sound is carried by waves. All sounds are the oscillation of pressure - vibrations in other words - through what's known as an elastic medium. Such mediums can include gases, liquids, solids, and even plasma, but, crucially, not in a vacuum. It's the presence of the medium that allows sound waves to be carried, and the composition of that medium goes a long way to determining the speed at which the sound travels.
The Varieties of Senses
So, if that's the quick version of how sound and light travel, how do these become the senses we experience in hearing and vision? In this regard, light and sound actually behave in fairly similar ways. While photons function as the individual units of light, as a whole light behaves like a wave traveling through space - this dual nature brings us to the edge of quantum mechanics, but thankfully we'll leave that to one side for today.
This means that both light and sound are essentially waves of energy. These are fundamentally different forms of energy than the electrical signaling used in our brains and nervous systems, and so our bodies have to convert the information carried by these waves into neural impulses. That's what our eyes and ears are for - they function as transducers that can handle the conversion process from one form of energy to another. They're not entirely identical processes, but there are definitely some key similarities, at least when compared to smell.
Our sense of smell, or olfaction, is a form of chemoreception, which means our noses transduce chemical signals into neural impulses. Our noses possess nearly four hundred olfactory receptors, and each of these bind with a specific molecular feature. Odorous molecules possess multiple features and so will trigger different receptors to varying degrees. These stimuli are then transduced into electrical signals that the brain can interpret.
And that's the key difference - while sound waves and visible light travel through the air so that our sensory organs can detect and transduce their information, smell is found in the odorous compounds that make up the air around us. So, then, determining the speed of smell is a bit like figuring out how fast air travels...in air. It's not quite as impossible as that might sound, but tracking the progress of odorous compounds is definitely a lot trickier than following the movement of photons and sound waves.
On the Odor of Compounds
Let's think for a moment about just where odors come from. Odors are the result of volatilized chemical compounds. In chemistry, volatility refers to the tendency of a substance to vaporize, or enter a gaseous state from its original liquid or solid form. Compounds are considered volatile when they have a low boiling point, which means large numbers of molecules can evaporate from the solid (like a flower) or the liquid (like a glass of wine) and enter the surrounding atmosphere.
Most odorous molecules are organic compounds, meaning they're carbon-based, although a few simple compounds like sulfur and ammonia also give off odors. This accords with our everyday experience - we know that plants and animals have odors, and by extension everything that that's made out of them, which can include everything from food and drink to wooden furniture to leather shoes. (And, just in case you're wondering, metal doesn't have a smell.) If you do run into an inorganic material that does have an odor, then the material is probably something human-made, and the odor was most likely an organic compound placed there by the manufacturers.
Our ability to detect odors depends on the amount of molecules available to our olfactory receptors. As I mentioned before, individual receptors respond to different compounds in different ways, but our olfactory system isn't really set up to detect specific compounds — instead, it reacts to all the various odorous stimuli all mixed together. Also, because our brains tend to ignore continuous stimuli, we lose the ability to detect odors after being around them for a while. This is why you generally have to ask somebody else if you want to find out what your own body odor smells like.
Sending Gas Through the Air
Now that we know that smells are carried by odorous gas molecules through the air, we can at least take a stab at working out the speed of smell. At the most basic level, particles tend to move from areas of high concentration to areas of low concentration until equilibrium is reached - this is known as diffusion. This is the basic driving force behind the movement of all odorous compounds and, thus, the fundamental determinant of the speed of smell.
Unfortunately, that doesn't tell us very much. In order to get to any single speed of smell, even just one that describes a particular compound, you need to know the temperature, the air pressure, and whether there's any external movement of the air such as, you know, wind. As we discussed earlier, there are similar factors in play that affect the precise speeds of light and sound. But the differences in the speed of light are insignificant, and we generally only care about the speed of sound in air as opposed to other mediums, so we can get away with ignoring these complicating factors and thinking of single values for the speeds of light and sound.
And that's where, in so many ways, the speed of smell falls down. Every smell is going to have a different speed depending on its own particular density, and then there are still so many external factors to control for that you can't really hope to come up with any particular value. We know that, thanks to diffusion, and odorous molecule will keep on diffusing until equilibrium is reached, meaning it's more or less evenly spread out in the air. Before that, the concentration of the odor will drop below the minimum threshold at which our noses can even detect its presence. And that's the final word on the speed of smell...
One Last Thing: Graham's Law
...or is it!? No, it isn't, because there's still one other way that we might think of the speed of smell. While smell doesn't really have any absolute speed, we can at least approximate in relative terms the speed at which different odorous compounds will travel. For that, we turn to Graham's Law of Effusion, which was formulated by the Scottish chemist Thomas Graham in the mid-1800s.
Graham's Law tells us that the effusion rate - or the speed at which gases flow through a hole without collisions between molecules - of a gas is inversely proportional to the square root of the mass of its individual particles, which is also known as the molar mass. Obviously, we're greatly oversimplifying here, because effusion isn't really the same thing as diffusion, but it's just close enough that we can come up with a basic estimate of how fast different smells will move, and this is about the only way we can deal with anything resembling a simple formula.
So then, let's use Graham's Law to compare the effusion rates of two odorous molecules, geraniol and skatole. Gerianol has a rose-like fragrance that is commonly used in perfumes, and it's naturally found in geraniums and lemons. Skatole is a somewhat toxic compound that occurs naturally in feces, and it's thought to be one of the main causes of odor in flatulence. Yes, in one of the most high-brow and intellectual thought experiments ever devised, I'm basically asking which odor, under ideal conditions, you would smell first: a rose or a fart?
Gerianol is composed of ten carbon atoms, eighteen hydrogen atoms, and a single oxygen atom, which gives it a molar mass of 154.25 grams per mole. (A mole is a unit equivalent to about 6*10^23 individual molecules). Skatole, one the other hand, has nine carbon atoms, nine hydrogen atoms, and one nitrogen atom, which adds up to a molar mass of 131.17 grams per mole. Graham's Law says that the rate of gerianol effusion divided by the rate of skatole effusion will equal the square root of the molar mass of skatole divided by the molar mass of gerianol. In other words...
Gerianol/Skatole = √(131.17/154.24) = √(.85) = .92
This means that the rate of effusion of gerianol is about 92% that of the rate of effusion of skatole. In other words, the speed of smell of a fart is faster than the speed of smell of a rose. Admittedly, that's all one hell of a massive approximation, but that still seems like the sort of information that's just worth knowing.