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Why can you still get sunburned on a cloudy day?

posted Jun 7, 2015, 1:24 PM by Patrick Poole   [ updated Jun 7, 2015, 1:24 PM ]

Sun behind clouds--thanks denebola2025!
Now that summer is upon those of us in the northern hemisphere, it’s a good time to talk about physics related to enjoying the warmer weather. One warning you’ll often hear is that you can still get sunburned on a cloudy day, and so you should still wear sunscreen even though it isn’t as bright out.

The sun emits many different frequencies of light, only some of which are visible

The nuclear reactions within the sun are constantly producing light. The details of solar activity are complicated and can have nuances that still are not well understood by scientists, but we do know a lot about the nature of light that the sun emits. Physicists call the sun a blackbody radiator, which refers to the light that is emitted from an opaque, non-reflective (hence black). It turns out this spectrum of light depends only on the temperature of the object, and the sun can be approximated as emitting such a blackbody spectrum based on its surface temperature of about 5000 kelvin. That has important implications for the nature of light that we see, but the details are another (upcoming) post.

Our sun emits quite a lot of visible light, but many other frequencies of light as well. The most harmful of these—x-rays and gamma rays, for example—get stopped or scattered in the Earth’s ozone layer, which is why it’s critical to protect. Light with frequency closer to the visible spectrum can get through this layer and reach the ground—this includes ultraviolet light, which has frequencies just higher than the visible spectrum, and infrared light, which has frequency just lower than visible.

Clouds are good at blocking out visible light, but not other frequencies

Clouds consist primarily of water vapor or water droplets, and this determines the way light interacts as it travels through them. The details of how visible light scatters in the cloud actually results in their white color, but that’s another post. It’s certainly true that dark clouds appear that way because their increased water content blocks light from passing through to reach the ground.

This isn’t true of all frequencies, though—visible light is scattered or absorbed quite well within clouds, but not ultraviolet or infrared light. In fact, a good rule of thumb (with plenty of counterexamples) is that if a material is transparent in the visible light range it is probably opaque to infrared and ultraviolet light, and vice versa.

Only visible light is blocked thoroughly by clouds
Ultraviolet light mostly goes through clouds, and is responsible for sunburn

Ultraviolet light, for example, is only cut down by about 30% when there are many clouds in the sky. Even if the sky is dark from overcast clouds as much as 30% of the UV light from the sun will still penetrate and reach the ground.

Ultraviolet light is responsible for the skin damage that results in sunburn, and subsequently in tanning. The sunburn is a result of the ultraviolet light causing damage directly to the DNA as it is absorbed within skin cells. Part of the body’s response to this damage is to cause the cells to die, which will eventually result in skin peeling. Increased melanin production is also triggered, which is a chemical that absorbs ultraviolet light and serves to protect the skin somewhat from further sunburn—as a pigment, it’s also responsible for skin tanning.

Nowadays you’ll see sunscreen that claims to block two types of ultraviolet radiation: the UVA band, which has frequency just higher than violet light, and the UVB band, which has frequency just higher than the UVA band. These two different regions of the ultraviolet spectrum are emitted from the sun with different intensities, and interestingly they affect skin in different ways. UVA light penetrates deep into the skin, and is the primary contributor to tanning. UVB, on the other hand, doesn’t penetrate skin as deep but is primarily responsible for the reddening and pain that is sunburn. It’s important to protect against both bands of ultraviolet light in order to prevent skin damage.

Thanks to Denebola2025 for the sun and clouds picture.

Why is static shock worse in the winter?

posted May 3, 2015, 10:29 AM by Patrick Poole   [ updated May 3, 2015, 10:36 AM ]

Hair raising!
There’s been a long hiatus for Everyday Physics because I was occupied writing my PhD thesis. Now that that’s complete, we can jump right back in!

If you’re living somewhere with a relatively cold winter, you’ve probably experienced a lot of small shocks as you touch metallic objects like doorknobs or coat hangers. Now that the weather is turning warmer you’ll experience it less and less. Many people know that this is built up electric charge on your body leaving, but have you ever wondered why it seems to happen more often in the winter?

Static electricity is a charge imbalance that builds up on an object

You may already know that static electricity can build up on an object if it is rubbed against another one. We like to demonstrate this today by rubbing balloons in someone’s hair, but it’s actually a very old idea: the Greeks originally discovered this behavior when they rubbed fur against amber rods. In fact, the Greek word for amber is elektros, which was used as the origin for the modern word electricity.

What’s happening here is electrons are moving from the fur to the amber because of the rubbing process. It turns out the atomic structure of the amber holds electrons more strongly than the structure in the fur, and so some electrons will be pulled from the fur when the two materials touch. This happens to some degree upon initial contact, but is a really prominent when the two materials are rubbed together.

Which way the electrons move depends on the atomic details of the materials. Amber will pull electrons from fur when they are rubbed together, but (for example) glass will give up electrons to silk if they come into contact, such that the glass rod will become positively charged from now having fewer electrons. Rubber can also accept electrons from carpet, which is one common way that you will become electrically charged in everyday life.

The excess charge will move to another object in order to restore balance if it can

In general, the extra electrons will try move out of an object as soon as it comes into contact with another material. In the case of a positively charged rod, electrons from another material will move into the rod when it comes into contact. Certain materials are better than others at moving electrons back and forth in this manner, and are called electrical conductors. You probably already know that metals are generally excellent conductors, which is why they are used in circuits.

Electrons travel through the air when your charged finger gets close to something metal

It’s easy for electrons to move between two materials in direct contact, but not otherwise. This is because the air acts as an insulator, preventing electrical flow. As the charge on an object builds up, however, it can eventually “jump” through the air in order to reach another material and restore balance. This occurs because the air is of course comprised of atoms with electrons just like a solid, only more dispersed: in the same way that electrons can move between two solids in contact, they can also move from a solid to the atoms and molecules that comprise the air.

High humidity, low chance of static

Air is a relatively good insulator, though, so it takes a large charge buildup on a surface and a nearby accepting surface before the electrons can travel through the air. Static discharge in the air occurs at around 10 kilovolts per centimeter. In other words, it’s not uncommon to build up electrical charge on your body such that the electrical potential between you and another object is a few thousand volts, so that electrical discharge occurs when you come within several millimeters of an object that is more electrically neutral.

The more electrical charge buildup there is, though, the larger the distance over which electrons can jump from surface to surface. For example, lightning is the same sort of electrical buildup and then discharge as you experience by walking on carpets, only many orders of magnitude more charge, which lets the discharge jump from clouds all the way to the ground.

Airborne water vapor impedes the flow of static discharge, and there is typically less humidity in the winter months

The 10 kV/cm number for electrical discharge will change, however, depending on the humidity present in the air. This is because higher water vapor content makes air a better insulator, preventing the flow of electricity.

Low humidity,much static!

As previously discussed, lower temperatures of air contain less humidity. As a result, winter air is typically drier than summer air, which means it is easier for electrical charge to jump through the air between materials.

This sort of static discharge can be slightly painful, and produces a small flash and tiny shock wave when it occurs. That’s not a big deal for humans, but it can be devastating to sensitive electronics.

Thanks to Chris Darling (wiki) for the static hair picture.

Why will melting ice caps cause the seas to rise?

posted Feb 9, 2015, 10:36 PM by Patrick Poole

Climate change picture
Climate change is possibly the most important problem facing humanity today, so it’s critical to understand its causes and effects. One outcome that is already occurring is the rising of sea level due to ice melting, but this can be a bit confusing to many people. You may have heard that if a glacier melts it doesn’t actually contribute to increasing the sea level because of the physics of flotation. Today I’ll talk about how floatation and buoyancy work, and why melting ice really is a big problem.

Archimedes’ Principle says that an object immersed in a fluid experiences a buoyant force equal to the weight of the fluid it displaces

Archimedes was one of the greatest scientists of the classical age, contributing a wide field of work in engineering, mathematics, and physics. The physics idea that bears his name, Archimedes Principle, deals with the buoyant force, which is an upward force that a fluid exerts on any object that is immersed within it.

When an object is placed in water, some of the water is pushed out of the way to make room. This water tries to move back into its previous location, pushed by the force of gravity that is pulling it down towards the Earth—in other words, its weight.

Buoyant force image

If that immersed object was a cube, then the force of water pushing on the four sides cancels out, leaving just the water pushing up from below, and possibly also pushing down from above if the object has been fully submerged. Either way, the pressure within the water increases with depth (this is why your ears pop if you go to the bottom of a pool, but not if you dunk your head just under the surface), so there will be more pressure pushing on the bottom of the cube than on the top. This extra pressure translates to extra force, and is the origin of the buoyant force.

(Note: a lot of people have heard of the Eureka! [Greek for I have found it!] story, where Archimedes discovered that the volume of water displaced by an object is equal to the volume of the object itself. This made measuring the volume of irregularly shaped objects simple, since they could just be immersed in a full container and the volume of water that spilled out could be measured. This is an important idea, but not exactly the same as Archimedes Principle, which deals specifically with the force exerted by that displaced volume.)

Floating objects displace their own weight of fluid (so the forces are balanced)

An object that is floating has its downward force from gravity exactly balanced by the upward force of buoyancy. Put another way, as an object is lowered into water it will begin to float once it has displaced an amount of water that weighs just as much as the entire object. This is why boats are able to float even though they are made of very large amounts of metal: a one ton brick of metal will sink, but if that metal is spread out into a bowl shape it will displace one ton of water before it sinks entirely below the surface, and therefore will float.

Bowls float

Glaciers work the same way: if you drop a glacier into the water it will sink until it has displaced its weight worth of sea water. Glaciers are typically formed from snow melting and re-freezing, which means they are fresh water—in addition, it turns out ice forming from sea water has a tendency to force the salt out of the forming ice crystal. In general fresh water ice is a bit less dense than fresh liquid water, and salt water is a bit denser than fresh water, so this means glaciers tend to be less dense than the sea water they are in: as a result, they float. The density isn’t too far off, though, which is why most of the glacier tends to be submerged: it takes most of the glacier’s volume to displace a weight of sea water equal to the total weight of the glacier.

There is a lot of ice resting on land, like on Antarctica, which will raise the sea level as soon as it melts

So the floating glacier displaced its weight worth of water, even though some of the glacier is still above the water surface. If the entire glacier melted to water, it would still weigh the same, and so it would still displace the same amount of volume. So, the glacier won’t displace any more water once it melts, which means the net result is no sea level rise.

Well then what’s the big problem with melting glaciers? It’s actually not the glaciers that are the problem, but rather the huge amounts of ice that are currently sitting frozen on land. Antarctica is considered a continent not because it’s one big chunk of floating ice, but because it’s a big chunk of land rising out of the sea floor that happens to be covered in ice and snow. In fact, Antarctica has 90% of the ice in the world, and most of that is sitting on land.

Glaciers on land

Now Antarctica is quite cold, so the worry isn’t that its ice will start melting soon—although if it did, that would raise the sea level by some 200 feet, which is enough to cover the entirety of the state of Florida (and many other places). Smaller amounts of ice melt from places closer to the equator would still be enough to ruin coastal cities, which is why we have to do whatever it takes to begin combating climate change now.

Bonus physics—Glacier colors
Blue glacier ice

Sometimes glacier ice that is especially pure will appear blue—that is, it was formed under higher than normal pressures so there are no air bubble imperfections. This can happen if the ice forms underwater and then is dislodged so that it can float to the surface. The reason why glacial ice looks blue is the same reason the ocean itself looks blue, but that’s for another post!

Thanks to Andreas Tille (wiki) for the blue glacier picture.

Why isn't the night sky full of stars?

posted Feb 1, 2015, 1:34 PM by Patrick Poole

Starry sky, from ForestWander (wiki)
You’ve probably heard that there are quite a lot of stars in the universe, and there is definitely a huge amount visible on a very dark night. Why doesn’t all that light wash out the dark spots in the sky, so that we see no black at all? This is actually a question that’s been debated a lot over the centuries called Olbers’ paradox, with even figures like Edgar Allen Poe weighing in. Today is the first time I’m talking about a question submitted to the Ask Questions page. Thanks for the great question!

The universe is 13.8 billion years old, and the speed of light is finite, so the light from most of the stars has not reached us

So if all those stars are around us emitting light, and they are more or less evenly distributed, shouldn’t the night sky be full of light? There are a couple of reasons why not.

One of the big ones is that the light from most of those stars hasn’t had enough time to reach us. Light travels at 3x108 meters every second, or 9.5x1015 meters every year. Those are huge distances, so rather than list all those zeros every time we can use the units of light-seconds and light-years. For example, the nearest star to us, Proxima Centauri, is 4x1016 meters away, or about 4.2 light years. That means it takes light from Proxima Centauri 4.2 years to reach us—or, put another way, the light that you can see from Earth when you look there is light that left Proxima Centauri 4.2 years ago. So really you’re seeing 4.2 years into the past.

The universe is incredibly old—13.8 billion years—but it’s also incredibly vast. Because light can only go so fast, there is a region of space around the Earth beyond which we cannot see—there are certainly more stars beyond this region, but the light from them hasn’t had time to reach us yet.

Observable universe with outside stars

It turns out this volume is a bit bigger than the 13.8 billion light years you might expect. Expansion that occurred in the early times of the universe pushed this volume of visible space, called the observable universe, up to about 84 billion light years. That’s still small enough (comparatively) to rule out seeing quite a lot of the stars in the universe.

Estimates for the number of stars in the observable universe are around 10 billion trillion (1022)

It’s tough to determine exactly how many stars are in the universe that we can see, but it’s clear the number is enormous. Part of what makes this fact difficult to obtain is the sheer size of the number—we can’t have people just count them, it would take too long—but there is also the standard problem of astronomy where the only tool you have for knowing anything about the universe is by what the universe sends towards the Earth. We can also send our own probes out, but only to very close objects, certainly not to other stars. So astronomers have to come up with clever ways to measure things based on observations of the light and particles that are sent toward their detectors on the Earth and knowledge of the principles of physics.

Estimating the number of stars in our galaxy is a good example of this synergy of detection and physics understanding. The Milky Way is rotating about its center, and special radio telescopes can determine the speed of stars near the edge of the galaxy. It turns out that the speed of rotation depends on the mass of the whole galaxy—based on the observed speed we can estimate the mass of our galaxy as the same as 100 billion of our suns. There are plenty of stars with mass more or less than our sun, but it’s a pretty good guess to say that there are somewhere around 100 billion stars in our galaxy.

That’s probably a good guess for most galaxies, based on other observations. So now we know the number of stars in one galaxy, we just need to know how many galaxies there are. The Hubble space telescope watched just one relatively tiny section of the night sky for over four months, adding up all the small amounts of light it saw from very, very distant stars in that region. The result was 10,000 galaxies visible in that small patch, and if you extrapolate that galaxy density up to the whole night sky, the resulting estimate is 100 billion galaxies all around us.

So our combined estimate is 100 billion stars per galaxy times 100 billion galaxies, or 10 billion trillion (1022) stars in the observable universe. That’s a huge number—that many 0.5 mm radius grains of sand would pile up to be the size of Mt. Everest!

Most of a star’s light won’t hit the Earth because we are so small and so far away

Stars emit an enormous amount of light, but they do so in all directions. The farther that light travels away from the source star, the more it gets spread out—this is just like the way sounds decrease in volume as the source gets farther from you, like we discussed back in the Doppler shift post.

This is why stars appear just as points of light in the night sky—of course they are really enormous, but they’re so far away we only see the light that is traveling directly from them towards the Earth. As an example, our own sun looks a lot different the farther out in the solar system you get. If you stand on the surface of Pluto, our sun wouldn’t look much bigger than any of the other stars in the sky. It would be much brighter though, but only enough to light up the surface about as much as the moon lights up Earth’s surface at night. This is because a lot of the sun’s light just misses Pluto because it travels so far to reach the little planetoid.

Most starlight misses us

The fraction of light that reaches us from even a close star can be very small. The human eye needs at least a few photons to detect light, so if less than that arrives from a distant star you won’t see it with your eyes! Modern telescopes with special detectors still have a chance, though—they can see this distant light by essentially doing a “long exposure”, leaving their camera shutters open to record those small amounts over a long period of time.

Additionally, light from some stars can be red-shifted out of the visible spectrum, or be blocked by interstellar clouds of dust, or be drowned out by nearby terrestrial lights

Those two points take care of most of the star light we might see, but there are still a few other things that keep the night sky dark. We discussed in the Doppler shift post how a wave appears changed if the source of that wave is moving with respect to the observer. There we were talking about sound and its frequency (or pitch) changing, but in the case of stars this frequency change translates to a color shift. Almost all galaxies are moving very fast away from us—which is evidence of some early behavior of our expanding universe, but that’s another post—and as a result their light is shifted toward the red end of the spectrum. It’s possible that the starlight can be redshifted so much that it’s no longer visible to the eye, but certain types of telescopes can still see them.

Another big problem with seeing more stars is if their small amount of light is drowned out by a brighter light source. This is definitely the case during the day, when the light from our sun easily dwarfs any light coming from another farther away star. Even at night, though, a full moon can prevent some stars from being seen. This is why large telescopes are often placed on mountains, or away from civilization—the light pollution from cities is especially bad at preventing starlight from being seen. If you ever want to watch a meteor shower, or just see the beautiful night sky in its full glory, drive out to the countryside as far away from city lights as you can.

Bonus physics—Twinkling stars

One last bit of star-related physics—have you ever wondered why stars twinkle? It turns out the light from the star can get scattered a bit by the water vapor and other molecules floating in our atmosphere. That starlight is essentially coming from just one point, so it’s easy for a bit of wind to come in and change the way that light scatters on its way to your eye one moment, and then change it again the next moment. You don’t notice this with something like the moon because it’s so large in the sky. Other stars “twinkle” with a definite pattern, which is evidence that there is some object passing regularly in front of them, like a planet orbiting that star, for example. This is one way that astronomers are searching for planets outside our solar system, but we’ll have to save that for another post.

Thanks to ForestWander (wiki) for the starry sky picture.

What causes the tides?

posted Jan 26, 2015, 3:53 PM by Patrick Poole

Thanks to Chris Gin for the great tide pic
Previously we talked about what makes waves crash on the shore, and mentioned tidal waves as some of the largest water waves on Earth. These waves actually don’t have anything to do with the tides, though. Today I’ll tell you what makes the tides we can observe here on Earth, and mention some other cool examples of this tidal force (like near black holes!).

Gravity is the attractive force between any two objects with mass, and decreases with the square of the distance between those objects

Gravity is an attraction between two objects based on how much mass they have. Recent experiments at the CERN particle collider revealed some details on how an object gets mass, but it’s enough to say that mass just describes how much stuff there is to something. Heavier things have more mass, and denser things have more mass per unit volume.

Gravity as a force depends on mass, which is why it’s harder to pick up a bowling ball than a balloon—the Earth is pulling down harder on the heavier object. The mass of the Earth matters in calculating the force, too—that’s why you’d weigh less on the Moon (about 83% less than your Earth weight), because its gravitational force would not pull you down as hard as the Earth does.

The moon pulls strongest on the near side of the Earth, so water here is affected most

So the force of gravity decreases if the masses involved decrease, but it also depends on how far away these objects are. This is why the Sun, which has much, much more mass than the Earth, doesn’t pull us all off into space with its gravity—it has a lot more mass, but it’s a lot farther away. It turns out the gravitational force changes as the square of the distance—physicists call this an “inverse square law”, meaning a twice greater distance decreases the force by a factor of 4.

That distance squared part can have a big effect. For example, the diameter of the Earth is just under 8000 miles (12,700 km). This means that any force pulling on the Earth will be a bit weaker on the far side. In the case of the moon pulling on the Earth, there is about a 4% weaker pull on the far side of the Earth compared to the near side.

Tidal pull from moon

As a result there is a little bit of stretching that occurs along the direction of the gravitational force—things closer to the moon get pulled toward it a bit harder than things near the middle of the Earth, which get pulled a bit harder than things on the far side. This force from the moon will be felt by all things on the Earth—including people—but it’s really only noticeable on something like ocean water. One the one hand there is quite a lot of water to be pulled on, and as a liquid it’s also able to be moved easily. The gravitational pull from the moon also stretches the solid material that makes up the Earth as well, but it’s way too small to be noticed easily.

Since the moon revolves around the Earth in just over one day, there are often two high tides and two low tides in a location

The Earth is rotating underneath the moon, and so the direction of this stretching is changing all the time. If you sit and watch the ocean at one beach you’ll probably notice two high tide points and two low tide points over the day. The high tide occurs once when the moon is more or less overhead and again when it’s more or less underfoot (on the other side of the Earth), and the two low tides happen when it’s halfway between these two points as the Earth rotates. In fact the tides occur on just a bit longer than 24 hour schedule because the moon is revolving around the Earth as well so it jumps out ahead of you just a bit as your beach rotates around underneath.

Spring tide--the sun helps
The sun also has a tidal effect, but it’s not as strong due to its larger distance

The sun also has this tidal effect on the Earth’s water, but it’s a little less than half as strong. This goes back to the inverse square dependence of gravity: even though the Sun is much more massive than the moon, the moon is a whole lot closer. If the sun lines up with the moon one side of the Earth, though, there will be just a bit bigger tide—these are called spring tides (named for the “spring upwards” in water level, not that it occurs during any particular season), and when the sun is working against the moon the tide can be at its minimum, called a neap tide.

Neap tide--the sun cancels the moon's effect a bit
Bonus physics—Tidal locking

This forces that cause tides on the Earth also have an effect on the moon. In this case tidal forces have over time caused the moon to become tidally locked to the Earth—this means that the moon rotates about its own axis at the exact same rate as it revolves around the Earth. The result of this is that the same side of the moon always faces towards us on Earth. This happens because of tidal forces—if the moon was rotating faster than it revolved around us then the Earth’s tidal forces would pull on the resulting bulge a little bit, slowing the rotation speed. This is why you can always see the same crater pattern on the moon—it’s the same side facing us all the time.

Bonus physics—Black hole tidal forces

Tidal forces are one problem with sending things into black holes—the gravity near one is so great that the tidal forces are enough to stretch out anything that gets too close. Just like the moon pulls more on one side of the Earth than the other, an incredibly strong source of gravity would pull much more on one end of, for example, a rope than the other, resulting in a stretching and eventually breaking of the rope. This process is somewhat comically known as “spaghettification”, and would most likely happen to any satellite or ship we may try to send inside a black hole.

Thanks to Chris Gin for the tides picture.

What's the loudest possible sound?

posted Jan 18, 2015, 11:59 AM by Patrick Poole   [ updated Jan 18, 2015, 11:59 AM ]

Nice ear shot
The human sense of hearing is quite remarkable—you’re able to perceive things from a quiet whisper up to a rock concert effortlessly. You’ve probably heard that prolonged exposure to concerts can be bad for your hearing, as can standing nearby a jet taking off. Today I’ll discuss a bit of what goes into measuring sounds and how your brain interprets loudness, and also tell you just how loud a sound can possible be.

Sound waves are traveling air compressions induced by the motion of some physical object

We’ve discussed before how sound waves are really air compressions traveling away from some source. Physical motion like a hand clap will push air out of the way somewhere, creating a denser region of air just nearby. That denser region only exists for a moment before the air molecules move to fill the less dense region nearby, and then that dense region will also move to fill the adjacent sparse region, and so on.

In this way a compression wave will travel away from some source, getting weaker as it goes because that compression is being spread out into more area. The sphere of compression is getting larger as it travels, but the source only had a finite amount of energy—so the sound gets weaker as it travels because the energy is spread over a larger area, and weaker compression waves mean the sound is more difficult to hear.

Louder sounds spread more air
Compressions (denser regions of air) and expansions (sparser regions) make up the traveling wave, and the difference between these densities is related to the loudness

Clapping softly and forcefully will both feel and sound different. When you clap hard, you’re pushing air out from between your hands more quickly, which knocks them into their neighboring air molecules more forcefully. The impact you feel is related to how quickly that air gets shoved.

The traveling sounds wave that emanates from your hands moves outward as compressions, or regions of greater than normal air density, and rarefactions, or region of lower than normal air density. You can see the same sort of wave travel if you hang a slinky from your hand and move your hand up and down—bits of the spring will expand and contract, so you could say there is more slinky density at some points and less at others as the wave travels.

Slinky sound
The power of a sound is measured in decibels, but its loudness also depends on how your brain interprets it

It’s important for scientist to use specific language when describing things, and to be explicit about the pieces involved in that explanation. For example, there are ways of characterizing the strength of a sound: you can describe the energy carried within the sound wave, and from that the power (which is energy per time) or intensity (which is energy per time per area) of the sound—all of which are different things.

None of those quantities, however, are exactly the same as loudness. How loud a sound seems is certainly related to how much energy or power is carried by the wave, but it also depends on how that sound affects your ear drum, and then how your brain interprets that signal into the perception of sound. It turns out your brain averages the last second or so of ear drum vibrations when it interprets a sound—in this way, the same energy sound wave will seem louder to you if that energy is spread out into a longer bit of time, as long as that time is less than one second.

Sound chart

The power carried in a sound wave is often described in units called decibels. Decibels can be a bit confusing because they are a logarithmic scale of measurement—this means that an increase of 10 decibels means the sound is 10 times as powerful, and an increase of 20 decibels means the sound is 100 times as powerful as before. Other logarithmic scales are the chemical pH scale, and the Richter scale for measuring earthquake strength. A 8.0 earthquake is really ten times(!) as strong as a 7.0, because the scale is logarithmic. Importantly, to use decibels you also need a reference point. For sound in air this is typically chosen to be 20 micropascals of air pressure, which is about the lower threshold for human hearing.

With that being said, human sound perception is also logarithmic—now I’m talking about how your brain interprets the loudness. To you, a 50 decibel indoor conversation will only seem twice as loud as a 40 decibel library, even though the actual sound power is ten times as great. This logarithmic sense of sound allows you to interpret noises over a much larger range, so you can quickly adjust from 20 decibel rustling leaves to 100 decibel jackhammers.

Even though I’ve titled this post “what’s the loudest sound”, I’m going to ignore the effects from human interpretation of a sound wave, and focus instead on the physics of the waves themselves. I really should have called the post “What’s the most powerful sound possible?”, but that doesn’t have the same ring to it.

The loudest possible sound (at sea level in air) is 194 dB, when a full rarefaction (vacuum pocket) occurs

Imagine you’re doing the slinky experiment again, but now you hold the slinky in both hands and pull apart quickly. If you do this hard enough you’ll break the slinky somewhere in the rarefied (or sparse) region, because there the wave motion is pulling apart the spring more than it can handle.

This same thing can happen in the air: at some point a strong sound wave will have no air molecules within its rarefaction area—they all went to one side into the compression zone, and left a small pocket of vacuum. A moment later the surrounding air will rush back in, and do so strongly enough that another vacuum pocket is formed where there was just a compressed region—in this way the strong sound wave propagates, but it couldn’t be any stronger because there isn’t any more air to displace from the rarefaction zone.

Slinky breaking wave

You can see how this will be different depending in the density of the air, and on the air pressure (pressurized air will resist being displaced more than normal pressure air). For sea-level pressure and temperature air (STP, or standard temperature and pressure, and with the standard reference of 20 micropascals of pressure) the intensity of a sound wave that has rarefaction regions with no air molecules in them is 194 decibels. At higher altitudes this value will be lower, since there is less air to move. Underwater where the density and pressure is much higher, this most intense sound is also much higher—a whopping 256 decibels.

For perspective remember what we said about logarithmic decibel scales: this is about 60 decibels higher than the loudest sound possible in air, which means to you it would sound 26 = 64 times as loud, and its power is 106 = 1,000,000 times larger! That’s as big of a difference as there is between an air conditioning unit and a thunderclap.

Bonus physics—Most intense laser
Plasma ball in air

There is a maximum amount of sound energy that can travel through the air, and the same is true for light energy as well. This will only happen for very intense levels of light, light those from modern lasers. If an intense laser is focused tightly enough, it’s possible to rip electrons from their atoms in the air itself and cause a small plasma streak to form, like in the image to the right—this effect is similar to lightning, but it is stationary because it will only happen where the laser intensity is high enough.

Even in vacuum with no air atoms to pull electrons from, there is still a maximum light intensity. Above an incredibly large intensity called the Schwinger limit, the light is strong enough to create a positron-electron pair out of the vacuum itself. Current lasers are nowhere near this intensity level, but scientists are working to reach this point one day in the future. I’ll leave the details to a future post.

How do thermometers work?

posted Jan 11, 2015, 8:16 PM by Patrick Poole   [ updated Jan 12, 2015, 12:09 PM ]

Mercury thermometer from Anonimski (wiki)
Winter has come, and it’s likely that you’ll come down with a cold sometime this season. To check for a fever you’ll probably use a digital thermometer, but an old fashioned mercury and glass one will work just as well. The mercury one operates on the principle of thermal expansion, which explains many everyday physics sights from the odd jagged connections bridges make with the rest of the road to why power lines sag on hot days.

Heat is a description of how much the molecules in an object are moving about

We’ve discussed before how molecules and atoms within a material are always wiggling about. This degree of vibration is heat, and measuring the temperature of something really measures the amount of kinetic energy stored in the wiggling of the atoms. You can heat something until its atoms break free of their bonds, which turns a solid into a liquid or liquid into a gas. You can also try to cool something down until there is no motion in the atoms—that point is absolute zero, or -459.67° Fahrenheit (-273.15° Celsius), and is pretty tough to reach, but that’s another post.

Different materials will have different thermal expansion coefficients, which describe how much they expand when heated

If the atoms in a material are hot they will be moving around bumping into each other—the frequency and energy of the collisions are related to the heat contained in the material. More energetic collisions means the particles will move farther from each other each time they hit. Imagine you’re in a room with a dozen or so beach balls—the harder you throw one ball at another, the further and faster it will fly away, and it will probably knock into other balls along the way.

Atoms inside solids are wiggling, too

The balls knocking around on the walls of the room are akin to the atoms of a gas knocking into their container. This is the source of pressure: atoms colliding with the walls of their container. In a solid or liquid those atoms are colliding with each other, but not quite enough to overcome the atomic bonds that are holding them into the solid or liquid form. So we don’t call the effect pressure, but there’s a similar idea going on: atoms moving faster collide with each other and move farther apart, which effectively increases the volume taken up by that solid or liquid.

Liquids expand more than solids, and metals expand more than glass, so mercury in glass makes a good thermometer

Most materials expand as they get hotter—there are a few that don’t work this way, but usually only do so over a small temperature range. One notable example is liquid water, which actually contracts a bit when heated from 0 °C to 4 °C. Everything else expands as it gets warmer, but does so by different amounts depending on what the material is. Liquids will typically expand more than solid because their atomic bonds aren’t quite as strong (which is why they are a liquid at that temperature in the first place). Metals also tend to expand more than glass when their temperatures are increased by the same amount.

Expanding minds and atoms

Mercury is the only metal that is in its liquid phase at room temperature and pressure. Because of this, some thermometers are made by placing the mercury inside a glass tube—here the glass doesn’t expand much when it’s heated, but the mercury will. It expands by a known amount as well, so by marking certain points along the glass an absolute temperature can be obtained. Alcohol is another good substance to use inside the glass—this is what’s inside any thermometer you see that has red fluid.

To calibrate such a thermometer, you have to use two known temperatures. The easiest thing to do is use the freezing point and boiling point of water. A glass of ice water will be at 0 °C (if there’s no ice it’s probably a bit warmer, and if there is all ice it could be colder, but as long as both are present the temperature must be 0 °C), and similarly a steam bath will be at 100 °C. Marking the position of the mercury in these two environments gives you two set points, and picking some gradation between them will give you a scale for measuring temperature. Interestingly, this is why you might see warnings to bring your thermometer inside if the temperature is going to be near -40 °C, because mercury will freeze here, which can break your thermometer!

Glass expands less than the liquid mercury

Digital thermometers tend to not use mercury—instead they rely on another property of a material that temperature can effect: namely the resistance. Resistance is how hard it is for electric current to flow through a material—since this depends on atoms transferring charge between each other (the details are another post!), it is also affected by their wiggling motion and thus the temperature of the material. These devices, which rely on the change of resistance with temperature, are called thermistors (for “thermal resistor”).

Bonus physics—Thermal expansion around you

Materials getting larger or longer as they get hotter happen all the time around you. For example, watch overhead power lines on cold and hot days—you’ll find that when it’s warm the lines will sag between the poles and be taught when it’s cold, because the materials in the lines expand from the heat. Another example of thermal expansion is in bridge connections—the longer a bridge the more it can expand as its temperature increases, and the force from this is easily great enough to crack the road on either side.

Thanks to Anonimski (wiki) for the mercury thermometer picture.

Why are turns worse on slippery roads?

posted Jan 4, 2015, 6:06 PM by Patrick Poole   [ updated Jan 5, 2015, 2:42 PM ]

Slow on the turn!
Most people know that it’s more dangerous to drive when the weather is bad—rain, snow, or ice all make roads more slippery. Have you ever thought about why most accidents in slippery conditions occur when a car is turning? Today I’ll talk about the physics that goes into driving on wet roads, and how you can maximize safety during your winter travels.

Friction is the force felt between two objects in contact, and depends on the motion and surface texture of those objects

When two objects are placed in contact and one of them is moved with respect to the other, there is a friction force between the objects that opposes that motion. This force arises from interactions between the molecules of the two objects just where they contact. There are a few different sources of friction that get lumped together into one term called the coefficient of friction, represented by the Greek letter µ (mu)—the higher the coefficient of friction of an object, the more force there will be opposing motion along that object’s surface.


For example, the coefficient of friction between concrete and rubber is 1.0, while the coefficient between wood and wood is around 0.3 (depending on what type of wood), and between Teflon and Teflon it’s 0.1. This is why non-stick pans are coated in Teflon: it’s hard for something to stick to them if the coefficient of friction is low.

There are a number of different types of friction depending on the nature of the motion. For example, the coefficient of static friction comes into play when two objects are being pushed against each other but neither is moving. This is what works against you when you try to push a heavy bookcase across a room. The coefficient of kinetic friction comes into play once one of the objects is moving—you’ll probably note that the bookcase is easier to push once you’ve managed to get it moving, which is because the coefficient is often lower for kinetic friction than static.

Slippery roads have reduced friction, so there is less available to hold car tires on their turning trajectory

Because friction depends on the interaction between two surfaces in contact, it will behave differently if there is something else preventing that contact. For example, a liquid like water will flow between the nooks and crannies of the two surfaces, such that they are no longer rubbing strictly against each other. If there is a full layer of water between the two objects a phenomenon called hydroplaning can occur, which is very dangerous for cars—in this case the tires have lost contact with the road so they cannot grip to control the car’s direction or speed.

Hopefully you aren't Bill Paxton

Even before hydroplaning occurs, though, some amount of water will reduce the effective coefficient of friction. In the case of concrete and rubber, the presence of water drops the coefficient from 1.0 all the way down to 0.3. The coefficient of wet asphalt can vary between 0.25 and 0.75 depending on the quality of the tire and road.

A turning car experiences a sideways force, and friction between the tires and road prevents it from deviating from its path

Here’s the important part: the static friction between your tire and the road is a set amount and will provide up to a set amount of force in response to attempts to push the car away from its current path. For example, if a strong gust of wind comes by to push sideways on your car, there will be a friction force that will oppose that wind force so that your car doesn’t move sideways. If you’re unlucky enough to be in a very strong windstorm, however, that wind force might overcome the maximum amount that can be provided by the tire-road frictional force, and then your car will be scooted sideways. In wet driving conditions this maximum amount of frictional force is diminished, meaning that it takes less force to overcome it and push your car in a direction you didn’t intend on going.

The thing a lot of people forget is what types of forces could try to do this to your car. To have a force you need some sort of acceleration, or change in velocity (that’s Newton’s second law of motion). Anytime your speedometer changes your car is accelerating, whether it’s speeding up or slowing down. These aren’t usually too bad because you’re the one controlling the acceleration, and it’s in the direction the tires are spinning anyway.

Watch that turn!

The problem comes in when you go around a turn: even if you’re turning at constant speed, your car is still accelerating because the direction it’s moving is changing every moment. Imagine you have a rock tied to a string, and you’re swinging this over your head: if you swing at a constant speed but then cut the string at some point, the rock will go sailing straight ahead (its trajectory will be tangent to the arc it was moving in), and if you cut the rock a bit later instead this direction would be different.

Changing direction is acceleration too—in fact you feel this every time you go around a corner sharply or quickly enough in your car. You will feel yourself be pushed away from the direction the car is turning, or away from the center of the circle your car is turning on. This is called centrifugal force—as the car started turning your body continued going straight, and has to be pulled back along the car’s circular path (usually by your seat and seatbelt).

This centrifugal force acts on your car wheels, pushing them perpendicular to the way the car is moving. That force is opposed by friction, but this can be overcome just like from a strong enough gust of wind—in this case the strength of the centrifugal force depends on how fast you’re going, and how tight a turn you are making. This is why interstate off-ramps have speed limitations, and why race tracks often have banked turns—both of these help ensure that the friction from your tires can overcome the forces endured while turning.

Slippery roads decrease the amount of friction available to your tires, and turning, breaking, and speeding up all utilize this friction—so don’t do two at once!

Unfortunately, many people go into these turns a bit too fast, and end up braking part way through. This is dangerous because braking is yet another deceleration—slowing down helps reduce the centrifugal force, but it also adds its own force, and if you aren’t careful it can be enough to overcome the tires’ friction before it starts to help.

The safest thing is to enter a turn slower than the recommended speed if the road is slippery, and then try not to break or accelerate at all while you’re turning.

Bonus physics—Friction and the Greeks

Before Newton came along in the 18th century and set things straight with his Laws of Motion, Aristotle had his own ideas about how forces worked. When he pushed a block along the ground it always stopped eventually, so he concluded that all objects in motion eventually cease to move. This is because he did not consider that another force, in this case friction, was acting on the block to stop it. If you have a frictionless environment (such as a block moving on perfect ice, or better yet in space) then a pushed block will never stop if it never encounters another force to slow it down.

How do fingerprint scanners work?

posted Dec 27, 2014, 10:19 PM by Patrick Poole

Thumbs up
Everyday Physics is back from the holiday break, this time with a bit more complicated topic—I promise there is a very easy experiment you can do in your own kitchen to help it make sense, though.
In addition to being the mode through which we view the world, light is integral to a number of different devices we use every day, from telecommunications to microwave ovens to radios. Many of these applications came about as scientists and engineers learned something fundamental about the behavior of light so that they could turn it towards some useful goal. One such goal is fingerprint scanning—nowadays it can be done with a number of different techniques, but one of them takes advantage of one of the stranger qualities of light. Even though it’s a little complex, you can see this effect yourself with a simple experiment you can do in your own kitchen! I’ll tell you how at the end of the post.

Light will both transmit and reflect when it encounters a new material

As we’ve discussed before, light is a traveling, oscillating electromagnetic wave. When light moves through a material it does so by affecting the atoms of that material with its electric field, and the atoms will respond in different ways depending on their surroundings (e.g. crystal structure) and the frequency of the light. Physicists lump all the different response effects into one variable called the index of refraction, n.

One of the first things to know about light is that when it encounters a material with a different index of refraction than the one it’s currently traveling through, a few things will happen: some light will get transmitted into the new material, some will be reflected away, and some might be absorbed by the new material (say, as heat energy). For now we’ll assume we’re dealing with a material like glass, where not too much visible light gets absorbed. The amount of light that gets transmitted and reflected, though, depends on the angle of incidence and the indices of refraction of the new and old material. This is shown in one of the simplest optical equations: Snell’s law, which deals with refraction, or the bending of a light ray when it encounters a new material. The equation looks like n1 sin⁡(θ1)=n2 sin⁡(θ2), where n1 is the index of refraction before the interface between materials, n2 is the index after the interface, and θ1 and θ2 (Greek letter theta) are the incoming and outgoing angle with respect to the interface.

Snell's law image
At some angles of incidence, nearly all of the light is reflected—this is called total internal reflectance

If you’re a little familiar with trigonometry, you know that sin⁡θ can never be bigger than 1 or less than -1. What this means is that if n1 is much bigger than n2, so that n1 ⁄ n2 is bigger than 1, then there is no angle θ2 that satisfies Snell’s law. This is a mathematical way of saying that no light can transmit into the new material, and instead it all gets reflected. Light that comes into an interface at an angle where this effect occurs is said to undergo total internal reflection.

Now the equation is correct, but it’s important not to just trust the mathematics blindly, especially if you aren’t familiar with where the equation comes from. What physically is going on that prevents light from transmitting in this case? Well it turns out to have to do with the nature of light moving into the new material—light propagates by polarizing(link) the material it’s moving through, causing that polar atom vibrates a bit, which emits more light. In general a bigger index of refraction means light has a tougher time wiggling the atoms. The angle matters too—it turns out that this re-radiation of light by the wiggling atom is easier to do in certain directions, and at steep angles the re-radiation is inhibited.

Even during total internal reflection a little bit of light tries to transmit—this is called the evanescent wave

Really, though, the light doesn’t just reach this interface at the appropriate angle and decide it can’t go any further—some of the light tries to get through, and is inhibited by the atoms in the new material. It takes a little bit of distance for this to happen though—this distance is called the skin depth, describing the very thin layer (typically only tens of nanometers thick in a metal, for example) into which light will propagate even though most of it reflects. In fact, if you can make a metal thinner than its skin depth (which is difficult, but possible with modern techniques) it will be transparent just like a glass window.

We call the little bit of light that moves into the skin depth the evanescent wave, because it’s sort of a ghost wave—you typically would never know it was there, unless…

Putting another material extremely close to the evanescent wave region will now allow it to transmit, and you’ll see a reflection from this third material

Here’s where the interesting part comes in—if you place a third material just behind and incredibly close to the second material, and if this third material has an index of refraction higher than n2, then this evanescent wave will reach through the second material to the third material, even though it couldn’t do this with no third material there! This effect is actually pretty close to quantum tunneling, where subatomic particles can move through regions of space that they normally wouldn’t be able to because there’s some small difference in the system—but that’s another post.

Frustratingly awesome physics

This effect is called frustrated total internal reflection, because the light would normally all reflect except that the presence of the third material lets a little bit of the evanescent wave through. The amount of light that gets through is very sensitive to the distance between the third and second material, which makes it useful for some optical applications.

The depth of your fingerprints is the right size to allow evanescent waves to reflect from the ridges but not the valleys

As luck would have it, the difference in height between the ridges and valleys of your finger is in the right range to turn this frustrated total internal reflection on and off. This is one of my favorite optical effects because while its explanation can get very technical, it’s very easy to see: just take a clear glass of water that’s mostly full and hold it in one hand. If you hold the glass up on a level with your eyes, you’ll see right through it. Now lower the glass, keeping your eyes on your fingers on the other side. Eventually you’ll be looking through the top of the water to the back side of the glass, where you’ll see a mirror surface now instead of seeing through the glass—this is total internal reflection kicking in because you’ve increased the angle.

Fingerprint science

But take a look at your fingers holding the back of the glass—you can now see your fingerprints! This is because there is a very small amount of air between the glass and your finger ridges that is acting as a third material to allows the evanescent wave to move through that air and reflect from your fingertips. The valleys of your finger are too far away to allow this, though, so you still see a mirror surface there.

If you set up a camera to take a picture of the fingerprint, you could then scan it into software and analyze the pattern just like in the crime shows. Taking advantage of frustrated total internal reflection in this way is exactly how some fingerprint scanners work. Try it yourself!

How do polarized sunglasses work?

posted Dec 14, 2014, 9:14 PM by Patrick Poole   [ updated Dec 14, 2014, 9:15 PM ]

Nice hat (and sunglasses)
Recently we talked about some cold weather physics, so this week I’m going to get your mind off of blizzards and onto beaches. You can probably guess that sunglasses make things look darker by preventing some sunlight from reaching your eyes, but what about polarizing sunglasses—are they really better for your eyes? (It turns out yes!) And what makes some screens look weird when you look at them through polarized sunglasses?

Most materials can become polarized when there is an electric field present—this means their positive and negative pieces spread out from each other just a bit

First let me explain where the word polarize comes from. The atoms that make up matter always have a positively charged nucleus with negatively charged electrons surrounding it. It’s the attraction from these oppositely charged particles that hold atoms as a whole together (although there are some other interesting forces at play that we’ll discuss in a future post).

Atoms have positive and negative parts

Usually the electrons of an atom are roughly evenly distributed about the nucleus, but that can change when an external electric field is turned on. Since the positive nucleus and negative electrons have different charge, they respond in different ways to this external electric field. The field pushes on the nucleus and pulls on the electrons, and the net result is just a little bit of imbalance in their positions. If you turn the electric field off the electrons will move back to being centered on the nucleus, but while the field is on there are held apart just a bit.

When the electrons aren’t quite centered on the nucleus we say the atom is polarized, meaning that it has a positive and negative electric pole (sort of like the North and South poles of a magnet). Other positive things will tend to move away from a positive pole and towards a negative pole. So if you have your external electric field near a block of material, all of the atoms in that material will tend to shift and be polarized in this way.

Electric fields polarize atoms
Light is composed of traveling and oscillating electric and magnetic fields, and we call the direction of the electric field the polarization direction

We’ve talked before about how light is sometimes best described as a particle and sometimes as a wave. In the wave picture, light is an oscillating, traveling electric and magnetic field. You can still think of little waves traveling along, with brighter light sources giving off more of these waves.

It turns out that this oscillating electric field will always be perpendicular to the magnetic field oscillation, and both of those are perpendicular to the direction the light is traveling. In this way light really is a three dimensional effect: you need one direction for the travel and one direction each for the electric and magnetic fields to oscillate.

We just mentioned how external electric fields will polarize an atom by shifting the negative electrons a little bit with respect to the positive nucleus. When a light wave goes through a material, the oscillating electric field does exactly the same thing—the only difference is that now the electric field is oscillating, too, so the amount of polarization of the atom will also change as the light wave goes past it. Since it’s the electric field of the light that will do the polarizing to an atom, we call the direction that the electric field points the polarization direction of the light wave.

Typically a light source will emit all polarizations (electric field directions) of light, which means it will cause atoms that it travels through to oscillate in many directions

Your everyday light bulb emits unpolarized light—that is, all of the light waves it’s sending out have electric fields that are oscillating in different directions. As that light goes through something like a piece of glass, or even air, it causes atoms in that material to oscillate. In this case one atom will oscillate in a totally different direction than its neighbor because they each got hit with different polarizations of light from the bulb.

Unpolarized light from bulb

It’s possible to have all of the waves emitted by a source of light have their electric fields in one direction. In this case we say the light is polarized, and we usually state what direction the oscillations happen in—horizontal or vertical with respect to the floor, for example. One of the properties of laser light that makes it useful is that the light can be polarized to a very high degree.

Polarized coatings on sunglasses have molecules that are inhibited from oscillating except in one direction

It turns out it’s possible to make a material where the atoms can oscillate in one direction much more easily than they can in other directions. As a result, light coming through the material won’t be able to travel through if its electric field is lined up with one of these inhibited directions. This is exactly how polarized coatings are made: the constituent atoms are only allowed to oscillate along one direction. So light waves that come in with exactly the wrong polarization will get cut out entirely, and light that comes in at an angle will only partially get through. The end result is at least half of the light gets cut down by the polarizing filter, and it could be more if you happen to be looking at light that is mostly polarized in that disallowed direction.

Polarizing filter

Bonus physics—Cool effects from polarized sunglasses

Polarized sunglasses are important because they cut down even more on the amount of light entering your eyes, including harmful ultraviolet rays from the sun. It’s important to protect your eyes with sunglasses, or even better polarized sunglasses, for the same reasons it’s important to protect your skin with sunscreen.

Polarized screen

Other technology takes advantage of light polarization, too. For example, a polarized coating is sometimes applied to car windshields, and if you’re wearing your own polarized sunglasses you’ll see a slight colored tint on those cars. Also, you’ll find that rotating your smart phone sideways will prevent you from seeing the light from the screen. That’s because the filters that make some displays use polarized light, too, but that’s another post.

Also, it turns out that the glare coming from water at the beach or a pool is typically polarized in a certain direction, even though the sunlight that made it initially wasn’t polarized at all! This is another interesting polarization topic we’ll discuss in a future post.

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