Now suppose you
start to move your arm up and down so that you make five peaks, while keeping
the height of the wave the same as before (see diagram).
(Aren't you glad this is just a thought experiment?) How has the wavelength
changed? How has the energy you put into the wave changed? Stop here and write
down a physical relationship between the input energy and the wavelength. A
simple phrase is fine. For example: "The wavelength ________ as the input
Standing waves. Tie a rope to a door knob and make a wavy pattern by moving your arm up and down. Which of these two patterns require more energy on your part?
Diagram by Debra A. Fischer
Done? Good, now you're a theoretical physicist! Hopefully, you have deduced that short wavelengths require more energy than long wavelengths. To become an experimental physicist, you have to actually tie the rope to the wall and make the measurements. Try using a long Slinky. It's easier to visualize standing waves in a rope, but easier to create them in a Slinky.
The same concept applies to electromagnetic radiation. The energy put into the wave equals the energy transmitted. Unit for unit, long-wavelength radiation (such as radio waves) transmits less energy than short wavelength radiation (such as x-rays). It's a big difference. If the wavelength changes 1 billion times, then the energy changes 1 billion times.
Now you can see why x-rays are generally more dangerous than radio waves. X-rays pack more punch. Not only that, but their small wavelength allows them to penetrate deep into the human body, right into our cells. For the same reasons, ultraviolet radiation is more dangerous than visible light.
The different types of radiation can also be defined by their frequency. The frequency is just the number of waves that go by each second. If you stretched the wavelength, fewer waves would go by every second, so the frequency would go down. In the rope experiment, the frequency was the number of times your arm went up and down each second. To make a shorter wavelength, you had to move your arm with a greater frequency.
X-rays have a smaller wavelength than radio waves; therefore, they have a greater frequency. This is what the frequencies on your radio dial mean. If you could somehow tune your radio receiver to 1 trillion megahertz, you could pick up x-rays. At 600 million megahertz, the receiver would detect light. In reality, though, no single receiver could detect all frequencies of electromagnetic radiation; the energies span too wide a range.
A radio antenna is one of the many contraptions that can detect or create electromagnetic radiation. The antenna does its thing because electrons inside the antenna accelerate up and down (assuming the antenna is vertical). This up-down motion occurs at a certain rate say, 1 million times per second, the frequency of a 1-megahertz AM (medium-wave) radio station. If the antenna is transmitting, the up-down motion of the electrons produces an electromagnetic wave with the same frequency. The energy carried by this wave comes from the energy used to push the electrons up and down; this energy, in turn, comes from the electric current from the radio transmitter. To increase the transmission frequency, you'd have to increase the frequency of the up-down motion, and, everything else being equal, this would take more energy. Your electric bill would go up.
Can you guess what that number might be? Like all great scientists, find a way to cheat, uh, I mean cleverly deduce the answer. A standard trick that scientists use is to look at the measurement units of the quantities being multiplied. Wavelengths are distances, usually measured in meters. Frequencies are numbers of waves per second. Therefore, wavelength times frequency must have units of "meters per second." That, of course, is the measurement unit of speed. The magnitude of this speed is the speed of light: 300 million meters (186,000 miles) per second. In the 19th century, scientists noticed that the speed of light equals the speed of an electromagnetic wave. This was evidence that light is a form of electromagnetic wave.
From this relationship of wavelength, frequency, and speed, you can calculate the wavelength for a particular frequency, or vice-versa. Just divide the frequency into the speed to get the wavelength. For instance, an FM radio station at 106 megahertz (106 million waves per second) broadcasts a wavelength of about 3 meters (9 feet). An AM (medium-wave) station at 1,000 kilohertz (1,000 thousand waves per second) broadcasts a wavelength of about 300 meters (1,000 feet). This is why AM stations, unlike FM ones, fade out when you drive under a bridge: The AM wave is too big to fit under the bridge.
Comparing the speed of light to the speed of an electromagnetic wave is one of the many ways that scientists have tried to unlock the secrets of radiation. Whenever we talk about radiation, we are like children with an early birthday present. We can pick it up and shake it. We try to guess what it is. But we are not allowed to open it. After all, you can't lay radiation on a laboratory bench and dissect it. In the 19th century, scientists shook the mysterious box of electromagnetic radiation -- "light," as its most familiar wavelengths are known -- and found that it was a wave.
Later, scientists shook the box a different way and found something else. Their experiments indicated that, in fact, electromagnetic radiation is a particle, like a minuscule grain of sand. They gave this particle a name: photon.
This means that light comes in little chunks. It's not a continuous wave, but more like a series of waves. Each of the chunks, the photons, has an energy that depends on its wavelength (or, equivalently, frequency). A radio-wave photon has a billionth the energy of an x-ray photon. If you want to send a certain amount of energy, you could send one x-ray photon, or you could send a billion radio photons.
The photons that fall upon the Earth provide the energy that keeps plants alive, powers our weather systems, and warms our skin on a sunny day. To collect the photon hailstones, you might imagine setting out a sort of bucket. A solar panel is an example of a photon bucket. So is a telescope. The rate at which these buckets collect energy is called the flux. Flux is measured as the energy per second that falls on a unit area, such as a square centimeter.
What happens when you tilt a bucket? How does this affect the number of photons or hailstones you catch? Try this with a readily available photon bucket: your hand. On a sunny day, hold your hand palm up. Wait a few seconds until you notice the warmth of the Sun. Then slowly rotate your hand so that your palm tilts away from the incoming light and your thumb points toward the sky. You should notice less heat on your palm. This is because flux of solar energy onto your palm has decreased. The flux that photon buckets intercept depends on the angle between the incoming photons and the opening of the bucket (see diagram).
Rain gauge. If photons of light are like raindrops, then telescopes are like buckets. The rate of rainfall onto a unit area is called the flux of rain. If two buckets, large and small, are sitting flat on the ground, the flux into both is the same. The large one traps more flux, and therefore more water left). If you tilt a bucket, it'll gather less rain; the flux into the bucket, relative to the area of the bucket, will decrease (right). The same ideas apply to telescopes and other light buckets. To gather the most light, you want as big a collecting area as possible, and you want to orient the area so that it isn't tilted with respect to the light source. Diagrams by Debra A. Fischer
A house plant that is starved for sunlight will turn the flat surface of its leaves toward a nearby window. The plant is reorienting its photon buckets to collect the greatest amount of flux. With time, the plant will develop a contorted shape as it grows toward the window, a process known as phototropism. Another way to demonstrate the concept of flux in the classroom is to use solar cells. Put a light bulb in a circuit powered by a solar cell. As you rotate the cell, watch the intensity of the bulb change.
This business of tilting photon buckets explains why we have seasons. The angle between sunlight and the surface of the Earth, and therefore the flux of the sunlight, is smaller in winter than in summer [see "To Every Season There Is a Reason," The Universe in the Classroom, Winter/Spring 1995].
These, then, are the three major principles that teachers can convey to students: Light is the same basic type of wave as radio, x-rays, and so on; it comes in little packets whose energy depends on wavelength; and collecting lots of these packets provides the energy to drive photosynthesis, climate, solar panels, and so on.
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