What is a wave?|
The precise definition of a wave involves too much math (involving the so-called "the wave equation," which requires calculus), so instead let us take as a working definition of a wave "a disturbance spreading through space, usually carrying energy." It isn't completely accurate, but it covers the waves studied here.
What kinds of waves to you know--other than light and its relatives? (List on the board the types proposed by students, then fill in gaps)
- --Ripples forming on the surface of water, after a stone is thrown in. (Strictly speaking, those are surface waves, almost 2-dimensional.)
- --Ocean waves. That also includes tides and tsunamis, a Japanese word for waves generated in the ocean by earthquakes (widely misnamed "tidal waves").
- Sound waves, in air, water and solid materials.
"Ultrasound" is sound too high-pitched for the human ear to hear (though dogs can hear some of its range).
"Infrasound" are sound-like waves too low in frequency for the ear--for instance, the shaking of the ground when a heavy truck or train passes nearby.
- Earthquakes propagate as waves in the solid earth.
- Waves on a string such as on a guitar string, or a "slinky" toy, or a rope whose end is waved (and even a flag waving in the wind). These can be viewed as one-dimensional waves, spreading along a given direction only.
- (Someone may name shock waves. Shocks are propagating disturbances and carry energy, but the equation they satisfy is not the wave equation, and they lose energy as they spread--material gets heated by the passage of a shock. Therefore scientists usually omit the "wave" designation. We never claimed our working definition was perfect!)
Light belongs to the family of "Electromagnetic Waves," described more accurately later. Anyone knows other waves in this family? (List on the board, then fill gaps)
- Infra red (IR) waves (also known as infra red light).
- Ultra violet (UV) waves or UV light (also "extreme ultra violet").
- Radio Waves.( AM, FM, TV are all ways in which radio waves are used to carry signals, not different kinds of waves.)
- Gamma rays
(But not cosmic rays--they are actually very fast nuclei of hydrogen and some other elements, originating in distant space. The name was given before people knew what they were, and the same happened in the naming of "alpha rays" and "beta rays" emitted from radioactive substances, really fast helium nuclei and electrons.
Unless raised by a student, the following is better skipped, to save time and potential confusion. Strictly speaking, any moving particles are also associated with so-called "matter waves." Such waves, describing the particle's "wave function" in quantum mechanics, are of a different kind, giving the probability of the particle being observed at various locations.)
(If someone mentions Alfvén waves or "whistlers", these are among known types of plasma waves, many of which are electromagnetic waves modified by the presence of plasma, for instance, in space around Earth.)
(If someone mentions "standing waves," these are waves of any kind confined between boundaries and therefore not traveling outside them. For instance, a wave on a guitar string, confined to the section between the bridge and the fret.)
What properties of a wave can we measure?
- Amplitude, the height of the crests, a measure of how strong the wave is; e.g. loudness of sound.
- Wavelength λ (Greek "lambda") the distance between two crests.
- Wave velocity v, the velocity with which crests advance in space. The "velocity of light" at which electromagnetic waves spread in vacuum is usually denoted by the small letter c.
- Frequency f or ν (Greek "nu"), the number of crests passing a fixed point each second
How do we find the relation between the wavelength, wave velocity and frequency? (Teacher starts the explanation)
The length v of the wave passing in one second through a given point in space contains many up-and-down swings, each of length λ. Their total number in that second is.... (a student may try complete on the board, or else, teacher continues)
(length of wave train)
(length of one wave)
f = v/
What difference does it make whether light is a wave or an array of "rays," of streams of "light particles"?
--In principle, a big difference:
- A ray propagates along a single line only.
- A wave fills all of space,
(Teacher explains) For many years it was believed that light consisted of rays. The rays were bent by prisms or lenses, and the laws of such bending helped design telescopes and other instruments.
Then, however, scientists discovered interference--when two or more rays from the same source overlapped, they could reinforce or weaken each other--depending whether their crests overlapped (reinforced) or crest matched dip (=crest in opposite direction), in which case they were weakened.
The diffraction grating (discussed in the the preceding lesson) is an example. It was then realized that light was a wave, but with a very small wavelength. Beams of light are well defined on distance scales much larger than a wavelength, but they "fuzz out" when one tries to define their boundaries within a wavelength or less.
Before discussing why light was recognized as an electromagnetic wave, one should understand what "electromagnetic" means.
What is a magnetic field?
(This should be familiar from section S-3 "The Magnetic Sun").
A magnetic field is the region in which magnetic forces can be observed--forces on an iron magnet or on an electric current.
What causes magnetic fields?
Iron magnets and electric currents are also the sources of magnetic fields.
The magnetism of the Earth is believed to be caused by electric currents in its core. The magnetism of sunspots is also due to electric currents.
(Teacher explains) An electric field is similarly the region where electric forces can be observed. You comb your hair on a dry winter day and find the comb is electrified--it can attract little bits of paper, the way a magnet attracts pins. In that case, an electric field exists around the comb.
Similarly, friction among dry garments in a clothes dryer creates an electric field, which makes them cling to each other. In a laser printer or a xerox-type copier, a roller is electrified and finely powdered carbon sticks to it; later, under the influence of light, electric charge is removed preferentially, leaving it (and the carbon sticking to it) only where it contributes to the printed picture.
All these electric fields persist, because the comb, fabric, roller and surrounding air are all insulating materials, which do not allow electric charges to move freely. On the other hand, an electric field in a metal wire that conducts electricity (=allows charges to move) will move charges and will create an electric current. That is how home electricity works.
Because such currents expend energy, electric fields in a conductor quickly die out, unless they are maintained by an electric battery or generator, which provide a steady input of energy.
Now the big question: can electric fields ever drive electric currents in a vacuum or in an insulator--currents that creat magnetic fields? Usually--no. However... (students answer, teacher supplements)
James Clerk Maxwell in 1861 found that if one added to the basic equations of electricity (now known as "Maxwell's equations") a certain term that permitted such a current, those equations had, as one solution, a wave which advanced in vacuum at the speed of light.
The additional term was only significant if the electric field changed very rapidly. When the electric field stayed steady, the extra term was absent. Maxwell showed that such a wave had properties actually observed in light, and proposed that the added term was indeed necessary, and that light was an electromagnetic (EM) wave.
Light is usually produced by heat, or by glowing gases. If Maxwell was right, however, it should be possible to produce EM waves by purely electrical means. Can it be done?
- Yes, and that is how radio waves are produced--for instance, by a current bouncing back and forth, very rapidly, in a conductor we call antenna. Heinrich Hertz in Germany did something like this in 1886.
What differences do you know between sound waves and electromagnetic (EM) waves?
- EM waves in air travel nearly a million times faster than sound waves
- EM waves are carried by rapidly varying magnetic and electric fields. Sound waves in air are carried by rapidly varying pressure changes.
- EM waves are transmitted through electrical insulators but are stopped by conductors. Sound propagation through a material depends on its elastic properties, not on electrical ones.
[Do not raise the following point unless some student does. In electromagnetic waves, the disturbances--the electric and magnetic forces which mark the waves--are transverse to the direction in which the wave travels--see
animated figure from section (S-5). The shaking is directed sideways--like a wave on a rope. Sound waves in air are longitudinal, with the oscillating pressure force along the direction in which the wave spreads. However, sound-like waves in solids--e.g. earthquake waves--may also be transverse.]
As an illustration of the 3rd difference above--how are windows on microwave ovens constructed--and why?
--They are of glass, but with a metal mesh in them. The glass allows one to see the cooking food, but because the holes are much smaller than the wavelength, the microwaves are reflected back by the mesh and cannot escape. Light has a very small wavelength and can pass the holes.
Most electromagnetic waves have a much higher frequency than sound waves--but not always. Ultrasound used in medicine and in cleaning small objects has a much higher frequency than the kind of sound we hear. And whistlers are electromagnetic waves in the same frequency range as regular sound, modified by the plasmas surrounding Earth and guided by the Earth's magnetic field lines--sometimes even bouncing back and forth along them, from one hemisphere to the other.
Whistlers can be picked up by long wire antennas. They were occasionally heard along the end of the 19th century, on long-distant telephone lines, sounding like long whistles dropping in pitch. In World War I (1914-8) they were heard on telephone lines employed by the armies in the field, and in 1919 the German scientist Heinrich Barkhausen proposed they were coming from outside Earth.
In 1953 Owen Storey showed that they were broadcast from lightning strokes.
Lightning emits a wide range of radio frequencies, as first shown in 1895 by Aleksandr Stepanovich Popov in Russia--indeed, its crackling is easily picked up by ordinary radios during thunderstorms. Storey showed that whistlers often started from lightning in the opposite hemisphere, near the other end of the observer's magnetic field line, whose attached plasma guided them. Whistlers have since then provided unique information about the density of ions and electrons in space around Earth.
(end of optional section)
Light and other EM radiations spread like waves, all over space. However, the way they give up their energy is distinctly not wavelike. Can you describe it?
- Absorption of energy always occurs in well-defined chunks of energy, known as photons.
What quality of light determines the energy of its photons?
Its frequency ν (nu)--or in other, equivalent terms, its wavelength λ (lambda), or for light, its color (all three statements are equivalent). When the frequency gets higher, the wavelength shorter or the color moves from red towards violet, the energy of each photon also gets larger.
Photons of blue light have more energy then those of red, which in turn have more than those of infra-red, and all these are less energetic than photons of ultra-violet. The energies of X-rays are even larger, and gamma-ray photons have energies larger still.
What formula gives the connection between photon energy E and the light's frequency ν ?
E = h ν
where h stands for a measurable quantity, a constant of nature, called "Planck's constant" because it was discovered by Max Planck in Germany in 1900. Today the chief scientific institution in Germany is the "Max Planck Institute."
You have an electric circuit triggered by an "electric eye," a tube empty of air with two metal contacts inside it. One is a plate of a suitable metal, with the property that, when light falls on it, it knocks out electrons. If the contacts are connected to a battery, the flow of such "photoelectrons ("photo" means, related to light) completes an electrical circuit, and if the circuit also contains an alarm, it will start ringing.
Question: You find that such a tube is triggered by blue light but not by red light. Can you guess the reason?
- The red photons do not have enough energy to knock out electrons, whereas the blue photons do, because each of them has a higher energy. Note that it is the quality of the light that makes the difference, not the quantity. An intense red beam will not trigger the tube, but a faint blue one will!
When developing film in a darkroom, no light is allowed, or else it would darken the exposed parts of the film. However, with old-type orthochromatic black-and-white film it was permissible to use a deep-red "safelight" in the darkroom. Why was this safe?
- Same reason as before. The red photons had too little energy to affect the light-sensitive material on the film.
Why do glowing gases (e.g. neon lights) emit well-defined spectral colors?
- They do because each of their atoms emits light independently, and can do so only after it is elevated (by collision or by absorbing light) to one of its higher energy levels. These levels (different for each atom) are well defined, and so is the final "ground level" of each type of atom in its usual (unexcited) state.
When the atom changes from its high level to a lower one (or to its ground level), the amount of energy given to the resulting photon is always fixed, equal to the difference between the energy levels. Therefore the emitted color is also fixed.
(Optional historical note)
The first clue for energy levels in atoms came in 1885. By then, the wavelength of typical atomic emissions of light had been measured with great precision. Complicated elements emit hundreds and thousands of well-defined "spectral lines", but hydrogen, the simplest elements, seemed to have just 4 "lines" of specific colors. Johann Balmer, a high school math teacher in Basel, Switzerland, found that the wavelength of all four fit a formula
1/λ = R [1/4 – 1/n2]
where n = 3,4,5.. and R is the experimentally obtained "Rydberg constant", later explained using quantum theory.
(A translation of his original article exists on the web.)
The lowest of these "lines" (n=3) is the red "hydrogen alpha" line (Hα for short), responsible for the dominant red color of the visible chromosphere of the Sun. That is the layer of the solar atmosphere just above the photosphere from which most of visible sunlight originates (light emitted deeper down is just reabsorbed and re-emitted).
The chromosphere emits relatively little light, which is normally drowned out by the much greater brightness of the photosphere. It becomes visible during a total eclipse of the Sun. Then, after the Moon completely covers the photosphere, a reddish glow becomes visible around the Sun, in a relatively narrow ring; above it is the corona whose light is even fainter.
The chromosphere is important because it is the site of energy releases associated with sunspot magnetism--the so called solar flares. Solar flares are only rarely bright enough to show themselves against the background of the photosphere (one such rare event was the first flare to be observed, seen by Richard Carrington in 1859). All this changed with the introduction of sensitive filters which only transmitted the narrow Hα line and blocked everything else. Through such filters flare activity and many other solar phenomena can be clearly seen and photographed.
After Balmer announced his series, Lyman found in the ultra-violet a series of lines1/λ = R [1 – 1/n2]
of which the "Lyman α" line is particularly prominent in the glow of the Earth's outer atmosphere, photographed by astronauts from the Moon. Also, Paschen found a series of lines in the infra-red1/λ = R [1/9 – 1/n2]
All these are now understood to represent jumps of the hydrogen atom between two of its main energy levels R/n2 (n = 1,2,3...). This was one of the early indications that the frequency ν of light (proportional to 1/λ) gave a measure of an energy associated with it. Later "spectral lines" of other atoms were also found to represent jumps between a smaller number of levels, though their values did not fit simple mathematics, the way the levels of hydrogen did. The details were gradually worked out between about 1900 and 1930, as the "quantum theory" of atoms evolved.
(End of optional historical note)
Atoms in a gas emit photons individually, and the peaks of the waves they produce are randomly distributed. On the other hand, in a laser, between tuned mirrors (and for appropriate energy levels) the atoms can match their emissions, the way crickets or frogs at night sometimes coordinate their sounds into a single chorus. These ordered ("coherent") light waves can be modified to carry signals through "optical cables" of super-transparent glass fibers, much more efficiently than metal cables can do so
(end of optional section)
Why do pictures of the Sun taken in "soft" X-rays show mainly the corona?
- Because the speed of atoms in a hot gas, and therefore their kinetic energy, increases with temperature. Atoms in the photosphere and chromosphere move too slowly for their collisions to provide enough energy to create an X-ray photon--for instance, by exciting one of the high energy levels of an atom (or ion). The corona, with its million-degree temperature, is hot enough for this to happen.