Wave mechanics & wave phenomena in technical theater
The wave phenomena that apply to lighting a stage of scenery and actors are diffusion, color mixing, thin lenses, and reflection and refraction. Diffusion is important because the incandescent and halogen bulbs used in theater lighting can be very harsh, and can give very high contract shadows. Directionality is important when considering shadows. An actor lit from above will have deep shadows under their eyes and lips, and will appear creepy or evil. Actors lit head on, almost horizontally will not appear to have any contours to their faces, and appear flat. Subjects lit from either the left, and right will throw shadows on either side of their face. A combination of these directions of lighting give appropriate shading and contouring to face, making subjects appear normal and 3D.
In light applications to technical theater, the length of the “can” in which the lightbulb is placed will vary. The lens that is placed in the can may also vary, and the distance from the bulb to the lens can change to give a larger or smaller spotlight. The longer the can, and the closer the lens, the narrower the spot. A smaller spot will also be brighter because more light is focused to a smaller area.
Several properties of waves apply directly to technical theater. Spotlights are often used to illuminate a small area of the stage, a single actor, or small grouping of actors. These are extremely bright, and can have a fuzzy edge or a sharp edge. Depending upon the size of the spot and the type of edge desired, different types of light boxes, and filters can be used for different effects. Diffusion gels can be used to scatter light in different patterns to create softer light that has a blurry effect.
Color mixing is fundamental to properly lighting a stage. Several lights are used to mix colors to provide different moods to the stage and the subjects. Different complexions and colors in costuming also have to be considered when lighting a stage. Mixing color with light is additive, not subtractive like color mixing in paint or ink. Additive refers to the spectral lines of the observed light. Additive color mixing puts more spectral lines in the product of the mixing, subtractive removes them, but color perception is not perfect in the human eye, and some spectra are observed to be brighter with more spectral lines than others. Intensity is also a large factor in color perception. Additive color mixing is when the primary colors are darker with more limited spectra, and the mixed color is brighter with broader spectra: for example, adding red light and green light gives yellow light, green and blue gives cyan light, lastly mixing red and blue gives magenta light. Subtractive color mixing, on the other hand, is the exact opposite, with brighter primary colors that have broad spectra that is diminished (or subtracted) to give darker secondary colors with more limited spectra. For example, adding cyan ink and yellow ink gives green ink.
Warm or cool themed lighting is the easiest way to convey a mood on stage. Having a mix of blue light and white light immediately evokes a feeling of melancholy in the audience. Mixing yellow light and white light, conveys a feeling of hope, of dawn, or new beginnings. On stage, lighting can be mixed wavelength by wavelength, using gel filters over halogen lamps.
Sound applications to technical theater
In a theater, full, even sound at all seats is desired so all patrons enjoy the full experience. This happens by minimizing constructive and destructive interference of the sound output by the speakers used in the sound system. Constructive interference in terms of sound is when two sound waves are played at the same time, and the amplitudes of their waves add up, resulting in a louder sound than originally output. These “hot spots” can create a much louder and vibrating sound in spots. Destructive interference is the opposite, the amplitudes are out of phase, and subtract from each other, creating a loss of sound or a severe decrease in volume, sometimes to the point of a loss of integrity, sometimes making a “cold spot” or making the sound feel “watery” or “squishy” in spots. The placement of these spots will change as the wavelength (or pitch) of the sound varies. Longer wavelengths will produce fewer hot spots and cold spots, and they will be farther apart. Minimizing the number of these spots creates a controllable setting, where every patron gets the sound experience that is the same, and is what the director designed.
There are several strategies to this complex system:
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Having 3D sound system with speakers at the left, right, top, and bottom of the stage that point toward the center of the main sections of the audience, orchestra, back, and balcony.
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Have small speakers at the front for the first few rows of patrons.
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Run the speakers in stereo (or surround sound), so each speaker only puts out certain ranges of frequencies, and they can never line up perfectly to double the amplitude or cancel each other out.
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Have a sound tech and sound board in the audience so they can adjust on the fly.
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Have a microphone in the audience if the soundboard is in a booth.
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Map the theater with a sound engineer.
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Use a shell for vocal choirs and instrumental groups to eliminate the need for microphones and speakers. This bounces the sound forward toward the audience, and fans it out, to reduce the number of waves that cross paths, and reduce interference.
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Have textured sound absorbing walls at the sides and back to prevent ricochet.
Light applications to astronomy
Doppler effect
Stars can be determined to be moving toward Earth or away from Earth by the frequency (or wavelength) of light they appear to emit. This is called redshift or blueshift. It is based on the Doppler effect, which says a source point of waves will appear to have a higher frequency when moving toward an observer, or blueshift, and a lower frequency when moving away, or redshift. Since almost all stars in our sky exhibit redshift, it is indicates that the universe is expanding, likely a result of an initial explosion that created the universe (the Big Bang Theory).
Finding exoplanets as a search for intelligent life
For several decades now, humans have been obsessed with the idea of intelligent aliens existing. This is an area of serious scientific research and discovery. The possibility of intelligent life on another planet was first legitimately estimated by Frank Drake, using a now famous Fermi-style estimation, called the Drake Equation. He estimated the number of planets in the solar system with the potential for intelligent life to be 50,000. The estimate is based on assumption and known values and known ratios, and has been the subject of scientific scrutiny for many years. Some of the assumptions have been discounted, such as the ratio of planets to stars, it was originally estimated as 0.4, but almost every known star has at least one planet, so the value is now known at 1.0. Most of the values ratios have been refined in the past 70 years, such as the fraction of planets that are capable of sustaining life. This has been refined from near zero, to near 0.4 pending the outcome of the search for bacteria on Mars. The overall estimate for the number of planets in the universe that can sustain and grow to intelligent life is in the tens of thousands. The real power of the Drake Equation is that it gave legitimacy to the search for alien life. We now have SETI (Search for Extra Terrestrial Intelligence) with a huge radiotelescope array, and several groups searching for habitable Earthlike planets, as well as Voyager, a probe transmitting evidence and messages of human life on Earth via radiowaves, to any life that can interpret them. These projects would not have been taken seriously, publicly funded, nor exist without Drake and his famous equation.
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Exoplanets are planets that exist outside our solar system, and are an area of great research, measurement, and discovery by astronomers. They are looking for Earthlike planets that have the right conditions for life to exist and thrive on a long enough timeline to evolve into intelligent beings. The first step is to find the planets. The next step is to measure their status to see if liquid water can exist.
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Based on what we know about water as a compound, it is liquid between 273-373 K at 100 kPa of atmospheric pressure (the atmospheric pressure at sea level). A planet would need to be roughly Earth sized, roughly Earth’s mass in order to have a gravitational field and an atmospheric pressure in the appropriate range. It would also need to be located in a similar sweet spot for temperature in terms of distance to its star, and its star’s intensity. Bing too close to a star would either make it too warm for liquid water, or burn the atmosphere off completely (for example, Mercury or Venus). Being too far would make it too cold, and only solid water would exist as is the case on Mars.
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Measuring the intensity with transit photometry
As planets orbit their suns, there is a period of time where they pass between their sun and us (or our best telescopes out in space). When this happens, the exoplanet will absorb or block a small amount of light emitted by that star. This is similar to an eclipse, but only a tiny amount of light is blocked as the planet moves across the sun. This is called a transit. The transit of Mercury across our sun was visible in May 2016 (unfortunately it was cloudy in New England where I live, and could not be seen.) As the planet blocks some of the sunlight, the observable intensity of that sun diminishes until the planet passes completely, and then the intensity is restored. By measuring the drop in intensity of light, and looking for a cyclical pattern of this observation, we can find stars that have planets very far away. The current range for small stars is within 160 light years (a light year is about 6 trillion miles), and is much farther for large planets orbiting around large suns.
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Measuring the wobble: angular velocity by Doppler spectrography
Planets are held in orbit by the gravitational attraction between them and their sun. The more massive the sun, the more strongly a planet is attracted to it. This also happens conversely, the more massive a planet, the more the sun is attracted to it. Massive planets exert a small pull on their stars, and often a star with exhibit a very slight wobble as its planet revolves around it (technically, they both rotate around their common center of mass, but the star moves very little). This phenomena can be simulated using the online simulation at phet.colorado.edu: (http://phet.colorado.edu/en/simulation/legacy/my-solar-system.) Since stars are continuously emitting light, we can see them, and we can measure this small periodic wobble using spectrography and the Doppler effect. As the star is pulled away from us, its light shifts slightly toward the red, and when pulled toward us, slightly toward the blue. This is similar to how stars are themselves receding from each other resulting in redshifted spectra as mentioned previously, but the difference between a wobble and the motion of the universe is much smaller in terms of scale, and the wobble is periodic.
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Measuring planetshine or planet emission by photometry
Planetshine is a very simple concept, as planets revolve around a star, they reflect light from that star back toward us, just like our moon does with our sun. The frequency of the light that is reflected is often in the visible ranges, (which is coincidentally similar to what the Earth reflects from the sun- though we also reflect some UV and infrared light). This can be measured when the planet is not in transit, and not eclipsed by its star, but is on the outer wings of its orbit, and is facing us. The planet will go through phases, like our moon does, so the intensity of this reflected light will vary in a regular pattern as the percentage of the planet that is both illuminated and facing us wanes or waxes.
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Planets will also absorb, use, and re-emit electromagnetic radiation from their stars. The frequency of the light that is re-emitted is lower than that of the star because some of the energy has been converted to internal energy of the planet. Earth does the same, emitting longwave radiation (infrared light), which causes the dark side of the Earth to cool at night. When looking for exoplanets, a slight increase in the intensity of lower frequency light can be detected when the planet is within the line of sight, but not when the planet is eclipsed by its star. Light that is re-emitted should not wax and wane with phases, as it is not depended on the rotating reflective surface, but should merely be constant.
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Spectral analysis to determine the atmosphere of the planet
Once an exoplanet’s existence is confirmed, the question of environment remains. Is this planet able to sustain life, as we know it? This is a complicated question to answer, but life on our Earth would not be possible without liquid water, atmospheric oxygen, and complex hydrocarbon compounds. Modern chemistry allows us to make atmospheric oxygen if liquid water exists, it is fairly simple chemistry, and could be modified to be done on a large scale if necessary. Hydrocarbons are a bit more complicated to synthesize, but again it could be done, as long as elemental carbon and liquid water exist on a planet. However, all of the oxygen and hydrocarbons on Earth are the result of photosynthesis (combining water and carbon dioxide using light to form hydrocarbons). That is why water is so important to life.
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The atmosphere of a planet can be detected based on spectral absorption. Each chemical has a spectral absorption signature, a combination of wavelengths of light that it absorbs. By measuring the wavelengths of light emitted by the star when the planet is in transit, and is eclipsed, we can subtract the two, and whatever wavelengths are missing while in transit have been absorbed by the planet’s atmosphere. We can then compare those wavelengths to the know spectra for all the elements and compounds on Earth, and have a reasonable estimation of what the atmosphere of the exoplanet is made of. We can then compare the boiling points of those elements and compounds to estimate ranges of pressure and temperature of the atmosphere of the planet, which is the beginning of the answer to the question: Could this planet support life?
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