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  1.     Waves are oscillations ocurring through some medium caused by a disturbance. A traveling wave is organized, and travels with a well-defined speed, of which there are two types: transverse waves, and longitundinal waves. A transverse wave is a wave that travels perpendicular to the displacement of the medium, for example waving a string upward and downward. A longitudinal wave, on the other hand, is a wave where the medium travels in the same direction as the wave. An example of a longitudinal wave would be a slinkie expanding. Waves such as in water are more complex, and share characteristics of both longitudinal and transverse waves. Waves can be categorized based on the medium as well: mechanical waves, which travel through a material medium, electronmagnetic waves, which is a self-sustaining oscillation of the electromagnetic field, and matter waves, which travel through material particles.
  2.     Waves of light from the sun transfer energy onto the earth, and loudspeakers transfer energy in the form of sound waves. The "power" of a wave is the rate at which the traveling wave transfers energy, measured in joules per second, otherwise known as watts. However, in addition to power, area is also significant in how intense the wave is. The "intensity" of a wave is the ratio of its power to the area it is impinging onto. It is formally defined as I = P / a, and the SI units for intensity are Watts per meter squared, or W/m^2. For a uniform spherical wave, its intensity can be calculated by the power of the source, divided by its surface area, which is 4 * pi * r^2. Likewise, a uniform circular wave's intensity could be calculated by dividing the power of the source divided by pi * r^2, for example when an object falls into water. Since a wave's intensity is proportional to the rate at which energy is transferred, and the oscillatory energy is proportional to the amplitude squared, for any wave it holds true that I = c * A^2, where c is a proportionality constant depending on the type of wave.
  3.     Since sound waves are transferred by matter, they can travel at different velocities depending on the properties of the medium since the energy can be transferred from one particle of the matter to another faster if they are closer together, such as with a solid. When at room temperature, sound can travel at air at 343 m/s, but varies depending on the temperature and perhaps the pressure as well. Sound travels at 331 m/s through air at 0 degrees Celsius, or can travel through aluminum as fast as 6420 m/s.
  4.     Can standing waves be constructive and cause the amplitude to increase greatly from even a very small vibration to start?
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