In a Wave-Particle Duality exam, you must understand the characteristics of waves and particles that are formed by their interaction. Particles take the form of peaks in the Fourier transform. The Fourier transform is a statistical method that determines what kinds of frequencies and what colors of light a wave produces as it interacts with particles of matter.
There are many ways to represent the frequency of a wave. One of the most common ways to represent a wave as a number of peaks in the Fourier transform is by dots. You must know how these dots are formed, what shapes they take, and how the shape of the wave depends on how it is shaped by particles.
The ones shapes that appear in the Fourier transform of a wave are called “C” shapes. When one peak becomes two peaks, then the wave is called a double peak. This is the case when the maximum or minimum of a wave is also found in the Fourier transform.
When one wave is broken into its components, then it becomes a wave. Then the Fourier transform can be viewed as a curve. A point, called a “figure”, appears at the curve and one point is called a “peak”.
Double peak waves can be produced by such shapes as a “U” shape. Double peaks appear as points on the surface of the wave. The peaks are separated by points that are called “intervals”. Each peak is closer to the “middle” of the wave than other points in the wave.
Two waves with the same maximum frequency and the same wave form can have two distinct colors. The color of the wavelength divided by the length of the wavelength is the difference between the peak lengths. When one wavelength is less than the other, then the wavelength is called equal, when one is greater than the other then the wavelength is called unequal.
If two waves with different wavelengths are measured by the same Fourier transform then the wave with the longer wavelength is the more important one and the color of the wavelength is ignored. The shorter wavelength wave is the point where the peak and the “circles” of the wave intersect. The same wave with the opposite wavelength also produces the same peak.
The color of the waves is determined by how the wavelengths change over time. The speed at which the waves travel changes the color of the wave. The speed is directly related to the wavelength and therefore the wavelength of the wave depends on the speed of the wave.
The speeds at which the waves are traveling change the shape of the wave and therefore the color. For example, a flat wave undergoes a small change in shape, for example, a top change from a top to a bottom. The change in shape is the color of the wave.
The speed at which the waves move depends on the frequency of the waves. If a wave travels faster, then the color of the wave changes more quickly. If a wave travels slower, then the color of the wave changes less quickly.
The colors of waves and particles form because of how the wave and particle interact. Taking a Wave-Particle Duality Exam is a good way to learn how waves interact with each other.
