A sine wave is a continuous, periodic function that can represent oscilation or rotation, and is seen in various aspects of natural and man-made life such as sound, light, electricity, or even financial markets. The function defined mathematically is y = sin x, or y = cos x. To represent something using the sine function, it must be manipulated using math through the formula y(t) = Asin(2πft + φ) + D. A is the amplitude of the function, which is the most the graph will deviate from its midline. f is the frequency of the graph, or how many cycles occur per second. t is time. φ is for the horizontal "phase shift", simply how much the graph is shifted left/right. D is the vertical shift, how many values up the midline has shifted. The midline, or sinusoidal axis, is the average of every point in the function and runs directly through its center. When transforming a sinusoidal graph, any transformations inside of the parentheses will apply inversely (1/f and -φ). Cosine functions, y = cos x, are simply transformations of the original sine function, shifted left π/2. Every sinusoidal function is periodic, meaning it repeats infinitely as x increases. However, not all periodic functions are sinusoidal. Overall, sinusoidal functions are useful tools for defining cycles and waves, and they make appearances in all types of math and science.
Sine Waves in the Real World
60hz hum
Electrical/Mains Hum
Sinusoidal functions can be seen an represented in many places in the universe. One is electrical hum, often called mains hum. The mains hum is is directly related to the voltage of an alternating current passing through an object. It can commonly be heard emanating from transformers in power grids and other equipment, where it is caused by vibrations due to changing electromagnetic fields. In the United states, where 60hz AC electricity is used, the frequency of the hum is 120hz. In the rest of the world, 50hz AC causes a 100hz hum.
