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How to Make a Wave Graph

Electromagnetic waves are key to modern-day society and are used in a diverse range of applications such as radar, radio and medical imaging. The mathematical properties of an electromagnetic wave, or any other type of wave, can be expressed using a simple sinusoidal function. There are two main sinusoidal functions and these are the trigonometric sine and cosine functions. These functions can be graphed in order to generate an oscillatory dependence which simulates a wave.

Things You'll Need

  • Graph paper
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Instructions

    • 1

      Write down the wave amplitude. The amplitude is the peak-to-trough vertical distance.

    • 2

      Write down the wavelength (period) of the wave. The wavelength of the wave is the distance between two peaks.

    • 3

      Write down the mathematical expression of the wave. The simplest form of a wave can be written as y = A * Cos (kx)

      Where A is the amplitude of the wave. k= 2*pi / wavelength. For a wavelength of 2 meters, and an amplitude of 5, the wave equation becomes y= 5 * Cos (3.14x).

    • 4

      Substitute some values for x into the wave equation in order to generate some points for the graph. Following the example:

      y= 5 * Cos (3.14x)

      y= 5 * Cos (3.14*1) = -5 Coordinates are (3.14, -5 )

      y= 5 * Cos (3.14*2) = +5 Coordinates are (6.28, +5)

      y= 5 * Cos (3.14*3) = -5 Coordinates are (9.42, -5)

      Draw the graph axes and label the x-axis "x." Label the y-axis "y= 5 * Cos (3.14x)." Plot the points on the graph, marking each point with a cross. The graph should have a wave-like oscillatory dependence.


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