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DOING PHYSICS WITH MATLAB

VISUALIZATION OF THE PHASE OF COMPLEX FUNCTIONS USING COLOR: A TRAVELLING TRANSVERSE WAVE

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wm_complex01.m

The phase of a complex number can be represented by an assigned color. The scripts calls the function ColorCode.m to assign a color for the phase of a complex number in the range from .

COMPLEX NUMBERS

A complex number can be represented by its magnitude and phase. It is not easy to show the magnitude and phase of a complex number. However, the phase of the complex number can be represented by an assigned color as shown in figure 1.

Fig. 1. A color is used for to show the phase of a complex number.

TRAVELLING TRANSVERSE WAVE

As an example of illustrating the phase of a complex number, we can consider the propagation of a [1D] transverse described by the exponential function

The phase of the wavefunction is calculated using the Matlab function angle. The wavefunction for 3 wavelengths is displayed in figure 2 for time increments of T/8 where T is the period.

Fig. 2. The wavefunction plotted for a series of time steps.

By examination of the sequence of plots in figure 2, the wave advances one wavelength in a time interval of one period. Points along the wave vibrate with different phases. Points along the wave that are separated by one wavelength, vibrate in phase.

The script wm_complex01.m can easily modified to animate the motion of the travelling wave. The animation can be saved as an animated gif or as an avi movie.