Purpose: To investigate how various wave patterns can be represented as a sum of harmonics.
Simulation Used: Fourier from the PhET at the University of Colorado.The idea behind Fourier Series is that any curve can be represented
as a sum of sin functions with a definite set of
amplitudes. Mathematically, the function describing the curve is
written as:
.
(Eq.1)
The Fourier series can be applied to interference of physical
waves. If we have several waves with different frequencies traveling
through space, the resultant displacement of a given particle (x=0)
will be given by:
(Eq.2)
Here, the physical time, t, in Eq.2 corresponds to the independent
variable x in Eq.1.
Though, mathematically there are infinite number of terms in the Eq.1 and Eq.2 above, in this simulation, the terms are limited to eleven. In real life experiments, the number of terms is determined by the desired accuracy of the final result.
The first term in the Eq.2 corresponds to the wave with the lowest frequency, the fundamental frequency. The next has a frequency twice the lowest, thus corresponds to the second harmonic. The third has a frequency three times the lowest - the third harmonic, etc.