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Sum of Sines

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The sum of two sine waves with the same frequency is again a sine wave with frequency . This is used for the analysis of linear electrical networks excited by sinusoidal sources with the frequency . In such a network all voltages and currents are sinusoidal. The addition of sine waves is very simple if their complex representation is used.

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This Demonstration shows the sum of two sine waves with amplitudes , and phases , , respectively. The complex representation , as vectors in the complex plane, is shown in the left graphics column. The sine function is the imaginary part of the vector, indicated by the projection onto the imaginary axis.

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Contributed by: Carsten Roppel (December 2011)
Open content licensed under CC BY-NC-SA

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