Sinusoids

Adding two sine waves with same frequency

Adding two sine waves with same frequency
  1. How do you add two sine equations?
  2. When two sinusoids of different frequencies are added together this results in?

How do you add two sine equations?

cosφ = sinφ tanφ= ( E20 sin δ Eθ0 )(E10 + E20 cosδ E20 sin δ ) = E10 + E20 cosδ Eθ0 , which completes the derivation. As a check, consider the case of equal amplitudes, E10 = E20 ≡ E0. Then, using the above results, Eθ0 = √2E0(1 + cosδ) . (1 + cosδ), we end up with: Eθ0 = 2E0| cos(δ/2)| .

When two sinusoids of different frequencies are added together this results in?

Adding sinusoids with different frequencies results in a signal that is no longer sinusoidal. But is it periodic? If the frequencies of the added sinusoids are integer multiples of the fundamental, the resulting signal will be periodic. Figure 2: Adding sinusoids at 3, 6, 9 Hz produces a periodic signal at 3 Hz.

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