Yes, there is a formula to add two sine waves with different amplitudes, periods, and phase shifts. The formula is as follows:
y(t) = A₁ * sin(ω₁ * t + φ₁) + A₂ * sin(ω₂ * t + φ₂)
Where:
- y(t) represents the resulting waveform.
- A₁ and A₂ are the amplitudes of the two sine waves.
- ω₁ and ω₂ are the angular frequencies of the two sine waves (ω = 2πf, where f is the frequency).
- t is the independent variable representing time.
- φ₁ and φ₂ are the phase shifts of the two sine waves.
By using this formula, you can calculate the combined waveform resulting from the addition of the two sine waves. The amplitudes, periods (or frequencies), and phase shifts of the individual sine waves determine the characteristics of the resulting waveform.