Addition of Frequencies: Combining Same Phase, Different Amplitudes

In summary, when adding two frequencies with the same phase but different amplitudes, the resulting wave is equal to the sum of the amplitudes multiplied by the sine of the phase. However, it is not possible for two signals to have the exact same phase, but they can have a common starting point to simplify the equation.
  • #1
henil
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i want to add two frequencies having same phase but different amplitudes, in what manner i can proceed ?
 
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  • #2
If you have two amplitudes ##a_1, a_2## and the same phase ##φ## then your waves are ##a_ 1 \sin{φ}## and ##a_ 2 \sin{φ}## so the resulting wave is ##(a_1 + a_2) \sin φ##.
 
  • #3
henil said:
i want to add two frequencies having same phase
The phases of any two signals with different frequencies will coincide momentarily at a rate equal to the difference in the frequencies
but they cannot 'have the same phase'. You can, of course, choose your time origin to be when the phases of both signals are both zero. This would make the starting equation simpler.
Could it be that you are adding two signals with the same frequency.
 

What is the concept of addition of frequencies?

The addition of frequencies refers to the process of combining two or more waves with different frequencies to create a new wave with a different frequency. This can occur when two waves of the same phase but different amplitudes are added together.

Why do we add frequencies?

We add frequencies in order to create a new wave that has a different frequency than the original waves. This can be useful in many applications, such as in signal processing or creating music, where we may want to create a specific frequency or tone.

What happens when we add frequencies with the same phase?

When we add frequencies with the same phase, the resulting wave will have a larger amplitude. This is because the peaks and troughs of the individual waves will align, creating a larger displacement.

What happens when we add frequencies with different amplitudes?

When we add frequencies with different amplitudes, the resulting wave will have a varying amplitude depending on the amplitudes of the individual waves. The amplitude of the resulting wave will be a combination of the amplitudes of the individual waves.

Can we add frequencies with different phases?

Yes, we can add frequencies with different phases. However, the resulting wave may have a different shape compared to the individual waves. This is because the peaks and troughs may not align, causing interference and creating a more complex waveform.

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