formula to calculate voltage of two sine waves with different phase (not polarity) AC

Discussion in 'Math' started by kostas, Jul 26, 2006.

  1. kostas

    Thread Starter New Member

    Jul 25, 2006
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    Hi

    Ah...nice start. Please ignore the title of the thread. It's close but not quite it. I can't change it now that I pushed the ''post'' button...


    I'm an audio engineer and the answer to my question would help a lot to make some critical decisions.

    I'm looking for an equation that would allow me to calculate the voltage output (AC) of two (or more) sine waves added together at any given time. I am mostly converned about the peaks but if I find this equation I know how to do the rest.

    Any help would be appreciated.

    Best regards,
    Kostas
     
  2. Dave

    Retired Moderator

    Nov 17, 2003
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    For two sine waves:

    y = sin(wt) + sin(wt + @)

    Where @ is a phase shift.

    Then:

    y = 2*sin((wt + (wt + @)) / 2) * cos((wt - (wt + @)) / 2)

    Simplifying to:

    y = 2*sin((2wt + @) / 2)*cos(@ / 2)

    For a maximum:

    y = abs(2*Cos(@/2))

    This is a somewhat awkward process and if you are looking at more than two sine waves you should ideally look at adding and analysing your waves using a tool such as MATLAB, or a similar free application such as Octave or FreeMAT.

    Dave
     
  3. kostas

    Thread Starter New Member

    Jul 25, 2006
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    Dave, thank you very much.

    It turns out that what I'm trying to do is slighly more complicated because I need to relate all that to amplitude and frequency, ie add sine waves of different amplitude, frequency and phase.

    I'm looking into how to integrate what you gave me to what I've found.

    MATLAB is the next step. I'm just trying to figure out the math part for two sine waves at the moment.

    Thanks again.

    Any further suggestions are more than welcome.
     
  4. Ron H

    AAC Fanatic!

    Apr 14, 2005
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    Sine waves of different frequencies, unless they are harmonically related, will eventually precess through all possible relative phases, so the maximum amplitude will be the sum of the peaks of the individual sine waves.
     
  5. kostas

    Thread Starter New Member

    Jul 25, 2006
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    Ahh yes

    Thanks Ron H.

    I'm going to try a bit of FFT analysis. That's where the answer is, no?

    As for the amplitudes (sine waves of same freqs but different voltages and phase), trigonometry (to calculate the resultant) gave me the results I needed.

    Thank you both, your help is appreciated.

    Best regards
     
  6. Dave

    Retired Moderator

    Nov 17, 2003
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    As for the Fourier Transform (the FFT is just a computationally efficient way of computing the Fourier Transform), why exactly do you propose doing such an analysis for addition of 2 sine waves?

    Dave
     
  7. kostas

    Thread Starter New Member

    Jul 25, 2006
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    Hi Dave

    The example of the two sine waves was just for me to understand some basic concepts.

    I was talking about sine waves because they are the basis of every complex sound. I am not working with sine waves, other than calibrating equipment and testing this or that.

    Besides that, all the work is done on computers. All audio production software uses algorithms based on the Fourier tranform to represent the waveform data in the frequency domain.

    I can use this information to fix problems on recordings, mic and speaker placement, to say the least.

    Regards,
    Kostas
     
  8. Dave

    Retired Moderator

    Nov 17, 2003
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    The only reason I asked my above question is that using the FT to analyse addition of sine waves is something that seems a touch odd. Using the FFT to convolve input signals and a range of filter coefficients is the main area I have seen this implemented.

    In a wider research project some time back, I had some experience in using the Motorola DSP56311 evaluation modules and Signal Wizard software for 'real-time' and 'off-line' audio signal processing. My focus in this area was software development of a range of audio filters for the DSP to condition and remove artifacts from a range of highly sensitive audio samples. Sadly complications arose, and we never continued the research further.

    Dave
     
  9. kostas

    Thread Starter New Member

    Jul 25, 2006
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    You know your stuff Dave!

    I am just starting to get the idea of how these things work, don't let me confuse you (that's highly unlikely, I know ;-) ).
    However, I am familiar with what you've mentioned and that's how FT is being used.

    I imagine that things have gotten better since the time you are referring to.
    Glitches from phase shifts, artifacts from temporal and spatial aliases, harmonic distortion etc due to signal processing have gone a long way in the last ten years.

    Let me get back to you in a little while because I'm in the process of moving out of my apartment.

    I have ordered the Art of Digital Audio by John Watkinson and downloaded The Scientist and Engineer's Guide to Digital Signal Processing by Steven W. Smith (that is free here: http://www.dspguide.com/) and I'm hoping to learn something.

    All the best
     
  10. Dave

    Retired Moderator

    Nov 17, 2003
    6,960
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    Great link, thanks. Its good to see people giving access to their work free for educational purposes. I will certainly have a look through the site when I get a chance.

    Dave
     
  11. mahantesh

    New Member

    Sep 18, 2007
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    (1-cosA+sinA)2=2(1+sinA)(1+cosA) prove
     
  12. sudhir bhatt

    New Member

    Jun 5, 2009
    1
    0
    Dear sir,

    Hope you all are fine and doing well.
    I want to find out the actual value of fourier transform of sin wt and the inverse fourier transform of the resultant value of the fourier transform of sin wt as well so,please help to do it because i want use this knowledge to understand the working of Vector Network Analyzer so,please give me a solution.

    Thanks
    Sudhir Bhatt
     
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