Turn Envelope Wave into one Sine Wave

1. Mar 19, 2013

1plus1is10

Hello everyone,
The sum of two sine waves that have close frequencies can produce an Envelope Wave:
http://en.wikipedia.org/wiki/Envelope_(waves)

What formula can I use to turn it into one wave (i.e. one frequency and amplitude)?

Example pic attached:
The blue "Envelope Wave" is actually 2 sine waves combined.
And the green sine wave is what I really want.

Finally, I am curious to know the proper keywords that would have allowed me to find this formula on Google, or are there not any?

Thank-you very much.

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2. Mar 19, 2013

Staff: Mentor

http://en.wikipedia.org/wiki/Beat_(acoustics [Broken])

When you add two sinusoids like that, you can express the resultant waveform as the multiplication of two other sinusoids -- one at the sum frequency (the green one in your plot) and one at the difference frequency (the beat frequency).

So to answer your question, the green waveform is at the sum of the two original frequencies, and the peak amplitude is the peak of the overall waveform.

Does that help?

Last edited by a moderator: May 6, 2017
3. Mar 20, 2013

1plus1is10

Yes that does, and thanks for the link too.
I was thinking it was really that simple (that's what I did), but I wanted to be sure.

As for Google, the keywords for me would have been "sum and difference frequencies".

Thanks again.