Explanation of two-tone frequencies that is combined into one graph

I am in the process of doing a project that deals with Voix Celeste and investigating how close two tone frequencies should be to each other before they no longer sound like two tones, but as a tone with vibrato.

I have created two set of two-tones as well as combination of them each. What I would like is an explanation of the combination graph, ie the bottom graph in both figures. The first pair consists of two dense frequencies of 440 Hz and 400 Hz. Where the second pair consists of a 440 Hz as well as 1500 Hz.

You can see in the graph below, from the top two graphs in the figure below, that there is no clear difference, but what can you say about the combination graph, ie the lower graph in the figure?

(The graph below is the 400 Hz and 440 Hz, and then the last one is a combined graf of them both.)

In the graph below, you can see from the top two graphs in the figure below that there is a clear difference, as both frequencies are far apart. But what can be said about the combination graph, ie the bottom graph in the figure?

(The graph below is the 440 Hz and 1500 Hz, and then the last one is a combined graf of them both.)

How should I describe a combination graph of two frequencies? What should I look for?

Answer 1

[Star Strider]

Referring from your Comment in another thread, I am not exactly certain how to approach this, or what sort of solution you want.

A mathematical approach is in the Wikipedia article section on Product-to-sum and sum-to-product identities .

[Anonym]

Sorry, didn't know how to start it :-) It's probably me who's not been accurate, did not mean a mathematical analysis, but a more visual explanation of the combined graph.

It's because, as you can see from the last graph in the first figure that the waves follow well, but what else can I tell about it?

(The image is attached below: Combined graph of 400 Hz and 440 Hz.)

And the graph below, it shows that there is no connection between the two waves, which means that the two waves are far apart, what else could I add?

(The image is attached below: Combined graph of 440 Hz and 1500 Hz.)

[Star Strider]

The differences are due to the differences in the signal frequencies, as well as how you combine them. The result of both is a ‘beat’ signal, that shares tthe characteristics of the frequencies that created it. The mathematical explanation is what I linked to. There is likely no better way to describe it.

[Anonym]

Alright, thanks for your help and time :)

[Star Strider]

As always, my pleasure!