How to make a wave on a wave.

[Lightmeow]

I am trying to figure out how to make a function for this wave. I drew it terribly, but I think it works:

 

 

So, how would I make that? I tried but I can't do it. This is not for home work, I'm just curious. If you can't understand that image, basically you have a sine wave on a sine wave.

 

Sorry, I'm not good at explaining things.

 

 

[swansont]

What you describe is called amplitude modulation. A sine wave has the basic form of A sin(x), where the amplitude A is usually a constant. What you are doing is making A also be a function, the modulation, and the underlying wave is called the carrier . In your function A has a higher frequency and its own amplitude (the modulation depth) is small relative to the amplitude of the carrier.

[md65536]

You can get something similar just by adding sine waves with different wavelengths.

https://www.wolframalpha.com/input/?i=sin(x)+%2B+sin(x*30)%2F10

 

You can generate such a wave in sound editing program. In Audacity, generate a low frequency, high amplitude tone, and generate a higher frequency, lower amplitude tone. Then merge the tracks (select both, "mix and render").

 

 

Just by adding two waves, you get a wave on top of another wave. However you can see that the graph doesn't quite look like what you drew. It looks like your high-frequency wave might be partly rotated along the curvature of the low-frequency wave? Is that what you want?

Edited March 19, 2014 by md65536

[studiot]

 

What you describe is called amplitude modulation

 

 

I beg to differ.

 

The sketch by light meow is strictly bias modulation, not amplitude modulation, which produces a different curve.

 

It is what you would achieve if you set a function generator to the higher frequency in lightmeow's sketch and manipulated the output bias control in accord with the lower frequency waveform.

 

True amplitude modulation appears about the zero line as here

 

https://www.google.co.uk/search?tbm=isch&hl=en-GB&source=hp&biw=&bih=&q=amplitude+modulation&gbv=2&oq=amplitude+modulation&gs_l=img.1.0.0l10.812.4469.0.6969.20.14.0.6.6.1.344.2079.0j8j2j1.11.0....0...1ac.1.34.img..4.16.1921.8jkP2z__saQ

 

 

Mathematically if the main wave is

 

A * sinw₁t

 

Where A is a constant called the amplitude we get amplitude modulation if we multiply A by a second sin frequency thus

 

B * sinw₂ t* A * sinw₁t

 

What lightmeow has drawn is what happens if we add a second frequency sin wave to the original waveform.

 

A * sinw₁t + B * sinw₂t

Edited March 20, 2014 by studiot

[swansont]

Yes, I was mistaken. The example looks like addition of the waves rather than multiplication.