Circles and Sine Waves

[Billy_B]

Hi,
I’m a new user, so please be patient.
I can find pics and animations of a rotating circle generating a sine wave using y=r sin (wt).
So I’m wondering if a linearly expanding (poor terminology?) Archimedian spiral or logarithmic Fibonacci spiral would generate a sine wave that increases in period and amplitude on each cycle, or would they generate something different?
I’m not very mathematically literate, so if anyone knows of any good animations, those would be helpful too. I looked, but only found circles, no spirals.
Thanks in advance,
Bill

 

[Dr.Peterson]

Of course it would not literally be a sine wave, since a sine wave has a fixed amplitude. It would be some variation, along the lines of y = at sin(wt). The details would depend on the spiral you choose; your examples are different. (The Archimedean spiral could be described as "linearly expanding", but the logarithmic spiral is not.)

You can generate such an animation by using a tool like GeoGebra.

What do you want to use it for?