What is the form of an equation that describes a sine wave “wrapped around” a circle of appropriate radius (by appropriate, I am assuming that only certain combinations of radii for the circle and wavelengths for the sine wave will ‘work’ to allow an integral number of wavelengths to fit around).
I won’t understand the specifics of the equation, I’m sure, but I am interested to know the form that such an equation might take, i.e. what it looks like algebraically.
Thank you for humouring me.
Wouldn’t it just be r = a + b sin(n theta)?
What?
Please to explain one’s self honorable sir.
A sinewave is a circlular wave spread out over time.
I think the easiest way would be to use polar coordinates:
r = a + sin(b*theta)
a being the radius of the “guide circle”, b determining the frequency of the sine wave.
I’m sure there are others, depending on how you interpret “sine wave wrapped around a circle”.
I believe he’s talking about something like this.
Thanks for your speedy responses.
I had thought that the equation would be more complicated and wonder if I have expressed myself properly.
Imagine a sine wave, say of one arbitrary wave length. Now wrap it around a circle. Is that what’s described by r=a+sin(b*theta)?
Simulpost. Sorry.
Yes! That’s what I meant, Philbuck
Yep, r=a + b sin(n theta) (adopting scr4’s formula to include altering the amplitude) gives the picture in Philbuck’s link.
By the way, specifically, Philbuck’s link is r = 1 + .1 sin(8 theta). Also, r = 1 + sin(theta), for example, is called a cardioid, because it kind of looks like an upside down heart.
This sort of thing is seen in books about the historical development of atomic physics. It was believed then that electrons literally orbited the nucleus, and that the electrons travelled in a wavy path, with an integral number of wavelengths in an orbit, exacly like Philbuck’s link. We now know that electrons don’t actually behave this way.
