I need a Cycloid

[HughBanton]

Trying to devise something for which I believe I need a cycloid waveform. One of these :

https://upload.wikimedia.org/wikipedia/ ... loid_f.gif

Anyone got a clue about how to generate a thing like that?

H

[adamszabo]

you can get a parabola wave which is similar, by multiplying the output of a saw with itself

[HughBanton]

Oh yes, so you do, thanks.

Not so strangely .. I had the tools to test this right in front of me, trying to find the answer myself! (But so far failing miserably).

And therefore, you get the whole shape if you multiply a triangle by itself. Bingo.

Hugh

[HughBanton]

Like so : (Since I just know that everyone's just desperate for a Cycloid too!)

Code: Select all

streamin inc; streamout out;
float count, temp;
//
count += inc;
count -= count & (count>=1); // reset count
temp = count &(count<0.5) + (1-count) & (count>0.5); // to triangle
out = -2*(temp*temp) + 0.5; // to Cycloid (-ish)


So, what am I going to do with it ....

H

[R&R]

So, what am I going to do with it ....

DC-adjust for use with rotary speaker... and open a portal unleashing doom-guy?

Would be interesting to see the spectral content of an actual cycloid waveform but inverted (alternating?... I don't know what it's called in the digital world... normalized? eh... sinusoidal... but, cycloid ) Damnit I painted myself into a corner...

[martinvicanek]

(Beware! Nerdy stuff ahead!)

A squared saw or triangle (same thing basically) is at best a poor man's cycloid. The cusp shape is not right. Atached is the real deal!
I am not sure if it is much of a practical value because the "right" cusp shape causes some nasty aliasing. Anyway, here it is, have fun!

[R&R]

[HughBanton]

Fabulous Martin. Somehow we all just knew you'd be the man with the true answer

Practical? Never stopped me before ...

H

[HughBanton]

So I should tell you about what my fevered brain has been thinking about .. (apologies for a complete tangent here)

When a real wind instrument is physically blown (that'll include organ pipes, innit..) there's inevitably going to be a 'DC' air-stream, which in the human case, I learn, is around 12m/S. Around 4% of the speed of sound.

So, does it follow then that the oscillating wave emitted at the end of the tube is actually travelling onwards 4% faster than the surrounding air? (And note, the harder the blowing, the greater the velocity differential).

So what happen next, as the wave travels outwards? I'm assuming it somehow slows down to a mean velocity before it reaches our ears.

So next question is, what happens when sound is forced to decelerate .. well we all know the answer to that one!

Is this real / worth investigating, or a total fallacy?

H

(I'll maybe come back to the cycloid bit anon )

[R&R]

Isn't the speed of sound always the speed of sound? I'm confused... But... that's not a rare occurrence
In other words how fast the pressure differentials (within the audible freq range) can ever propagate through air medium? (at normal altitude / air composition)

Anyone correct me if i'm off at any point...

Low frequencies are pretty much omni directional... and the higher you go, the more dissipation (high freq = low kinetic energy). Since high frequencies are also very directional they are also subject to diffusion. Both high and low frequencies reflect, but they act very differently in that regard. High frequencies reflect almost at angle the higher you go, and low freq acts like a gas... almost accumulates at pressure zones or "nodes". Nodes of course being present at all frequencies but low frequencies often being discussed in acoustics.

I would imagine the airstream itself... causing the oscillations at the pipe opening (or where the standing waves meets the air outside the pipe? is that how it works? )... drops of immediately when leaving the pipe? The only moving air is the air traveling between low and hi pressure zones of the wavefront itself?

Why do I imagine Spogg is a guru at this stuff...