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Author Topic: Random Stuff Part III  (Read 242517 times)

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silverspawn

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Re: Random Stuff Part III
« Reply #2425 on: March 21, 2017, 05:19:42 pm »
0

Does sin(x) (with some parameters) describe water waves exactly, or does it just look kind of similar because they're both round and go up and down?

I can't find an answer to this simple question through google!

I'm afraid this question is far from simple. What sort of waves in particular are you interested in? I'm guessing surface waves? Like a pebble in a lake or more like wind generated waves? I can probably dig up an old textbook on the subject later, but I'm expecting the answer to be derived from the navier Stokes equations, which are a set of partial differential equations and only reducible under specific conditions.

I'm teaching a school lesson in two days and was wondering whether it'd be accurate to introduce the sine function by saying "hey this will be totally neat it'll model waves perfectly".

I think the thread sufficiently answered the question for me not to do it. If it only kinda looks like waves, then that's not impressive.
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Awaclus

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Re: Random Stuff Part III
« Reply #2426 on: March 21, 2017, 05:27:13 pm »
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Does sin(x) (with some parameters) describe water waves exactly, or does it just look kind of similar because they're both round and go up and down?

I can't find an answer to this simple question through google!

I'm afraid this question is far from simple. What sort of waves in particular are you interested in? I'm guessing surface waves? Like a pebble in a lake or more like wind generated waves? I can probably dig up an old textbook on the subject later, but I'm expecting the answer to be derived from the navier Stokes equations, which are a set of partial differential equations and only reducible under specific conditions.

I'm teaching a school lesson in two days and was wondering whether it'd be accurate to introduce the sine function by saying "hey this will be totally neat it'll model waves perfectly".

I think the thread sufficiently answered the question for me not to do it. If it only kinda looks like waves, then that's not impressive.

But it is a wave. A sine wave, to be precise.

I think that it's a lot more neat that you can create literally any waveform by stacking a bunch of sines on top of one another though. What's also neat about sine waves is that when you play two of them 4 octaves apart and distort them a lot, you get that dubstep sound.
« Last Edit: March 21, 2017, 05:30:13 pm by Awaclus »
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silverspawn

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Re: Random Stuff Part III
« Reply #2427 on: March 21, 2017, 05:51:05 pm »
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yeah but that's way too complicated. I also don't find it impressive.
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Re: Random Stuff Part III
« Reply #2428 on: March 22, 2017, 02:22:50 am »
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As long as the acceleration equals the negative displacement, you'll get a sine wave.  So if you manage to show that's how water works (barring other minor forces), it should be correct.  On a side note, my favorite introduction to the sine and cosine is to talk about periodic functions and trying to find a smooth periodic function, just like how ex is smooth growth.
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Re: Random Stuff Part III
« Reply #2429 on: March 22, 2017, 06:21:18 am »
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yeah but that's way too complicated. I also don't find it impressive.

I didn't totally believe my tech studies teacher in high school when he told me I could make any periodic signal just out of summing sine waves...it just didn't seem intuitive to me at the time, so I'd assumed there would have had to be a lot of caveats, and that it wouldn't work for anything particularly interesting. It wasn't till a few years later at university that I met the actual maths behind it and understood how neat it was :-)
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Re: Random Stuff Part III
« Reply #2430 on: March 22, 2017, 07:01:51 am »
+1

yeah but that's way too complicated. I also don't find it impressive.

I didn't totally believe my tech studies teacher in high school when he told me I could make any periodic signal just out of summing sine waves...it just didn't seem intuitive to me at the time, so I'd assumed there would have had to be a lot of caveats, and that it wouldn't work for anything particularly interesting. It wasn't till a few years later at university that I met the actual maths behind it and understood how neat it was :-)

I think it's a lot more intuitive if you think about actual physical sounds, because you can hear that most sounds have lower frequencies and higher frequencies in them, and that a sine wave only has one frequency. I was taught this in music listening class in high school, for the record.
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Re: Random Stuff Part III
« Reply #2431 on: March 22, 2017, 07:18:06 am »
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yeah but that's way too complicated. I also don't find it impressive.

I didn't totally believe my tech studies teacher in high school when he told me I could make any periodic signal just out of summing sine waves...it just didn't seem intuitive to me at the time, so I'd assumed there would have had to be a lot of caveats, and that it wouldn't work for anything particularly interesting. It wasn't till a few years later at university that I met the actual maths behind it and understood how neat it was :-)

I think it's a lot more intuitive if you think about actual physical sounds, because you can hear that most sounds have lower frequencies and higher frequencies in them, and that a sine wave only has one frequency. I was taught this in music listening class in high school, for the record.
Yes but the fact that it's any (well, edge-cases, edge-cases) periodic signal is surprising even when you consider this.  (Well, I found it surprising anyway).
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Awaclus

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Re: Random Stuff Part III
« Reply #2432 on: March 22, 2017, 07:35:10 am »
0

yeah but that's way too complicated. I also don't find it impressive.

I didn't totally believe my tech studies teacher in high school when he told me I could make any periodic signal just out of summing sine waves...it just didn't seem intuitive to me at the time, so I'd assumed there would have had to be a lot of caveats, and that it wouldn't work for anything particularly interesting. It wasn't till a few years later at university that I met the actual maths behind it and understood how neat it was :-)

I think it's a lot more intuitive if you think about actual physical sounds, because you can hear that most sounds have lower frequencies and higher frequencies in them, and that a sine wave only has one frequency. I was taught this in music listening class in high school, for the record.
Yes but the fact that it's any (well, edge-cases, edge-cases) periodic signal is surprising even when you consider this.  (Well, I found it surprising anyway).

Well, sounds can be any periodic signal.
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Re: Random Stuff Part III
« Reply #2433 on: March 22, 2017, 07:47:06 am »
0

yeah but that's way too complicated. I also don't find it impressive.

I didn't totally believe my tech studies teacher in high school when he told me I could make any periodic signal just out of summing sine waves...it just didn't seem intuitive to me at the time, so I'd assumed there would have had to be a lot of caveats, and that it wouldn't work for anything particularly interesting. It wasn't till a few years later at university that I met the actual maths behind it and understood how neat it was :-)

I think it's a lot more intuitive if you think about actual physical sounds, because you can hear that most sounds have lower frequencies and higher frequencies in them, and that a sine wave only has one frequency. I was taught this in music listening class in high school, for the record.
Yes but the fact that it's any (well, edge-cases, edge-cases) periodic signal is surprising even when you consider this.  (Well, I found it surprising anyway).

Well, sounds can be any periodic signal.
That can't be true.  And even if it were, we wouldn't be capable of hearing most of them, so it doesn't exactly help our intuition.
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Re: Random Stuff Part III
« Reply #2434 on: March 22, 2017, 08:54:41 am »
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yeah but that's way too complicated. I also don't find it impressive.

I didn't totally believe my tech studies teacher in high school when he told me I could make any periodic signal just out of summing sine waves...it just didn't seem intuitive to me at the time, so I'd assumed there would have had to be a lot of caveats, and that it wouldn't work for anything particularly interesting. It wasn't till a few years later at university that I met the actual maths behind it and understood how neat it was :-)

I think it's a lot more intuitive if you think about actual physical sounds, because you can hear that most sounds have lower frequencies and higher frequencies in them, and that a sine wave only has one frequency. I was taught this in music listening class in high school, for the record.
Yes but the fact that it's any (well, edge-cases, edge-cases) periodic signal is surprising even when you consider this.  (Well, I found it surprising anyway).

Well, sounds can be any periodic signal.
That can't be true.  And even if it were, we wouldn't be capable of hearing most of them, so it doesn't exactly help our intuition.

Any function you can get by summing an arbitrarily large series of sine waves can also be an actual physical sound. I actually have no idea why you would think otherwise in the first place. I would argue that since we aren't capable of hearing an infinitely high frequency, it actually helps our intuition more because you only need a finite series of sine waves to perfectly replicate any sound to the degree that anyone can tell, which makes it possible to demonstrate it physically.

This is how additive synthesis works, by the way.
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Re: Random Stuff Part III
« Reply #2435 on: March 22, 2017, 09:33:54 am »
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yeah but that's way too complicated. I also don't find it impressive.

I didn't totally believe my tech studies teacher in high school when he told me I could make any periodic signal just out of summing sine waves...it just didn't seem intuitive to me at the time, so I'd assumed there would have had to be a lot of caveats, and that it wouldn't work for anything particularly interesting. It wasn't till a few years later at university that I met the actual maths behind it and understood how neat it was :-)

I think it's a lot more intuitive if you think about actual physical sounds, because you can hear that most sounds have lower frequencies and higher frequencies in them, and that a sine wave only has one frequency. I was taught this in music listening class in high school, for the record.
Yes but the fact that it's any (well, edge-cases, edge-cases) periodic signal is surprising even when you consider this.  (Well, I found it surprising anyway).

Well, sounds can be any periodic signal.
That can't be true.  And even if it were, we wouldn't be capable of hearing most of them, so it doesn't exactly help our intuition.

Any function you can get by summing an arbitrarily large series of sine waves can also be an actual physical sound.
That's not the same thing as "any periodic signal".  Take any function that fails to be Lebesgue measurable, for instance.
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SpaceAnemone

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Re: Random Stuff Part III
« Reply #2436 on: March 22, 2017, 09:36:25 am »
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Any function you can get by summing an arbitrarily large series of sine waves can also be an actual physical sound. I actually have no idea why you would think otherwise in the first place. I would argue that since we aren't capable of hearing an infinitely high frequency, it actually helps our intuition more because you only need a finite series of sine waves to perfectly replicate any sound to the degree that anyone can tell, which makes it possible to demonstrate it physically.

This is how additive synthesis works, by the way.

So what you're really saying is that what we call sounds are band-pass-filtered versions of those "arbitrarily large series of sine waves", which I broadly agree with.

The thing is, with music, most people are so used to thinking about something that relates to frequency space (i.e. notes) that it's not at all surprising to hear that playing two notes at once adds up sounds. We also tend to name them (mostly) after the fundamental frequency, and most of us certainly can't listen to a square wave and comment intuitively about its various frequency components and their offsets or ratios, so we automatically simplify out some of the interesting detail. I just somehow find it more surprising and neat to be able to represent a sawtooth wave (or anything else that's defined based on its appearance in the spatial domain rather than the frequency domain) as a bunch of sines.
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Re: Random Stuff Part III
« Reply #2437 on: March 22, 2017, 09:54:35 am »
0

Any function you can get by summing an arbitrarily large series of sine waves can also be an actual physical sound. I actually have no idea why you would think otherwise in the first place. I would argue that since we aren't capable of hearing an infinitely high frequency, it actually helps our intuition more because you only need a finite series of sine waves to perfectly replicate any sound to the degree that anyone can tell, which makes it possible to demonstrate it physically.

This is how additive synthesis works, by the way.

So what you're really saying is that what we call sounds are band-pass-filtered versions of those "arbitrarily large series of sine waves", which I broadly agree with.

The thing is, with music, most people are so used to thinking about something that relates to frequency space (i.e. notes) that it's not at all surprising to hear that playing two notes at once adds up sounds. We also tend to name them (mostly) after the fundamental frequency, and most of us certainly can't listen to a square wave and comment intuitively about its various frequency components and their offsets or ratios, so we automatically simplify out some of the interesting detail. I just somehow find it more surprising and neat to be able to represent a sawtooth wave (or anything else that's defined based on its appearance in the spatial domain rather than the frequency domain) as a bunch of sines.

It's even more amazing than that.  You can take basically any function (say on a compact set), that appears to have no kind of periodic behavior, and (as long as it is L^2, I guess), and still represent it as a series of periodic functions. 

Though I suppose that's the same idea as considering a periodic extension of such a function and then taking the Fourier series of that.  However, it can be a a very ugly function (not even continuous), as long as it's square integrable. 
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Awaclus

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Re: Random Stuff Part III
« Reply #2438 on: March 22, 2017, 10:27:40 am »
0

most of us certainly can't listen to a square wave and comment intuitively about its various frequency components and their offsets or ratios

I don't think that's the case, though. If you listen to a song with cell phone speakers, most people can tell that it doesn't have as much bass in it as it would have when played through a better sound system. And that's exactly commenting intuitively about its various frequency components.
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Re: Random Stuff Part III
« Reply #2439 on: March 22, 2017, 10:37:37 am »
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I would assume you can't have any periodic gnal as a sound (even if our ears could somehow process all frequencies), because the physical properties of air limit the frequencies that can move through it. But to be fair, I've always been terrible at fluid mechanics.
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Re: Random Stuff Part III
« Reply #2440 on: March 22, 2017, 01:36:12 pm »
+1

Still don't find it impressive. You can describe a function by an infinite set of points; why shouldn't you be able to describe it through an infinite set of functions? That's "way more" for the same thing.

I'll just say it has infinite passes through the X axis.
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Awaclus

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Re: Random Stuff Part III
« Reply #2441 on: March 22, 2017, 02:01:16 pm »
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Still don't find it impressive. You can describe a function by an infinite set of points; why shouldn't you be able to describe it through an infinite set of functions? That's "way more" for the same thing.

I'll just say it has infinite passes through the X axis.

Surely, additive synthesis is more impressive than the fact that a waveform has infinite passes through the X axis.
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Re: Random Stuff Part III
« Reply #2442 on: March 22, 2017, 02:05:11 pm »
+1

additive synthesis are just two foreign terms for a bunch of 16 year olds who aren't particularly interested in maths.
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Awaclus

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Re: Random Stuff Part III
« Reply #2443 on: March 22, 2017, 03:24:28 pm »
0

additive synthesis are just two foreign terms for a bunch of 16 year olds who aren't particularly interested in maths.

I'm pretty sure at least some of them listen to some kind of music that utilizes additive synths, though.
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Re: Random Stuff Part III
« Reply #2444 on: March 23, 2017, 08:06:24 am »
+3

I'm a bit annoyed at my director/choreographer. I'm involved with a dance number in the show I'm in. It's Temptations-like where we are in a line. We do a 270, and I can only see one other dancer in front of me. I notice that she goes right into the rocking motion after she turns, and I felt as if I have to wait half a measure.

I asked the director about this because I want to make sure we're all on the same page on when we're supposed to rock. After all, dance numbers in musicals are supposed to look uniform (except where they're not). The director said that it's weird because I turn too soon. I didn't notice because I was too busy turning 270 degree. I learn this on the final rehearsal night. Was she just going to let me do the entire show out of sync with the other dancers? Does she not care how that looks to the audience? I know I care. I don't want to be that lug who can't coordinate with the others.

I'm guessing it's because she was afraid of causing offense. I've heard of diva performers, but I can't imagine that I come off as one. I am fully aware that choreography is not my strong suit. I need guidance.
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Re: Random Stuff Part III
« Reply #2445 on: March 23, 2017, 08:19:24 am »
0

I'm a bit annoyed at my director/choreographer. I'm involved with a dance number in the show I'm in. It's Temptations-like where we are in a line. We do a 270, and I can only see one other dancer in front of me. I notice that she goes right into the rocking motion after she turns, and I felt as if I have to wait half a measure.

I asked the director about this because I want to make sure we're all on the same page on when we're supposed to rock. After all, dance numbers in musicals are supposed to look uniform (except where they're not). The director said that it's weird because I turn too soon. I didn't notice because I was too busy turning 270 degree. I learn this on the final rehearsal night. Was she just going to let me do the entire show out of sync with the other dancers? Does she not care how that looks to the audience? I know I care. I don't want to be that lug who can't coordinate with the others.

I'm guessing it's because she was afraid of causing offense. I've heard of diva performers, but I can't imagine that I come off as one. I am fully aware that choreography is not my strong suit. I need guidance.
Man, I feel you.  I so sympathise with this.  I really struggle with the dance aspect of shows, and I have to start every one just saying to the choreographer "Look, I'm gonna need lots of help here, please don't be afraid to tell me what to do!".
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Re: Random Stuff Part III
« Reply #2446 on: March 23, 2017, 08:56:10 am »
0

Actually, I do remember a diva moment in an earlier show. This actress was really abrasive and talked back to the music director. At home, I rehearsed with the practice music we set up, which was recorded with the correct counts. At some point I realized that we started slipping into a trend where it took us two measures to sing one particular measure.

When I realized that things were sounding different from my practice music, I asked the music director about it. She said that yeah we were way off, but it was easier to make the orchestra vamp an additional measure to give us time. The abrasive actress had successfully cowed the director into not fighting it. The change wouldn't be so bad except that it'd be nice to have a formal announcement of the change.

It's gotten to the point that I don't even want to see show with this actress in it. Her backstage shenanigans were horrid, and I don't know how she keeps getting cast.
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Kirian

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Re: Random Stuff Part III
« Reply #2447 on: March 23, 2017, 11:51:59 am »
+4

Just explain to the choreographer that she can describe the dance as the summation of an infinite number of sine waves.
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Witherweaver

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Re: Random Stuff Part III
« Reply #2448 on: March 23, 2017, 11:54:10 am »
+1

Obligatory:

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Kirian

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Re: Random Stuff Part III
« Reply #2449 on: March 23, 2017, 11:57:27 am »
+2

Also, tangentially related to the sound discussion:

The cochlea is a mechanical Fourier transform calculator.
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