The Science Of The Waveform

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The Science Of The Waveform

Postby Brotuulaan » January 19th, 2016, 2:24 pm

So I'm the kind of guy who believes that you can do a thing best when you understand the why behind the what. Sometimes I take that to the extreme, such as in this case.

As such, this is a question that will require some more experienced peeps to answer, but the Newb Stuff is the best category I could find. Maybe a technical section would be good for this sort of thing?

Anyway, here's my question:

So I was just reading up on phase cancellation and such, and I've been thinking a lot over the past six months or so about the sciences of waveforms and audio reproduction via electricity, magnets, and speaker cones.

This Sound On Sound article by Mike Senior that I was reading has a graph about 1/4 of the way down that shows how a complex waveform is made out of multiple sine waves (individual frequencies). I've never come across a definition of the process of creating a complex waveform, so let's see if I have this right.

1) Each frequency (sine wave) is summed at a given point (be that at a guitar pickup, a mic diaphragm, etc).

2) As they are summed, the total positive/negative values are added together, thus providing a contour and an amplitude amalgamation of the collection of frequencies.

3) That waveform is reproduced by a speaker by direct translation to physical movement forward and backward.

4) Our ear hears that reproduction and translates the complex waveform as a complex waveform as if the individual frequencies had still been separate because the ear "sums" frequencies in the same fashion, based on incoming positive energy and negative energy (i.e. sine waves).

To you scientific audio people, does that sound like an adequate (if simplistic) explanation of the complex waveform and how we use it?
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Re: The Science Of The Waveform

Postby Brotuulaan » January 19th, 2016, 2:25 pm

And of course, the complex waveform's summing would be done at the sample rate of the equipment used.
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Re: The Science Of The Waveform

Postby Brotuulaan » January 19th, 2016, 2:30 pm

Digitally speaking.
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Re: The Science Of The Waveform

Postby Farview » January 19th, 2016, 3:36 pm

A complex waveform can be described as a bunch of sine waves summed together, but that concept is only useful in certain circumstances, when doing certain calculations. It isn't really a practical way of looking at it.

The practical way of looking at it is
1. Something vibrates
2. that vibration vibrates the diaphragm on a mic, which turns that vibration into an electrical signal that mimics the movement of the diaphragm.
3. That signal is amplified and sent to a speaker, which mimics the original waveform.
4. the speakers movements vibrate the air in the same way the source vibrated the air
5. our ear pick up that vibration and we sense it as sound.

Sample rate has nothing to do with it. Don't make it harder than it needs to be.
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Re: The Science Of The Waveform

Postby Farview » January 19th, 2016, 3:45 pm

The only way that the multiple sine waves thing will help you with the phase question is this: The comb filtering you hear from timing (phase) issues is caused by some of the sine waves being cancelled out, while others aren't. If you think of a complex waveform as multiple sine waves, a delay of a certain time will line up some sine waves 180 degrees out of phase and line up others in phase.

But again, it's really only useful to do that if you are trying to do the math to figure out what frequency will be cancelled at what delay time. That's also not the only way to look at it.
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Re: The Science Of The Waveform

Postby Brotuulaan » January 20th, 2016, 11:05 am

Thanks for your response! My question was actually kind of a bubble inside the phase cancellation subject. I wasn't specifically looking to find how one affected the other, but rather just the conceptual side of the waveform, aside from the comb filtering issue.

And thank you for the description, but I already know the generic picture of how a sound is ultimately transferred via diaphragm from source to speaker reproduction. My question is driven by curiosity rather than practicality, so I'm probably asking specifically for the impractical. :P
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Re: The Science Of The Waveform

Postby Farview » January 20th, 2016, 4:55 pm

Brotuulaan wrote:1) Each frequency (sine wave) is summed at a given point (be that at a guitar pickup, a mic diaphragm, etc).
Not really. At no time is a complex waveform individual sine waves that get summed together.

Brotuulaan wrote:2) As they are summed, the total positive/negative values are added together, thus providing a contour and an amplitude amalgamation of the collection of frequencies.
See number 1

Brotuulaan wrote:3) That waveform is reproduced by a speaker by direct translation to physical movement forward and backward.
Yes

Brotuulaan wrote:4) Our ear hears that reproduction and translates the complex waveform as a complex waveform as if the individual frequencies had still been separate because the ear "sums" frequencies in the same fashion, based on incoming positive energy and negative energy (i.e. sine waves).
This doesn't make sense. The ear 'hears' the complex waveform as a complex waveform. It does not separate it into individual sine waves.

Brotuulaan wrote:To you scientific audio people, does that sound like an adequate (if simplistic) explanation of the complex waveform and how we use it?
Nope.

You can treat complex waveforms as a series of sine waves for the purpose of doing math related to sound. But at no time is a complex wave actually a series of sinewaves. (except during synthesis...like in a synthesizer)
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Re: The Science Of The Waveform

Postby Brotuulaan » January 21st, 2016, 11:01 am

After our conversations here and in the other thread, this makes a lot more sense to me now. Thanks!
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