Digital audio fundamental question

[asliarun]

yes, agree with the part that the analog wave can't change. But let's assume the four point data given to one is not on peaks but at different locations. You would still have difficulty drawing it.

True, but the key thing is that the samples (for digital recordings) are taken rapidly enough that they will always "sample" or taste any change or transition in the analog wave.

And whether we like it or not, the lower frequencies are getting sampled at higher rate. A 20Hz frequency is getting sampled at 2205. That's how much data is there. Now, I am not a DAC designer, so can't say if the conversion software throws out all that data and uses only 4 samples out of it. But that doesn't seem likely.

But extra information doesn't matter as to the quality of the reproduction, right? Case in point - CD and WAV files are constant sized based on length of recording. They are not any smaller because they only record bass heavy music for example.

Not sure how this matters to the discussions at hand. I am not good at digressing into other things, but seems like this is going opposite to what you said above. First you said wave can't change, meaning its continuous. Now you say its discrete and non-continuous. If its not continuous, then we should have more discrete data, no?

No, I always maintained that sound, our perception of sound, and the reproduction of sound (instruments, analog players, or digital players) are all discrete phenomena. They are a sequence of transitions - transitions of tone and volume. Nothing is stored or played back in parallel. The transitions happen so rapidly that we perceive or imagine that multiple sounds are occurring in parallel.

even if there is one groove, the groove is made with various depths. Are you trying to say that its not possible to put all the frequency data together in one groove?

Yes, but sound is only generated when the stylus transitions sequentially from one groove depth to another. Again, this happens very fast so we don't perceive it this way.

Nice write up, but I don't understand what this has to do with discussion at hand. Sound existed before digital, before analog or any electronics was invented. And eardrum may vibrate once at any given point, but it can vibrate many times over, almost 15000 times in a sec. Brain just pieces that information together for us. Same way, a speaker can produce so many frequencies, even though its vibrating once at any given time. But we hear it all together. Our eyes do the same thing. We know all this - but what does it have to do with sampling rate in digital?

I was trying to illustrate the fact that absolutely nothing in nature is truly continuous. And this is the false belief that the analog purists continue to hold. That the signal is somehow continuous and thus any discrete sampling causes loss of information. In reality, everything, sound light energy, everything, occurs in discrete pulses.

Sorry, I didn't mean to digress or to confuse. I was trying to address the underlying false notion - which is why I have said the same thing in many different ways in this thread. Now I am sure people are getting pissed off at me

 

[Sawyer]

Lets say, if I have a thin steel rod, upright and joined at bottom. If I push on the top very slightly, how the top of bar move during vibration?

I am using steel bar here for better visualization, but the vibration will be very same in the air molecules too.

That is a pretty close description of a tuning fork. The rod will move back and forth, i.e., vibrate. And will cause back and forth movement of the air molecules next to it. Vibrations. Which each molecule will pass on to the adjacent ones.

 

[Sawyer]

I have said the same thing in many different ways in this thread. Now I am sure people are getting pissed off at me

Not to worry. One way of saying the same thing may not work for everyone.

 

[manoj.p]

True, but the key thing is that the samples (for digital recordings) are taken rapidly enough that they will always "sample" or taste any change or transition in the analog wave.

Yes, the samples are taken at constant time. But that may be rapid for some frequencies and not so rapid for other frequencies. Meaning at 20 Hz, it may seem rapid, but not so much at 20Khz. It's relative. For example, we see elephants as slow compared to us. But a fly will see humans as quite slow. It's the same time unit, but perceived differently.

But extra information doesn't matter as to the quality of the reproduction, right? Case in point - CD and WAV files are constant sized based on length of recording. They are not any smaller because they only record bass heavy music for example.

That is because the way WAV stores data. They will take full samples and store the 0's and 1's for all the frequencies, even if there is no input. There is no compression involved for wav and cd data. FLAC on the other hand, will take all this data and junk all the empty space. That's why FLAC will have smaller size for the same lossless data.

No, I always maintained that sound, our perception of sound, and the reproduction of sound (instruments, analog players, or digital players) are all discrete phenomena. They are a sequence of transitions - transitions of tone and volume. Nothing is stored or played back in parallel. The transitions happen so rapidly that we perceive or imagine that multiple sounds are occurring in parallel.

If you are talking about one instrument, then yes its sequential. What if multiple instruments are playing at the same time. Won't the recording device be able to record these simultaneously? Offcourse, when that happens, the louder sounds will mask the other sounds to some extent, but it will be recorded parallel, not consequential. Simply because the recording mic does not know that sounds initiated from different sources. All it will see what vibrations reached it at the same time.

Our stereo sound is based on this belief. Two speakers, spaced apart at equidistant, if played a mono signal, we hear the center image. This is not happening only due to 2 ears. If we place a mic at exactly center position, it will record a single mono signal, combined from these two speakers. And those were playing it parallel - not consequential. Hope this clears.

Yes, but sound is only generated when the stylus transitions sequentially from one groove depth to another. Again, this happens very fast so we don't perceive it this way.




I was trying to illustrate the fact that absolutely nothing in nature is truly continuous. And this is the false belief that the analog purists continue to hold. That the signal is somehow continuous and thus any discrete sampling causes loss of information. In reality, everything, sound light energy, everything, occurs in discrete pulses.

Sorry, I didn't mean to digress or to confuse. I was trying to address the underlying false notion - which is why I have said the same thing in many different ways in this thread. Now I am sure people are getting pissed off at me

Arun, I guess I am trying to say the same thing but may be differently.

 

[Thad E Ginathom]

I would disagree with this because a sine wave is supposed "perfect" or exact in frequency and amplitude over time. No non-electronic musical instrument is such. A bow across a violin is producing varying frequencies from the complex string and bow interaction along with harmonic resonances from the body of the violin, etc that would not deconstruct to the "perfect" sine wave for perhaps not even more than one cycle of the wave.

You missed my point: "lots of."

And please bear with me and more questions. how does a vibration look like? Lets say, if I have a thin steel rod, upright and joined at bottom. If I push on the top very slightly, how the top of bar move during vibration?

I am using steel bar here for better visualization, but the vibration will be very same in the air molecules too.

How about if we take a piece of rope? When you flick a piece of rope the impulses passes along its free end as a definite wave. If we look at vibrations in strings, we see waves.

What does sound look like in air? i think this has been answered, or linked to, in a picture of alternately compressed and spaced out molecules. Perhaps that can be defined as a wave.

But its also a fact that more samples give better wave form.

It is not, and never was a fact! There is a minimum number of points required to perfectly reconstruct the wave, and more will not make it better.

I know you are very attached to this idea. To begin with, put away ideas about pencils, and look again at my spring strip analogy: this device will allow the curve in your analogy to be drawn perfectly every time.

Next, all I can suggest is that you go and read some of the stuff I recommended, because there is nothing like the horse's mouth, and I can't even begin to explain stuff in the way that Monty does (Xiph gave us FLAC, OGG, etc: those people know digital sound!) and that J_J, a digital sound pioneer, does. Have you watched the Xiph videos? Please do. Really, that was perhaps the beginning of understanding for me. I know a 1khz sine wave is not music, but actually seeing 1khz sine wave in ---> 1Khz sine wave out, perfect curves, no steps is a mighty powerful demonstration.

You might almost say that it changed my life hyeah:

 

[manoj.p]

That is a pretty close description of a tuning fork. The rod will move back and forth, i.e., vibrate. And will cause back and forth movement of the air molecules next to it. Vibrations. Which each molecule will pass on to the adjacent ones.

Yes, exactly. The rod will move forward, come to original position, go back in opposite direction and then come back to original. The opposite direction will be little different due to friction and stiffness, but it will be there. That's a wave motion. This was all I was trying to say.

 

[manoj.p]

How about if we take a piece of rope? When you flick a piece of rope the impulses passes along its free end as a definite wave. If we look at vibrations in strings, we see waves.

What does sound look like in air? i think this has been answered, or linked to, in a picture of alternately compressed and spaced out molecules. Perhaps that can be defined as a wave.

Thad, that's what I was trying to say all along. But I was told sound is not a wave but vibration. We have been going in circles about it.

It is not, and never was a fact! There is a minimum number of points required to perfectly reconstruct the wave, and more will not make it better.

I know you are very attached to this idea. To begin with, put away ideas about pencils, and look again at my spring strip analogy: this device will allow the curve in your analogy to be drawn perfectly every time.

Next, all I can suggest is that you go and read some of the stuff I recommended, because there is nothing like the horse's mouth, and I can't even begin to explain stuff in the way that Monty does (Xiph gave us FLAC, OGG, etc: those people know digital sound!) and that J_J, a digital sound pioneer, does. Have you watched the Xiph videos? Please do. Really, that was perhaps the beginning of understanding for me. I know a 1khz sine wave is not music, but actually seeing 1khz sine wave in ---> 1Khz sine wave out, perfect curves, no steps is a mighty powerful demonstration.

You might almost say that it changed my life hyeah:

Well, I will go and read those. But one question for quickly satiating my thrust. What that min no is to perfectly draw a wave? I have struggled to find an answer but looks like google has missed this one (or I have missed this one) And what if the original wave is not a pure sine wave?

 

[rsud]

No they don't.

That is the number-one biggest misconception of digital music. This has nothing to do with ears, belief, faith, or what format we choose to buy our music in, it is simple science. Simple science that, as I said, I for one only became aware of amazingly recently in my long[ish] life.

More samples do not give a better, or more accurate, waveform. The do give the possibility of a bigger frequency range, and whether that is better or not is another issue entirely.

Please consult the science on this: it is there all over the web, and not too hard to find, but we have to be able to accept the counter-intuitive on this. "common" sense does not help: more samples does not leave less out!

Will try to catch up with the rest of the thread later, have to go out now

There seems to be an overall hypnosis in these discussions that the electronics create a perfect representation of the theory. Electronics are nowhere near perfect and that is where the problem still lies with digital production when compared to good analogue (vinyl and turntable) based reproduction.

So in practice (ie, building audio devices using electronics) higher sampling rates will give a better construction of the original audio wave because it allows for getting past the limits of the electronics.

 

[Thad E Ginathom]

Thad, that's what I was trying to say all along. But I was told sound is not a wave but vibration. We have been going in circles about it.

I don't think this is easy stuff. Some of it may be school-physics, and some of it is ultimate-geek level. Ultimate-genius, in those who developed it!

I can live with going around in a few circles, and I absolutely have to live without picking up more than a morsel on each run I take at this.

I can sit on a beach and watch the waves. I can even know a little bit more about them than some of my fellow enjoyers of the sea. I know that, for instance, until it reaches the beach, the water in a wave does not move, it is energy moving through the water that creates the wave. I know that, like the sine-wave diagram, there is as much of the wave under the water as we see on top. I know that it is "tripping up" the lower part of the wave that makes it break. I know these things because I love boats, and, even the illiterate fisherman a few metres away from me knows these things too, because his life may depend on it.

I don't know how exactly these waves in water correspond to the way that sound moves in air (whoa! sound can move in water too ). I should have listened more ins school.

What that min no is to perfectly draw a wave?

I'm sur eI've read this, 'though I'm not so sure I understood it, and sorry, I can't remember. I bet Arun can! It should be covered in any source that tries to explain the basics. If I find one I'll post

There seems to be an overall hypnosis in these discussions that the electronics create a perfect representation of the theory. Electronics are nowhere near perfect and that is where the problem still lies with digital production when compared to good analogue (vinyl and turntable) based reproduction.

No such hypothesis exists here, because we are discussing the theory, not the practice. We are, for once, dealing with the basics, rwther than throwing numbers at each other

but

So in practice (ie, building audio devices using electronics) higher sampling rates will give a better construction of the original audio wave because it allows for getting past the limits of the electronics.

No. It does not follow. It is simply not a logical extension of your first statement that the electronics are not perfect. In fact, the opposite might be true!

 

[asliarun]

Another analogy of the wave is ripples in a pond if you throw a stone, or if you take a quick dubki in our birthday suit.

Now we can see the wave propogate across the pond.

Now imagine if there 20,000 tuning forks that were so sensitive that ripples in the pond would make them vibrate. These tuning forks were also individually tuned to different frequencies (this is also called the resonant frequency) - ranging from 20Hz to 20KHz.

So now you have a full blown 20,000 piece orchestra waiting for someone to be the conductor! How awesome is that?! Now if I slap the pond quite rapidly, say 500 times a second, these successive waves would hit our tuning fork orchestra 500 times a second. Or instead of using our hands, if we pluck a guitar string and immerse the string in the pond while it was still vibrating (at say, 5000 times a second), we can reasonably expect that tiny little water waves would reach our sensitive tuning fork orchestra and would hit them 5000 times a second.

Now the tuning forks that have a fundamental frequency of 500Hz or 5000Hz (depending on our hand or guitar example) would start vibrating like crazy - as if the conductor (us!) has individually singled them out and given them the signal to start performing. All other tuning forks couldn't be bothered less because they are literally "tuned out".

Now if we start beating our pond with different frequencies and beating the water with different levels of intensity, we are in effect truly conducting our own little symphony.

So the thing to note here is - we can model the water way any number of waves - sine wave and what not. But how does it matter? What matters the most is how the wave passes energy to the tuning fork (and gets it ringing).

As you can appreciate, this is done in a sequential and discrete way - not in a continuous way.

The most fascinating thing here is that this is not even an analogy! Our ears actually work in this exact same way - we literally have 20,000 tuning forks inside our little ears, and when our tuning fork orchestra starts playing (each at its fundamental or resonant frequency), it excites the cells underneath which sends signals to our brains. The louder the sound, the more the tuning fork vibrates, and more cells get excited.

And on a side note, because the cells are finite in number for each tuning fork, even the way our brain detects volume (by adding up the cells that get excited) are a discrete number (not continuous or infinite).

An utterly fascinating article explaining this.

 

[manoj.p]

Another analogy of the wave is ripples in a pond if you throw a stone, or if you take a quick dubki in our birthday suit.

Now we can see the wave propogate across the pond.

Now imagine if there 20,000 tuning forks that were so sensitive that ripples in the pond would make them vibrate. These tuning forks were also individually tuned to different frequencies (this is also called the resonant frequency) - ranging from 20Hz to 20KHz.

So now you have a full blown 20,000 piece orchestra waiting for someone to be the conductor! How awesome is that?! Now if I slap the pond quite rapidly, say 500 times a second, these successive waves would hit our tuning fork orchestra 500 times a second. Or instead of using our hands, if we pluck a guitar string and immerse the string in the pond while it was still vibrating (at say, 5000 times a second), we can reasonably expect that tiny little water waves would reach our sensitive tuning fork orchestra and would hit them 5000 times a second.

Now the tuning forks that have a fundamental frequency of 500Hz or 5000Hz (depending on our hand or guitar example) would start vibrating like crazy - as if the conductor (us!) has individually singled them out and given them the signal to start performing. All other tuning forks couldn't be bothered less because they are literally "tuned out".

Now if we start beating our pond with different frequencies and beating the water with different levels of intensity, we are in effect truly conducting our own little symphony.

So the thing to note here is - we can model the water way any number of waves - sine wave and what not. But how does it matter? What matters the most is how the wave passes energy to the tuning fork (and gets it ringing).

As you can appreciate, this is done in a sequential and discrete way - not in a continuous way.

The most fascinating thing here is that this is not even an analogy! Our ears actually work in this exact same way - we literally have 20,000 tuning forks inside our little ears, and when our tuning fork orchestra starts playing (each at its fundamental or resonant frequency), it excites the cells underneath which sends signals to our brains. The louder the sound, the more the tuning fork vibrates, and more cells get excited.

And on a side note, because the cells are finite in number for each tuning fork, even the way our brain detects volume (by adding up the cells that get excited) are a discrete number (not continuous or infinite).

An utterly fascinating article explaining this.

I am not sure how you come to the conclusion I made in bold. The sound creation (throwing a stone in water) may be a discrete event. But the wave generated from each of that stone is continuous. It's not like wave stops at certain time and then keeps going. Same thing is with sound wave - it moves continuously, not like stop-go-stop-go. At no point of time the wave stops in between till it reaches the end.

 

[asliarun]

I am not sure how you come to the conclusion I made in bold. The sound creation (throwing a stone in water) may be a discrete event. But the wave generated from each of that stone is continuous. It's not like wave stops at certain time and then keeps going. Same thing is with sound wave - it moves continuously, not like stop-go-stop-go. At no point of time the wave stops in between till it reaches the end.

Manoj, my point was that forget about the wave. At the end of the day, you are hearing a single tone because a single basilar membrane hair in your ear (page 5 in the article I linked earlier) starts vibrating. This is similar to a guitar string vibrating. How does it matter if you used a finger or a guitar pick to pluck a string, or if a really strong gust of wind ended up causing the guitar string to vibrate?

All that matters to our ears (to hear a tone) is:
1. A particular basilar membrane hair started vibrating (which makes our ear hear a particular tone)
2. How strongly it vibrated (which indicates how much energy was used to vibrate the hair) - which indicates the loudness of the tone we hear

Two things to note here:
a. The hair vibrated because of a single discrete action (nothing continuous)
b. The hair stops vibrating shortly afterwards. If you want to continue hearing the tone, the hair has to be periodically re-vibrated. Again, these re-vibrations are all discrete.

Just like a guitar note will die down unless you keep re-strumming the string.

 

[manoj.p]

Manoj, my point was that forget about the wave. At the end of the day, you are hearing a single tone because a single basilar membrane hair in your ear (page 5 in the article I linked earlier) starts vibrating. This is similar to a guitar string vibrating. How does it matter if you used a finger or a guitar pick to pluck a string, or if a really strong gust of wind ended up causing the guitar string to vibrate?

All that matters to our ears (to hear a tone) is:
1. A particular basilar membrane hair started vibrating (which makes our ear hear a particular tone)
2. How strongly it vibrated (which indicates how much energy was used to vibrate the hair) - which indicates the loudness of the tone we hear

Two things to note here:
a. The hair vibrated because of a single discrete action (nothing continuous)
b. The hair stops vibrating shortly afterwards. If you want to continue hearing the tone, the hair has to be periodically re-vibrated. Again, these re-vibrations are all discrete.

Just like a guitar note will die down unless you keep re-strumming the string.

Arun,

I dont know how we digressed into this. But all along, I have been trying to say that the sound is a continuous event after its created and thats how its recorded by the microphone, (which is analog by the way) or till the sound dies. The creation of it may be unique and discrete, what happens after that is not unique/discrete. When we hear it, our eardrum vibrates and it also moves in wave motion during that vibration. If you still think transfer of sound or energy (as pointed by how the waves meet the tuning forks) is not continuous, then its a new theory. I haven't heard/read anywhere that sound or waves being discontinuous phenomenon.

Anyway, again this is going in circles. I am not even sure how it matters to the original discussion anyway.

 

[asliarun]

Arun,

I dont know how we digressed into this. But all along, I have been trying to say that the sound is a continuous event after its created and thats how its recorded by the microphone, (which is analog by the way) or till the sound dies. The creation of it may be unique and discrete, what happens after that is not unique/discrete. When we hear it, our eardrum vibrates and it also moves in wave motion during that vibration. If you still think transfer of sound or energy (as pointed by how the waves meet the tuning forks) is not continuous, then its a new theory. I haven't heard/read anywhere that sound or waves being discontinuous phenomenon.

Anyway, again this is going in circles. I am not even sure how it matters to the original discussion anyway.

Manoj, maybe we are going around in circles because I basically said the same thing a dozen times myself.

Can you please try and read the article I posted earlier about how our ear works, how the hair in our ears vibrate, and the tuning fork example I gave? This is how our ear really works and also tells you that after the eardrum, what exactly happens.

For that matter, do you really think that a speaker drive goes back and forth in a wave-like sinusoidal manner to generate sound?? I mean, regardless of the analog/digital debate, the driver only plays back an analog signal. The thing you are continually failing to note or acknowledge is that one single back and forth motion of the speaker driver produces one single note (a single pressure wave) - it doesn't produce a range of notes on its way back and forth. And if it is moving back and forth 20 times a second, your ears receive 20 pressure waves a second, and it thus perceive it as a 20Hz note because your ear hair (or ear drum) gets hit 20 times a second.

I have tried and failed to explain my understanding (you can call it viewpoint since you disagree) - which is that sound is not a continuous event but a discrete event. It is nothing but a discrete set of pressure waves.

But I give up now. And I guess we can all have our own understanding of the world. Mine is a pretty simplistic one at best too.

 

[manoj.p]

Manoj, maybe we are going around in circles because I basically said the same thing a dozen times myself.

Can you please try and read the article I posted earlier about how our ear works, how the hair in our ears vibrate, and the tuning fork example I gave? This is how our ear really works and also tells you that after the eardrum, what exactly happens.

For that matter, do you really think that a speaker drive goes back and forth in a wave-like sinusoidal manner to generate sound??

Yes, a driver moves back and forth in both the directions. You can see this on subwoofers. After a driver moves forward, on the way back, it goes back and then comes back up to default position. This is how it works. Unless you use a servo amp and driver.

I mean, regardless of the analog/digital debate, the driver only plays back an analog signal. The thing you are continually failing to note or acknowledge is that one single back and forth motion of the speaker driver produces one single note (a single pressure wave) - it doesn't produce a range of notes on its way back and forth. And if it is moving back and forth 20 times a second, your ears receive 20 pressure waves a second, and it thus perceive it as a 20Hz note because your ear hair (or ear drum) gets hit 20 times a second.

I never said that if there is one note, the driver will keep producing it. It will just play it as long as there is signal. However, when that wave is formed, it will keep moving till it dies or reflected. It is still one wave if its just one note and thats how you will hear it. But it is a continuous wave, it does not have breakage. This is the first time I am hearing that sound is not continuous. You can persue it, may be we have a nobel prize at hand.

I have tried and failed to explain my understanding (you can call it viewpoint since you disagree) - which is that sound is not a continuous event but a discrete event. It is nothing but a discrete set of pressure waves.

But I give up now. And I guess we can all have our own understanding of the world. Mine is a pretty simplistic one at best too.

Its quite mutual.

 

[asliarun]

Yes, a driver moves back and forth in both the directions. You can see this on subwoofers. After a driver moves forward, on the way back, it goes back and then comes back up to default position. This is how it works. Unless you use a servo amp and driver.

I never said that if there is one note, the driver will keep producing it. It will just play it as long as there is signal. However, when that wave is formed, it will keep moving till it dies or reflected. It is still one wave if its just one note and thats how you will hear it. But it is a continuous wave, it does not have breakage. This is the first time I am hearing that sound is not continuous. You can persue it, may be we have a nobel prize at hand.


Its quite mutual.

Well well. You were saying a minute ago that the eardrum moves in a sine wave.. So not sure if you are saying the ear drum moves differently from a driver??

Perhaps I should apply for the no-bull prize instead because that is what I am trying to clarify to myself.

And perhaps you should back up your stand with more detail than the one liners you are providing. For example:
1. How do you think our brain and ear is able to understand a 20hz tone? I get that it waxes and wanes with the wave. But how does it differentiate between 20hz and 21hz?
2. Do you also believe that our ears capture sound in a continuous way? If so, how?

 

[Sawyer]

But it is a continuous wave, it does not have breakage. This is the first time I am hearing that sound is not continuous. You can persue it, may be we have a nobel prize at hand.

manoj, now that I have had a good sleep, maybe I can win the Nobel.
Jokes apart, let me take another stab at this. Because the teaching side is the one that has not been successful - neither the theory nor the student is at fault.

Let me take the same tuning fork example. To start, for simplicity, let us assume that the rod receives a steady impulse to vibrate, such that it keeps vibrating in the same way forever.
In this scenario, the vibrating rod has just two variables based on the strength of the impulse. One, the distance it will move away from the resting position, back and forth from it. And two, the speed at which it moves, i.e., how many times a second it does so. The distance is amplitude, the speed is frequency.
For simplicity's sake let us also assume that the rod is moving one inch forward and one backwards in two seconds, for a total of two inches.
To capture the complete nature of this vibration, what data points matter? Just two. The amplitude, 1 inch. And frequency, once in two seconds. No other data point exists for the continuous movement of the rod from the resting centre position to the extreme right or left position it reaches before it changes direction by 180 degrees.
Now take a pencil and paper and draw the Y axis and X axis, to draw a representation of this movement. X axis marked in seconds, Y in inches, using the same scale for each. The first data point to be marked will be one inch above the Y axis, half a second along the X axis. The second to be marked will be one inch below, one and a half seconds along the X axis. The third will be one inch above, two and a half seconds along on the X axis. And so on, as long as the steady impulse is not withdrawn. After say 10 seconds, join the dots and voila - there is your sound "wave"! Distance between peaks from left to right on the X axis is 2 seconds, and the distance between peaks from top to bottom on the Y axis is 2 inches. While the continuous motion of the rod is represented by the line between the dots, there is no need for any more data points to draw it correctly. Two dots can be joined only in one way. End of representation talk.
Coming to the actually vibrating tuning fork, if these dots/data points are known, the continuous vibration that will be produced using these, will be identical to the original continuous vibration. No need to have data points on the movement of the rod other than these data points. All that is needed is knowing 2 inches in 2 seconds for the same tuning fork to produce the same sound.
Before moving away from the simplicities in this, are you ok with this? It is the foundation of this subject.
Also, if anyone else sees a flaw in this, jump in! I have understood this just a little over 24 hours ago. It is an important first step in the learning of these fundamentals. It therefore needs to be flawless.

 

[Sawyer]

While waiting for your response, I can bring in room acoustics, speaker construction, speaker/listener placement, and speaker cone material characteristics into this simplicity right away.
If you move the same tuning fork to another acoustic environment, the same vibrations will sound different - room acoustics effect.
If you sit in a different place, the same vibrations will sound different - speaker/listener placement effect.
If you use a tuning fork of even the exact same dimensions, but made of different materials, the vibrations will sound different - speaker cone material effect.
There is also a speaker acoustics effect, caused by the nature of the construction of the speaker enclosure with respect to how it affects the air inside the enclosure.
These are the variables that make a difference to the sound heard - not because the two vibrations are any different in themselves.

 

[manoj.p]

manoj, now that I have had a good sleep, maybe I can win the Nobel.
Jokes apart, let me take another stab at this. Because the teaching side is the one that has not been successful - neither the theory nor the student is at fault.

Let me take the same tuning fork example. To start, for simplicity, let us assume that the rod receives a steady impulse to vibrate, such that it keeps vibrating in the same way forever.
In this scenario, the vibrating rod has just two variables based on the strength of the impulse. One, the distance it will move away from the resting position, back and forth from it. And two, the speed at which it moves, i.e., how many times a second it does so. The distance is amplitude, the speed is frequency.
For simplicity's sake let us also assume that the rod is moving one inch forward and one backwards in two seconds, for a total of two inches.
To capture the complete nature of this vibration, what data points matter? Just two. The amplitude, 1 inch. And frequency, once in two seconds. No other data point exists for the continuous movement of the rod from the resting centre position to the extreme right or left position it reaches before it changes direction by 180 degrees.
Now take a pencil and paper and draw the Y axis and X axis, to draw a representation of this movement. X axis marked in seconds, Y in inches, using the same scale for each. The first data point to be marked will be one inch above the Y axis, half a second along the X axis. The second to be marked will be one inch below, one and a half seconds along the X axis. The third will be one inch above, two and a half seconds along on the X axis. And so on, as long as the steady impulse is not withdrawn. After say 10 seconds, join the dots and voila - there is your sound "wave"! Distance between peaks from left to right on the X axis is 2 seconds, and the distance between peaks from top to bottom on the Y axis is 2 inches. While the continuous motion of the rod is represented by the line between the dots, there is no need for any more data points to draw it correctly. Two dots can be joined only in one way. End of representation talk.
Coming to the actually vibrating tuning fork, if these dots/data points are known, the continuous vibration that will be produced using these, will be identical to the original continuous vibration. No need to have data points on the movement of the rod other than these data points. All that is needed is knowing 2 inches in 2 seconds for the same tuning fork to produce the same sound.
Before moving away from the simplicities in this, are you ok with this? It is the foundation of this subject.
Also, if anyone else sees a flaw in this, jump in! I have understood this just a little over 24 hours ago. It is an important first step in the learning of these fundamentals. It therefore needs to be flawless.

Okay, let's continue with the same experiment but in a different way.
Assumption no 1: You don't know the frequency.
Assumption no 2: You take 2 measurements of the displacement from neutral position, spaced 1 sec apart.

Now, take a pencil, draw the neutral position. Place these 2 measurements of displacement on the chart as X, time as Y. Draw a wave. Let's see if we can get an accurate one.

 

[manoj.p]

While waiting for your response, I can bring in room acoustics, speaker construction, speaker/listener placement, and speaker cone material characteristics into this simplicity right away.
If you move the same tuning fork to another acoustic environment, the same vibrations will sound different - room acoustics effect.
If you sit in a different place, the same vibrations will sound different - speaker/listener placement effect.
If you use a tuning fork of even the exact same dimensions, but made of different materials, the vibrations will sound different - speaker cone material effect.
There is also a speaker acoustics effect, caused by the nature of the construction of the speaker enclosure with respect to how it affects the air inside the enclosure.
These are the variables that make a difference to the sound heard - not because the two vibrations are any different in themselves.

I don't see the need of bringing it into discussion. These are all external factors and are known. I can talk about standing waves, room modes, mode cancellations. Bringing those in will only dilute the discussion at hand. Incidentally, these can be used to divert attention in cleaver way though.

To keep it simple, let's stick with the original discussion. How the analog sound is captured into digital and the effect of sampling rate, Nyquist theorem etc where this discussion began. The theorem is quite simple and was not derived with keeping audio in mind. Using it for digital audio is just the applied science side of it.