Constructive and destructive interference in audio

[Azathoth]

So today I had a discussion with a friend that argued 192kHz is better than 44.1kHz, he said this

If a sound at a single interval plays at 4 different frequencies, 4khz, 5khz, and 20khz and 3hz
Your record cannot physically record at those frequencies at the same time.
That’s where 192khz matters.
In that 1 time period for that 4 frequencies are played, we are now able to record 4 distinct frequencies.
And that 4 distinct frequencies when played back in a set with 4 different drivers will produce the same four different sound.
NyQuist Shannon theory still holds
Whereas if you have that 1 singular sound, it plays back at 1 average frequency which then only gets played back by 1 single speaker.
That’s neither accurate or precise

Could anyone explain this to me? I've never encountered the issue of constructive or destructive interference before with regards to high resolution audio, and would really like to know more about this.

 

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So today I had a discussion with a friend that argued 192kHz is better than 44.1kHz, he said this



Could anyone explain this to me? I've never encountered the issue of constructive or destructive interference before with regards to high resolution audio, and would really like to know more about this.

It's nonsense. Frequencies at or below half the sampling rate are able to be recorded.

Edit: the theorem is:

If a function x(t) contains no frequencies higher than B hertz, it is completely determined by giving its ordinates at a series of points spaced 1/(2B) seconds apart.

Emphasis on "contains no frequencies higher than" and "completely determined".

 

[Azathoth]

It's nonsense. Frequencies at or below half the sampling rate are able to be recorded.

So he continues, bringing in Nyquist from a previous point I made where I said the same thing as you did.

https://www.sciencedirect.com/science/article/pii/B9780750646376500113
Mathematically what nyquist theorem says is correct, to perfectly replicate a single frequency.
But unless you only listen to a single frequency at a certain time that argument does not hold true.
Ergo why I say if you record 4 distinct tracks in 48k sampling rate, scientifically speaking, re-recording it back to a 48k track will create a 4:1 bitrate loss.
Realistically it’s way less than that.

He keeps bringing in 'physics' and 'science' but I don't think he really knows what he's saying here, is it not?

 

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So he continues, bringing in Nyquist from a previous point I made where I said the same thing as you did.



He keeps bringing in 'physics' and 'science' but I don't think he really knows what he's saying here, is it not?

The Nyquist theorem says nothing about perfectly replicating one frequency - it refers to perfectly replicating all frequencies below half the sample rate.

When you sum 4 frequencies (i.e. 4 sine waves), they form a function that contains all 4, not a simple sine wave at an average of the 4.

 

[LTig]

He keeps bringing in 'physics' and 'science' but I don't think he really knows what he's saying here, is it not?

Correct.

If he specifies those 4 frequencies (frequency and amplitude) I can supply flac files at 44 and 192 for him to listen to, and their FFTs.

 

[BrEpBrEpBrEpBrEp]

Correct.

If he specifies those 4 frequencies (frequency and amplitude) I can supply flac files at 44 and 192 for him to listen to, and their FFTs.

Bold of you to assume someone making those arguments knows what a Fourier Transform is.

 

[Azathoth]

The Nyquist theorem says nothing about perfectly replicating one frequency - it refers to perfectly replicating all frequencies below half the sample rate.

When you sum 4 frequencies (i.e. 4 sine waves), they form a function that contains all 4, not a simple sine wave at an average of the 4.

Then if I may ask, how could he get to that conclusion? I really wonder how does he think sounds have been recorded since we understood signal processing since the early 1900s? It doesn't help that he compares this to the refresh rates on monitors, saying that the higher numbers mean something. Isn't image quality and audio quality two different things?

Bold of you to assume someone making those arguments knows what a Fourier Transform is.

I mentioned this, he didn't seem to respond to it so it is no surprise.

 

[pozz]

Tell him look up "Fourier series". You can play with some examples here:

• http://www.jezzamon.com/fourier/
• https://lpsa.swarthmore.edu/Fourier/Series/ExFS.html

 

[DVDdoug]

Azathoth,

This is for you, not necessarily for whomever you are arguing with...

Could anyone explain this to me? I've never encountered the issue of constructive or destructive interference before

To me, that sounds like standing waves (where a wave is combined or mixed with itself) or when a wave is delayed (or not) and combined with itself. Or if you have two very-close frequencies (like when you're tuning an instrument) they will "beat" as they go-between adding (in-phase) and subtracting (out-of-phase).

Mixing is done by summation. When sounds mix acoustically the air pressure sums (AKA "superposition"). Analog mixers are built around summing amplifiers. When you mix digitally, the samples are summed sample-by-sample.. Sample-1 from wave-1 is added to sample-1 from wave-2, etc. (i.e, 44.100 samples per second). Of course, this means all of the tracks must have the same same sample rate before they can be mixed.

At any instant in time, if both samples are positive you are adding two positive values ("constructive"?) and if one sample is negative you are "adding negative", effectively subtracting (destructive"?). And of course you can add two negatives to go more-negative. So with multiple (possibly unrelated) frequencies they could be adding or subtracting at any point in time.

 

[Cbdb2]

This has nothing to do with interference. Sounds like your friend thinks a speaker can only play one freq. at a time. He needs to go back to sound basics, most sounds have harmonics, they are already more than one sinewave. Simple proof for him. Play a 1khz tone thru a single driver, than play a 500hz tone, than play the 2 together. Ask if he hears both tones. Do you really need to do this or is the thought experiment enough?

 

[amirm]

A DAC doesn't get told which frequencies to play. It actually isn't given any frequencies at all! It is given a varying digital value in *time* domain which is the sum of those four frequencies. It simply converts those digital samples to voltages. It cares not what the spectrum is. So his entire understanding of the matter is incorrect.

 

[Beershaun]

A DAC doesn't get told which frequencies to play. It actually isn't given any frequencies at all! It is given a varying digital value in *time* domain which is the sum of those four frequencies. It simply converts those digital samples to voltages. It cares not what the spectrum is. So his entire understanding of the matter is incorrect.

YouTube video idea! Explain th gozinta' and gozoutta' of a dac!