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http://www.digital-recordings.com/publ/publife.html#entropy

I'll do one better. The best rough estimate I could find of the power transferred from the Sun to the Earth was here (link). According to that we receive about 1.7x10^17 W from the Sun. Since Watts are Joules per second, we can do a little math and find that the energy total for a year comes to around 5.4x10^24 J/year. Now, the best estimate I could find for total worldwide energy consumption (link) puts us at around 5.418x10^20 J/year.

What does this mean? It means the Earth receives each year from the sun, approximately ten-thousand (10000) times the energy that we consume. What this in turn means is that the sum of our methods for capturing this energy and putting it to use needs only to achieve 0.1% efficiency.

If you're going to be proclaiming something as grandiose as the statement that the sun cannot possibly deliver enough energy to earth to meet our needs, then you really should have something better to back it up. Furthermore if you're talking about something at a global scale, you should analyze it at a global scale, not a unit scale.

You may have misunderstood my point. Sampling and harmonic analysis cannot yield a perfect representation of the original waveform unless there is a priori knowledge of the function used to generate that waveform. For general audio recording, that isn't the case.

http://www.digital-recordings.com/publ/pubneq.html

I Googled to see if I could find an online hearing test that would do something similar to what you describe (tones at different frequencies and amplitudes). I found these, in particular this. They're pretty cool, although they do require a Java-enabled browser, decent headphones, and someone with good hearing in order to calibrate the tests.

I Googled to see if I could find an online hearing test that would do something similar to what you describe (tones at different frequencies and amplitudes). I found these, in particular this. They're pretty cool, although they do require a Java-enabled browser, decent headphones, and someone with good hearing in order to calibrate the tests.

Quoth the parent and grandparent:

Subliminal messages are in the range above conscious hearing. This is generally agreed to be 20KHz. Therefore, you would take the spoken portion, and boost it by 20KHz, then add in the music at the normal frequencies.

Don't forget the sample rate; according to nyquist, the sample rate must be at least twice the highest frequency represented. CD sample rate is 44 KHz... therefore this method CANNOT be used to record to CD; there isn't enough representational accuracy in the 20 - 22 KHz range

Quoth malachid69:

Hmmm. well you are still talking about a single stereo source to go through the headphones. Why would you need to change the sample rate?

It all comes down to the Nyquist Theorem, which basically states that in order to accurately represent any sound, it's frequency must be less than half the sample rate. Even for sounds less than half the sample rate, to get true high fidelity, they must be far less than half the sample rate, or the consequences are poor representation. I would imagine that any subliminal messaging occuring in the ultrasound spectrum would have to be relatively high fidelity, considering that the ear is not physically well-suited to pick up ultrasound...

Well, CDs are sampled at 44,100 Hz. As mentioned in the above "consequences" link, a 20 KHz tone would only be represented by 2.205 samples per period; not an incredibly high quality recording. The nuances, the voice itself, would be lost to the sampling process. The engineers that designed the CD spec chose it specifically for that feature; this is the lowest sample rate that can reproduce all the sounds audible to a human (up to about 16 KHz) without any appreciable loss in quality. Sounds just barely above the threshold are recorded, but the loss in quality becomes quite rapid as you approach 22 KHz. Above 22 KHz, any sound comes out as a bunch of mid-range noise, and nothing else.

Actually, 44.1k allows you to capture up to 20kHz, not 22kHz. What you're talking about is the Nyquist Theorem, and you've got the right idea, but you're leaving out one subtlety.

A low-pass filter is used prior to sampling the audio, and this filter is set to have a ceiling of 20kHz. However, the cuttoff at 20k is not a "brick wall", it's a slope. By the time the audio is completely cut off, it's up around 22.05k, which, x 2, is 44.1k. Geddit? I guess, technically, some sound above 20k gets through, but the highest frequency fully reproduced is 20k.

Okay, I just went through the replies to the grandparent post and I was suprised to find that my post was the only one to mention anything about filters. I guess slashdotters could use a little bit more explanation:

The grandparent poster was referring to Nyquist's theorem. Here's a good link on the subject.

The problem is that he doesn't seem to understand how this is applied in practice. You can't just hook a mic up to the D/A convertor. There is a possibility that signals above the nyquist frequency of your setup are present. These would result in an aliasing effect.
Ex:
If your mic is putting out a 23 KHz sinewave. and you're sampling at 44KHz, this sinewave is going to get shifted down to 1KHz. This is bad, because it trashes the real 1KHz signal that you wanted to listen to, and you get to listend to aliased electrical noise instead.

To prevent high frequencies from messing up your recording, you must place a filter before the A/D convertor. This will block those high frequencies from being digitized, but it introduces a new problem:
no filter is perfect. In an ideal world, you want a filter that would pass everything below 22KHz exactly and block everything above it completely. The problem is that sucha filter is impossible to implement. This means that you end up involved in a trade-off situation. That sharper the cutoff, the less smooth the filter response, etc.

It's a pretty complex subject that I've spent a couple years studying and still don't fully grasp (people spend their whole lives studying filters), but the main point I'm trying to get across is that pretty much any A/D converter has a filter in front of it, and the more extra samples above the nyquist rate you can squeeze in, the less demands are placed on this filter.

uhh... no... just don't listen to it loud, tinnitis is caused by - among other things - exposure to overly loud sounds, symptoms of which include a ringing noise in the ear which can in serious cases be heard by others near your ears. our ears hear in selective ranges of sound, and listening to something loud can damage parts of your ear responsible for "hearing" the various frequency ranges. For most people the high frequencies go first because it takes more precision to hear them, hence why bass is often the only thing you can hear when the neighbors start pumping the gansta rap downstairs. Listening to something at about 90 dB for an hour or so can give you or start to give you tinnitis. It's not the music, it's the volume. And the louder you listen the faster you loose it. A good resource for info on hearing and damage due to sound levels check out some Common Misconceptions About Hearing at Digital Recordings. There are other factors than just sound levels that can cause tinnitis. For a more in depth discussion of the syndrome itself check out the tinnitis FAQ .

Actually, a square wave at Xhz consists of an infinite number of sin waves One of which has the frequency X, and the others having frequencies 3X 5X 7X and so on

No, a square wave is a square wave is a square wave. Sine waves operate on entirely different principles. A true sine wave is the result of a trigeometry identity - sine. They are not an "infinite number of sine waves" rolled into one. All you've done here is a nice graphing trick - just like a good way of representing pi is 22/7.

People can hear frequencies up to something in the 20Khz range...

No, typically only young children can hear into the 20khz range. Most adults aged 21 or older are only capable of hearing to about 18.5 - 19.5Khz.

...that means they can hear the components of a signal whose frequencies are lower than that.

Yes, they're called harmonics, and since the human ear cannot hear beyond about 20khz, it doesn't matter if an instrument has a fundamental frequency higher than that, as the ear is picking up the harmonics at 1/2, 1/4, 1/8th, etc of that original frequency. That is what your equipment needs to be able to reproduce, not the fundamental.

So yeas, to represent a square wave at 22Khz fairly well you'd need to sample at atleast 100Khz, preferably 200Khz.

You are confusing bits/second with sampling rate. To capture and reproduce a sine wave, you need only sample at double the highest frequency. ie, to capture 22khz or lower, you sample at 44khz. This is the Nyquist Criteria, which I believe may have been mentioned earlier in this thread. The formula is somewhat complex to write out here, so please visit these guys for the formula.

Now, I suspect you were talking about the bits/second, so I'd like to get into that for a minute, since this is likely where the large numbers came from. A CD-ROM typically encodes at 32 bits/second, per channel. The thing is, whenever you convert from analog to digital, you do lose a finite amount of information. This is expressed as a "quantization error". It can be up to +/- 0.5 dB between the original signal, and the real signal. The smaller the quantization error, the better the digital signal represents the original (analog) signal. This isn't important to go into, beyond to understand that too low of a bitrate means a greater error rate - the signal will be skewed, even if the sampling rate is sufficiently high.

Most "audiophiles" are idiots.

Most "audiophiles" tend to educate themselves on what all of what I just said means. They know about signal degregation, they know about harmonic distortion, intermodulation distortion, etc. Why? Because that is their hobby - and like any good hobbiest they're going to read up on the issue. This is in sharp contrast to people who merely want something that goes thump-thump to impress their friends. Those people are merely interested in music - but hardly an enthusiast. The number of parallels between car audiophiles and computer geeks is uncanny, having been pigeonholed by others as both, I can safely say this. They take their hobby/craft/profession just as seriously as /.'r that looked for a 300A from the Brazil fab.

For instance most audiophiles do not understand what the term "digital" means.

Excuse me? Everybody who doesn't live under a rock knows what digital means - little ones and zeros, little bits of data. With all the hype about the internet and e-commerce, the idea that someone might NOT have heard the word "digital" in today's world is preposterous.

It's entirely pointless spending money on more expensive and "better" cables and pickup-assemblies to read and transmit the ones and zeroes.

So can I get away with using CAT3 wiring when I need to use CAT5 wiring in my network? This aside, had you any experience in the installation of audio systems, you would know that as soon as it leaves the head (the thing you put the CD in), it is an analog signal. At this point, Shannon's Law takes over and signal strength and attentuation become supremely important. Also, because it is an electrical signal - digital or analog, it is suseptible to interference. I take it you haven't ever competed in IASCA or IDBL then. Let me make a case in point about my own experience with high end car audio.

I have a setup that uses 1000 watts of power, drawing 83.3 amps on 4 ga wire capable of handling 85 amps. First point, cabling is critical to be able to handle your load, from one end to another.

My head unit than takes the signal and puts it out through several pre-outs. This signal is than passed from the head unit to the amplifiers. The amplifiers do their bit and than send the signal to the speakers. At the power levels I am running at (1000 watts), any weak point in the system would invariably become an immediate issue. I had at one point, cheap $45 cables running from the deck to the amplifiers, and the amount of /noise/ in the system was absolutely unacceptable. I /fixed/ the problem after replacing the cabling with much higher quality cabling.

1st, A heavy duty cable makes a world of difference, and can be detected in a heartbeat. Do you think a lowend cable can ever take the place of a quality componenet? Think about it, would you use a cheap cable for your brand new ultra 160 raid 5 array? Are you going to run generic cat 5 for your network backbone? Why on earth do you think that audio issues are going to be any fundamentally different than computer issues. A cable is a cable, and quality makes a difference regardless of the application it used for! A cheap cable is more prone to attenuation and distortion at higher frequencies, regardless of what it is used for.

A better cable provides additional ground, which means much better shielding and allows a signal to go through with less distortion.

Purchasing high quality speakers and not using high quality speaker wire nullifies your investment in high quality speakers.

While I certainly don't dispute there are people who just want something loud that goes thump, these are the people that tend to get put in their place if the actually enter a competition.

Now if you really want to press your point that cabling does not make a difference, let me suggest another slashdot like forum for you. The friendly people over at SoundDomain.com will be more than happy to discuss all those little details with you.

What's the point of sampling sound at 96kHz when human ear and speakers can do only (in the best case) 20kHz?

The consequences of the 44.1K sampling rate are quite severe. They can be understood in depth from the following article: Consequences of Nyquist Theorem for Acoustic Signals Stored in Digital Format

Essentially this article points out that since the sound reproduced at f/2 (the sampling frequency divided by 2) is derived from only two samples per second, the error in sound reproduced is actually larger than the sound itself . This means at 20 kHz you actually have more than 50% distortion in the CD audio format.

Other factors include introduction of phase inaccuracies from the introduction of a 18-db/octave anti-aliasing filter at the 22 KHz cutoff frequency. Loss of phase accuracy of course leads to odd cancellations in the room sound field.

In addition it has long been known that the stereo sound field quite poorly reproduced by only two speakers. For decades experimenters have known that at least a center channel improves the sound image dramatically. Home theatre enthusiasts have also become very aware of the practical benefits of a seperate subwoofer channel and amplifier. At the very least they no longer have the problem of tweeter burnout from distortion harmonics induced by amplifier overload.

Take a look at http://fagersta.com/electronics/audio.html for more information.