My follow-up questions to Joe Norris and his responses:
Dear Mr Norris:
I'm the guy who posted the message to Silicon Investor that you responded to today (it was forwarded to you by Ty Cronus). I figured that rather than continuing to filter things through him, I'd follow up with you directly and then post both my questions and your reply to Silicon Investor after the fact.
Thanks a lot for your reply. It really helped me to understand, and I appreciate the time it took for you to put it together. Again, please pardon my ignorance of physics, but there are a few things I still don't understand.
Let me try to parrot back to you what you said first and you can correct me if I've got it wrong. Then you'll also understand any misconceptions behind my questions.
If I understand you correctly, you're basically taking advantage of the fact that sound doesn't propagate through air "purely"; the air itself affects the waveform. The speed of sound varies with the density of the air. Since the density is higher at the high-pressure parts of the waveform (obviously) and lower at the low-pressure parts, the different points along the waveform don't all move at the same speed; the "peaks" move faster than the "valleys".
The tendency of the peaks to overtake the valleys results in distortion, which mathematically equates to additional frequencies in the signal. For waveforms of low amplitude, this distortion is too small to make an audible difference, but with waveforms of high amplitude, it's large enough to be audible. (It's tempting to use "loud" and "soft" here, but I think loudness is a function of the energy in the signal, which would mean both frequency and amplitude affect it.) With a two-frequency signal, the distortion includes a sum frequency and a difference frequency. With HSS, we hear the difference frequency only, the others being way outside the range of human hearing.
To the extent that I grasp this, it makes sense. My questions:
1) Your description leads me to think you'd also get distortion doing this with a pure sine-wave tone. What does that distortion look like?
2) Your description also says that sum and difference frequencies are "among" the distortion components with a two-tone signal. What are the others? And why don't we hear them? Is it because they're all much higher in frequency, or because the sum and difference tones are by far the largest distortion components, or both, or something else?
3) The original ultrasonic signal still gets absorbed by the air not too far from the transducer. I guess that even though the "carrier signal" produces the audible signal in the air, once the audible signal is there it has a "life of its own," just like any other audible sound, and doesn't need the "carrier signal" to keep it going. Is this right?
4) I guess it also stands to reason that the audible signal is going to keep the dispersion pattern of the signal that created it. I can't see anything that would make the waves "spread" more once they got started. Is this why the signal remains directional even at low frequencies?
5) In fact, it makes me think that maybe my understanding that high frequencies tend to "beam" and low frequencies tend to spread out more evenly is based primarily on what conventional louspeakers do. In other words, this effect is a byproduct of producing the sound with a large flat surface flapping back and forth, and isn't inherent in the sound itself. This would suggest that the low-frequency components of a note from a trombone would be must more directional than the same low-frequency components of a trombone note reproduced through a conventional subwoofer. Is this correct?
6) If this is true, then bass reproduced using HSS really would be affected less by the size and shape of the room than bass reproduced with conventional louspeakers because it wouldn't have the same tendency to spread out evenly through the room that it does when produced with a regular louspeaker. Am I right? If so, it also seems like the more non-directional you make the transducer's dispersion pattern, the more trouble you'd have with standing waves in the bass frequencies. Right?
7) You mention large amplitude a number of times. Do you mean "large amplitude" in the absolute sense, or does the amplitude of the wave only have to be large relative to the wavelength of the sound? I'm guessing it must be the latter, since a piezoelectric crystal isn't going to have an excursion distance measured in inches. If I'm right, that suggests the job is actually easier at higher frequencies than it is at lower frequencies, that you'd need a transducer that could move back and forth a lot farther if your carrier signal were, say, 20 kHz. Am I understanding this correctly?
8) This may be a dangerous question, but what the heck: Can you think of any reason why this technology wouldn't work? Or if this fails, will it have to be because of something that totally blinsided you? In other words, as your company and Carver go through the process of producing a high-quality prototype, do you have any anxieties?
Anyway, thanks again for your time and patience. I really do appreciate it.
***
Rich,
Thanks for the good questions. It helps to have an intelligent discussion of the facts rather than dwelling on speculation, or fiction. People can make wiser decisions if they understand what we are doing.
Let me take your questions in order. I'm pretty busy here, but I'm happy to entertain good questions once and a while.
1) If you emit a single, pure sine wave (of sufficient amplitude) into the air, the waveform will be altered as it propagates. Harmonics appear in the waveform, changing its shape. For example, if a single 50kHz sine wave is emitted at 130dB ref., progressively smaller amplitude 100kHz, 150kHz, 200kHz, etc. components appear in the wave, making it begin to look like a sawtooth wave. These new harmonics are created by exactly the same mechanism that creates the HSS difference tones when using two frequencies.
2) I stated that the sum and difference tones are "among" other components of a two-tone signal. This is true. If I emit two frequencies, say f1 and f2, I will get sum and difference components, (f1+f2) and (f1-f2). I will also get 2f1, 2f2, 3f1, 3f2, etc. If f1 and f2 are ultrasonic, the only tone detected by the ear is (f1-f2).
By the way, when using frequencies that are ultrasonic, the difference tone has a much greater amplitude than the sum tone and all of the harmonics.
This is because the amplitude of the difference tone is proportional to the inverse square of the frequency difference value, or (f1-f2)^-2. The sum tone amplitude is proportional to the inverse square of the sum value, or (f1+f2)^-2. The harmonics amplitudes are proportional to the inverse square of their frequency value, for example (2f1)^-2.
You will notice that as f1 and f2 become larger values (ultrasonic), that the amplitudes of all of the nonlinear components approach zero quickly, except the amplitude of the difference frequency because it only depends of the inverse square of the difference. This amplitude is same if I use 30kHz & 31kHz, or 900kHz & 901kHz. Either way I will get the same amplitude 1kHz difference.
3) The newly-created audio waves (daughter waves) are true sound waves so they do not require an ultrasonic (mother wave) to exist.
4) The HSS audible signals do retain their original dispersion pattern
directions. It should be noted that lower audio frequencies are much more omni-directional than higher audio frequencies. The same is true of HSS. However, since new audio waves are continually being created in the ultrasonic column, a higher degree of directionality can be achieved.
5) High frequencies do tend to beam, and lower ones do tend to spread out in every direction. However, low frequencies do not spread out because of the large woofer size. On the contrary.
Large drivers tend to give MORE of a beaming effect than you would normally get, at any given frequency. Small drivers give less of a beam. Speakers are designed this way (among other reasons) because the
dispersion pattern of the woofer should be similar to that of the tweeter. If all of the drivers were the same size, the bass would be too omni-directional and the treble would be to directional (beam-like).
In other words, the tweeter is not small in order to make the treble beam, it is small so the treble will not beam so much. The woofer is not large in order to make the bass omni-directional, it is large so the bass will not be so omni-directional.
6) The overall bass dispersion pattern of HSS is more narrow than the bass dispersion pattern of a conventional speaker because with HSS, new bass is created all the way down a long ultrasonic column. Once it is created though, it spreads like bass normally does.
So the bass created by HSS does spread, but new bass signals are being created downstream in the column. Hence, the net effect one of directionality.
7) By large amplitude, I mean of sufficient intensity (measured in dB). Remember the 12dB/octave rule? This rule states that if a given driver is moving through a fixed length, back and forth, at a given frequency, I get X dB. If I double the frequency--go up an octave--without changing how far the driver moves (only how fast it moves), I will get X+12 dB. If I double the frequency again, I get X+24 dB, and so on. This is a fancy way of saying that energy goes up with frequency, for a given displacement.
So high frequency drivers do not have to move as far as low frequency ones for the same dB level, or intensity level. Ever notice how you can see a woofer moving and the tweeter doesn't really move?
8) The only small hurdle to overcome is the transducer development, which is happening now. The technology does work right now with transducers that are not built for this application. More importantly, the proof-of-concept test results agree with the applicable nonlinear acoustics theory. These theories point to very promising results when applied correctly.
I hope I have been able to clear up any misconceptions. Take care. |
