Rich
I received this reply today.
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ATC follow-up
Date:
Fri, 21 Feb 97 15:29:38 -0800
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From:
Joe Norris <joe@atcsd.com>
Ty,
Let me take a shot at answering your questions.
There was a question as to whether actual sound is created or whether an artifact of the ear was responsible for what is heard. This is a good question. If the new frequencies were a form of beats, or subjective only, only difference tones could be detected. HSS creates sum frequencies in addition to the difference frequencies. Actual (or
objective) sum and difference tones that are created in the air were
documented by Helmholtz well over a century ago. Also see P.J.
Westervelt, JASA Vol. 35, No. 4, p535, etc.
There was also some speculation as to the cause of the new tones. There are two effects responsible. The first effect is called convection. The sound wave sets particles of the fluid (air is a fluid) in motion, back and forth, in the direction the wave is traveling. The molecules add their own thermal velocities, u, to the that of the sound wave, c. The propagation speed of any point of the wave is:
v = dx/dt = c + u, not just c.
Moreover, c itself is not constant but rather varies over the waveform. For gases, the speed of sound varies with the square root of the absolute temperature. Since the higher pressure parts of the wave have, by compression, raised local temperature slightly, c is a little higher there. Conversely the temperature is a little lower in the expansion parts of the wave, and this makes c a little lower in these regions. The nonconstancy of c due to variation of temperature over the wave is the result of the nonlinear relation between pressure and density for the fluid. This effect turns out to have the following mathematical expression:
c = c_0 + (gamma - 1)/2
for a gas, where c_0 is the ordinary speed of sound (found in tables) and gamma is the ratio of the specific heats of the gas. Put the two
equations together and you get:
v = c_0 + [(gamma) + 1)/2}u
For ordinary sound waves the second term is negligible compared to c_0, and all points on the waveform propagate with the same speed, in other words, the waveform does not change as it travels.
For high-amplitude waves the second term, though small, is not
negligible. It tells you that the peaks of the wave travel faster than
the troughs. The tendency of the peaks to overtake the troughs makes a
sine wave begin to look like a sawtooth wave as it travels. In the
frequency domain, the changed waveform takes the the form of harmonics.
In the case of a two-frequency source, the distortion components include sum and difference components. When you use ultrasonic sources, the only component your ear hears is the difference frequency.
We are using one transducer (per channel), so the ultrasonic signals do not need to be superimposed in the air. We are not, however, broadcasting any audible signals. Sorry if this is too technical, but I am assuming this will be posted on the chat page for technical types to review.
The audible signals are created in the ultrasonic column, and travel with it. The column does not diverge radically so if your ears are not in it, they hear the reflected sound from an apparent source (a reflector). Audible sound leaks from the column, but your ear tends to hear the loudest sounds, wherever that happens to be.
The radiation pattern of an HSS system can be made to be directional or otherwise (by using a convex array of transducers) so the sound energy will be spent on the listeners, not on the absorption of the room.
I hope this information helps to answer both questions posted. The
earlier ATC reply was also written by me, it was just given to Connie
(the secretary) to proof read before it was mailed.
Cheers,
___________________________________________________________
Joe Norris
ATC Physics ATC
mailto:joe@atcsd.com 12725 Stowe Drive
ph: (619)679-3173 Poway, CA 92064
fax:(619)679-0545 atcsd.com
/////////////////////////////////////////////////////////////////////
Thank you Joe!
Ty |
