Page 26 - Fall 2005

quite unique.
A range of physical phenomena precluded by linear
acoustic theory are manifest at high amplitudes. The goal of this article has been to introduce a few of the most basic concepts in nonlinear acoustics, point out how these con- cepts differ from linear acoustic theory, and discuss practi- cal consequences of them. In so doing, it is hoped that read- ers are 1) aware of a branch of acoustics with which they may have been previously unfamiliar, and 2) better able to explore this intriguing field further on their own.AT
References
1. M.F. Hamilton and D.T. Blackstock, eds., Nonlinear Acoustics, Academic Press, San Diego (1998).
2. R.T. Beyer, Nonlinear Acoustics, Acoustical Society of America, Melville (1994).
3. K. Naugolnykh and L. Ostrovsky, Nonlinear Wave Processes in Acoustics, Cambridge University Press, Cambridge (1998).
4. R.T. Beyer, “The parameter B/A,” Ch. 2 in Ref 1.
5. “Audio spotlight” is a registered trademark of Holosonic Research
Fig. 6. If two sinusoidal stimuli are applied to a nonlinear system, the output con- sists of harmonics of the two input signals, as well as all the possible sum and dif- ference frequencies combinations.
that f1 = 40,000 Hz and f2 = 40,400 Hz, both tones inaudi- ble to humans. As the wave propagates, signals will appear at the harmonics of 40,000 Hz, e.g., 80,000 Hz, 120,000 Hz,...; at the harmonics of 40,400 Hz, e.g., 80,800 Hz, 121,200 Hz, ...; and at the sum and difference frequencies, e.g., 400 Hz, 80,400 Hz, ...; in other words a quite compli- cated spectrum. The 400-Hz term is audible.
The absorption coefficient of sound in fluids is, very approximately, proportional to f 2. Therefore, the two primary signals as well as their harmonics and sum frequencies are absorbed within a relatively short distance from the source compared to the 400-Hz difference frequency. As a result, only the difference frequency is heard far from the source.
There are certainly easier and more direct ways to gen- erate a 400-Hz tone. In addition, the conversion efficiency from the two primary signals to the difference frequency is very low. So what is the advantage of generating a signal this way? The primary advantage is directivity. The width of a sound beam radiated directly from a source of radius a is proportional to a/λ, where λ is the wavelength of the sound. However, it can be shown that the width of this parametri- cally generated beam is proportional to La/λ, where La is the absorption length of the primary beams. At 40 kHz, La is approximately 7 m. Therefore, the beam width of the para- metrically generated beam is many times narrower than one generated with a conventional loudspeaker. This property has given rise to the term “audio spotlight.”5 Potential appli- cations include museum displays and public address sys- tems. Although reproducing high-fidelity sound is techni- cally challenging, the listening experience is, nevertheless,
Anthony Atchley received
a B.A. in Physics from the
University of the South, an M.S.
in Physics from the New
Mexico Institute of Mining and
Technology, and a Ph.D. in
Physics from the University of
Mississippi. From 1985—1997,
he was a faculty member in the
Physics Department of the
Naval Postgraduate School. He
has been awarded the ASA’s F.V.
Hunt Postdoctoral Fellowship and the R. Bruce Lindsay Award, and is a Fellow of the Society. He has conducted research in a broad range of areas including measurements of jet noise from both military and commercial aircraft, sonic booms, nonlinear acoustics, thermoacoustic heat transport, optical imaging of sound fields, and ultrasonics. Since 1997, he has served as Head of Penn State’s Graduate Program in Acoustics and is currently President-Elect of the ASA.
24 Acoustics Today, October 2005