ABCs of Acoustics: Organ Pipes
We offer this issue’s ABCs of Acoustics with great sadness. Our author, colleague, and friend Dr. Eric Ungar has passed away. As we see with this series his work will live on for many years. Eric was a master of vibration, acoustics, and communication. His papers and books are informative, engaging, and easy to read and understand. He brought us the famous Vibration Criteria (VC curves) which are used throughout the building acoustics community to ensure vibration is within simple specifications. He and his colleagues, Kerwin and Ross, developed the famous RKU theory for estimating damping from constrained layer systems. These are far from his only contributions, and we’re planning a longer tribute to Eric in a future issue. For now, please enjoy his poetry and musings on Organ sound and Propagation.
An ORGAN pipe emits a tone
When air into one end is blown.
Its pitch is given by its length
And somewhat by the blowing strength.
In many instruments, indeed,
The tone’s established by a reed.
Every introductory text on acoustics talks about organ pipes and how their lengths are related to the wavelengths and frequencies of the tones they produce. However, discussions of how steady blowing into a pipe produces oscillations generally are left to specialized texts. Clearly, if the injected airflow were entirely smooth, no oscillations would occur.
There are two basic types of organ pipes: flue pipes and reed pipes. In the former the incoming air stream passes through a narrow passage formed by a ‘flue’ and then impinges on the edge of a thin plate ‘lip.’ The resulting flow turbulence generates a rather broad band of frequencies in the pipe’s air volume, which responds predominantly at its natural frequencies. The resulting oscillations then interact with the turbulent jet to stabilize both that jet and the acoustic oscillations. Reed pipes, as the name implies, use a vibrating brass reed to modulate the injected air, with the pipe and reed generally tuned to the same frequency. More details can be found in the excellent books by Rossing, Strong and Plitnik [1,2]
The mechanism by which flutes produce sound is somewhat different: it is the same mechanism as that responsible for the whistle one hears as one blows across a bottle. A flute player essentially blows across a hole in the flute, resulting in some turbulence, which generates standing waves in the flute’s volume and thus produces tones. A piccolo is a woodwind instrument that is about half the size of a standard flute. Its development has an interesting history. Professor Peter Schickele reports that a hungry Italian constructed the first piccolo by sautéing an ordinary flute in a frying pan until it had shrunk about fifty percent. This event later came to be known as the Mediterranean Flute Fry [3].
1. The Science of Sound, T. D. Rossing, Addison-Wesley Publishing Co., New York, 2nd Edition, 1990.
2. Music Speech Audio, W. J. Strong and G. R. Plitnik, Soundprint, Provo, UT, 1992.
3. From “Bach to the Future,” Diane Cyr, U.S. Airways Attaché, July 1999.
In PROPAGATION through the air
Indoors, outdoors, everywhere,
Sound waves that spread out from a source
Take energy away, of course.
Pressure by spreading is abated
And some by losses dissipated
The basics of sound propagation in the atmosphere have been understood ever since the wave nature of sound has been recognized. Sound pressure decreases with increasing distance from a source because the energy injected by the source is spread over larger and larger areas at locations further away from the source, and also because acoustic energy is dissipated as sound passes through the air. The attenuation due to dissipation is more pronounced at high frequencies and when the humidity is high. As Philip Morrison [4] puts it: “Energy loss in sound transport is the result of internal diffusion that wipes away the contrast between compressed crests and rarefied troughs as any pressure wave advances. The longer the wavelength of the sound, the farther it can go.”
One can easily visualize that winds whose speeds increase with increasing altitude tend to refract sound propagating in the windward direction toward the ground, because here the sound travels faster (with respect to the ground) in areas of higher wind-speed. Because the speed of sound in air is proportional to the square-root of the absolute temperature, an atmospheric temperature profile marked by increasing temperature with increasing altitude has a similar effect. Thus, wind (and temperature) gradients can result in focusing of sound downwind from a source and the formation of quiet “shadow zones” upwind. In the 1960s, test firing of large rockets at NASA’s Marshall Space Flight Center in Alabama was found occasionally to damage some buildings in downtown Huntsville several miles away as the result of atmospheric focusing of the rockets’ intense low-frequency sound. NASA eventually instituted the use of meteorological balloons to measure the wind and temperature profiles before each planned test firing and postponed the testing when calculations indicated a potential for focusing in built-up areas [5].
Since sound that propagates from an atmospheric layer with a lower temperature to one with a higher temperature is refracted back toward the cooler layer, sound can be “trapped” in a “sound channel” formed by a cooler layer that is located between two warmer layers. Such trapped sound decreases with distance much less than freely propagating sound, sometimes enabling acoustic phenomena to be detected at very large distances. In the earth’s atmosphere there exists a relatively permanent sound channel at high altitude, and it has been reported that the 1883 Krakatoa volcano eruption could be heard on the other side of the world. I have some doubts about that, because the audible components of the sound would have been attenuated over such long distances. However, the low-frequency components of the sound produced by the 1991 Mount Pinatubo eruption and by some nuclear explosions were detected by instruments thousands of miles away. Similarly, in the “Sofar Channel,” a sound channel in the deep portions of the oceans, sound signals have been transmitted and received over great distances. [6]
As long as we are on the subject of atmospheric refraction, it is also interesting to consider wind blowing along the ground and across a noise barrier. The wind needs to accelerate to get over the barrier, resulting in a wind profile that may refract the sound toward the ground beyond the barrier – thus reducing its effectiveness.
4. “Wonders: Double Bass Redoubled,” P.Morrison, Scientific A m erican, May 1998.
5. Rudy Volin wrote: “. . .During a visit to the Marshall Space Flight Center (Huntsville, Alabama) in February 1967 my hosts asked me if I wanted to visit a static test firing of a Saturn second stage . . . I declined . . . Sure enough, the motel began to shake, followed by a brief low-frequency rumbling noise . . . I also heard, and I forget where, that occasionally focusing caused the noise from rocket firings at the Marshall Space Center to be transmitted to Birmingham, AL, which is a little over 100 miles southeast of Huntsville.”
6. Sound Waves and Light Waves, W. E. Kock, Anchor Books, New York, 1965.
