Switching gears... (? )
https://en.wikipedia.org/wiki/Duke_Chapel
Physics 136 / Music 126 Duke University Fall 2012 Handout 19
Acoustics and Duke Chapel
The original drawings for Duke Chapel were delivered to the University in 1930 by the Philadelphia firm of Horace Trumbauer, the same architects who designed Baldwin and Page auditoriums. The principal designer was Julian Abele, hired by Trumbauer at age 17, when he already was a graduate both of Philadelphia's Institute for Colored Youth and the University of Pennsylvania. Trumbauer supported Abele's studies at the Ecole des Beaux-Arts in Paris and appointed him chief designer of the firm soon after his return. There is no record of Abele ever having visited Durham. Much of the firm's business involved the design of mansions for wealthy clients and, while Abele remained on the payroll, the firm closed its offices for eight years after the stock market crash of 1929. Architecturally, Duke Chapel represents faithful adherence to gothic design principles. The basic fabric of the building is, just as it appears, weight-bearing stone.
That acoustical considerations also figured in the initial design of Duke Chapel is evident in such details as the large cavities originally provided in the wooden canopy over the pulpit (seen in the lower right corner of the photograph below of the Æolian organ) and in the stone wall between the choir and the Memorial Chapel -- both designed to house loudspeakers.
The principal axis of the cruciform building -- through nave and choir -- is 300 feet long, the width including side aisles is about 65 feet. The inner vaulting is 40 feet wide and reaches 75 feet above the floor of the nave. The original design included seating for approximately 2200 in the nave and transepts and 150 in the choir. It is instructive to approach the room in several different ways acoustically:
(1) Consider the Chapel to be a gigantic Helmholtz resonator. If, with its doors open, the narthex entrance were thought of as defining an oscillating mass of air, the cross section of that mass might be roughly ten square meters and its length ten meters. The main volume of air enclosed by the Chapel, about 3 x 104 cubic meters, then would serve as a spring providing a restoring force to the mass of air in the narthex. This would lead to a resonant frequency of about 0.1 Hz. The resonance might be observed by a dedicated investigator prepared to spend some considerable time with a window fan at the open doors of the Chapel, reversing the fan's direction every five seconds or so. [Helmholtz resonances at frequencies far below the audible range can have practical consequences. Steady winds blowing past the mouths of caves can drive such resonances. Visitors lost in such caves sometimes try to find their way out by following a breeze, only to discover eventually that the breeze periodically reverses direction.]
(2) It is also possible to take a Modal Analysis view of the Chapel as an enormous pipe, closed at both ends. The lowest frequency mode then would correspond to a standing wave along the principal nave-choir axis: Thus the room will have a set of normal modes spaced no more than 2 Hz apart (harmonics of this 2 Hz "fundamental"). Since the lowest audible frequencies are at least three octaves above this "fundamental" there are plenty of room modes available to provide a smooth response, even for low pitched musical tones. The lowest mode along the transept axis (L = 112 feet) has a frequency of about 5 Hz.
(3) Ray Analysis. If one gazes along virtually any path that a ray of sound might take within the Chapel, he or she will observe surfaces that scatter sound diffusively over a wide range of frequencies. Gothic architecture typically subdivides massive stone elements into multiple convex surfaces, down to the scale of the span of a person's hand. Thus a massive pillar, for instance, will diffusely scatter sounds over the entire range of audible wavelengths in air -- from less than an inch to tens of feet. Thus reflected sound within the Chapel will not convey an image of its source, and the reverberant sound amplitude at any given frequency will have an equilibrium value that is the same everywhere in the room. This, in turn, means that the Chapel is ideally suited for . . .
(4) Sabine Analysis. The predominance of diffuse scattering at all frequencies in the Chapel ensures the validity of this approach, which assumes a steady-state or equilibrium condition in which the reverberant sound at each frequency is uniformly distributed throughout the room. In its present state, the Chapel's volume is approximately 1.1 x 106 cubic feet and its mid-frequency reverberation time is said to approach seven seconds. That would indicate the mid-frequency total absorption as little as square feet.
The Chapel's reverberation time was not always so long. Originally it was a mere 2.5 to 3 seconds. What appears to be stone between the ribs of the vaulting and on the flat surfaces of the upper walls is in fact a material called Akoustolith, manufactured by the R. Guastavino Co. in New Jersey and designed to be acoustically absorbent. In one-inch thicknesses, this porous cast material originally had octave band absorption coefficients (band center frequencies from 125 Hz to 4 kHz) of .09, .17, .46, .77, .77, and .56, while five-inch layers had coefficients of .43, .92, .91, .88, .86, and .74. It was used extensively in the Chapel to maximize speech intelligibility for sermons. (It was also popular at the time for limiting the noise levels in monumental banks, libraries, and government buildings.) Akoustolith is only about one third as dense as the stone it is designed to resemble. The resulting saving in weight in the vaulting of Duke Chapel is one reason the building's buttresses can be so small as to arouse suspicion in some visitors that they must contain structural steel. [Another reason the buttresses can be so slender is that local building codes required that the exterior roof be supported by steel trusses rather than any traditional gothic arrangement. The only other place structural steel has been used in the Chapel is within the wood columns supporting the rear gallery and its heavy organ case.]
In the late 1960s, when D. A. Flentrop was approached about building a large pipe organ for the Chapel, he insisted that the room's acoustics be made consistent with its appearance. The consulting firm of Bolt, Beranek, and Newman was hired to identify a substance that could be applied to the Akoustolith to seal its pores (thus reducing its sound absorption) without making its appearance objectionable (shiny, for instance). A beeswax-like material was applied in two stages to much of the Akoustolith in the room, with dramatic acoustical results. [Evidence of trial applications of such materials can still be seen just inside the doorway at the top of the stairs to the crypt.]
We turn now to a consideration of some of the consequences of having such a long reverberation time:
(1) Sound absorption by the air itself becomes a significant factor. With a very long reverberation time, sound travels so far back and forth through the air in the room that its absorption by the air, normally insignificant in comparison with absorption by room surfaces, becomes considerable. In metric units, where at a frequency of 1 kHz the air absorption coefficient square meters per 100 cubic meters of air, assuming a 50 percent relative humidity. Thus the additional absorption by the air itself in Duke Chapel is about 100 square meters, the equivalent of the the sound that would escape through a ten by ten meter hole in a wall!
(2) Modest continuing inputs of sound power can result in surprisingly high levels of noise. A quiet conversation in a far corner of the Chapel will produce a constant level of indistinct noise throughout the room. The threshold for detecting the softest musical sounds can be raised significantly in such a circumstance, and the overall dynamic range available for music accordingly reduced. [The threshold for pain -- defining the upper limit of the available dynamic range -- will remain unchanged.] [Such an effect in the Malabar Caves was featured in E. M. Forster's novel A Passage to India. Forster's account emphasized that, whatever the nature of the sounds created by humans in the cave -- angry shouts, resigned sighs, desperate screams -- the reverberant response was the same, an undefinable sustained sound he likened to the meditation syllable "Om". For Forster this served, in part, as a metaphor for the doomed efforts of the colonial British to effect rapid changes in Indian society.]
(3) A long reverberation time not only imposes a slow decay of sound rather than a sudden silence at the conclusion of a musical note, it also provides a built-in crescendo of reverberant sound for any note that is sustained for several seconds. The temporal structure of music performed in the Chapel -- rhythm, phrasing, etc. -- must be conveyed by direct sound alone -- sound traveling directly from source to listener plus reflected sound arriving at the listener's ear within the association time (35 to 50 milliseconds) of that earliest arrival. At times this direct sound may have to compete with reverberant sound for the listener's perception and/or attention. In typical music performance situations, the distinction between direct and reverberant sound is a subtle one, with the reverberant sound sharing and conveying much of the temporal structure of the music. A room like the Chapel offers an excellent opportunity to observe and understand the distinction, because in this case the two play very different roles and the distinction between them is not at all subtle. In such a room the ratio discussed in the next section varies from seat to seat and has real practical implications for listeners and performers.
(4) Consider the ratio of direct to reverberant sound intensity. As noted above, the near-ideal conditions in the Chapel for the diffuse scattering of sound means that the reverberant sound intensity will be the same anywhere in the room. Specifically, at a given frequency, where is the total sound absorption, and is the intensity of reverberant sound for a continuous input of sound power W.
The direct sound intensity on the other hand, will depend on the listener's distance r from the sound source:. [It is assumed that there is no barrier between source and listener. The equality holds when the source radiates sound equally in all directions.] We calculated above that square feet for the Chapel. Then:, where r is in feet. Thus in the "worst case" (i.e. if there are no nearby reflecting surfaces concentrating the direct sound toward the audience) the direct and reverberant sound intensities will be equal at a distance feet from the source. Put another way, in that case the reverberant intensity anywhere in the room will equal the direct intensity at 50 feet. Now consider a situation in which there is a flat reflecting surface right behind the sound source, so that all the direct sound is concentrated into only half of all the available directions. will be doubled, and will be multiplied by a factor of, becoming about 70 feet. Exactly what ratio of direct to reverberant sound intensity is optimal will depend on personal taste and the nature of the music being performed. Notice that placing a pipe organ at the rear of the nave lets it speak directly along the main axis of the room. Placing it on a gallery well above the floor of the nave both (a) allows direct rays of sound to reach the maximum number of seats without grazing over the heads of intervening listeners, and (b) avoids having the rearmost seats too close to the sound source. Placing the pipes in a massive wooden case concentrates the direct sound toward the listeners. Each of these factors helps achieve desirable ratios of direct to reverberant sound over a significant fraction of the listeners' seats. Notice that, as the size of the audience increases, so too do and the distance r at which any given optimum ratio is achieved, so the best seats at an organ recital will be further from the organ the larger the audience.
(5) Long reverberation times present a special set of problems. All of that Akoustolith was installed originally to ensure acceptable levels of speech intelligibility in the Chapel. In addition, an unobtrusive location was provided for a reinforcing loudspeaker in the canopy above the pulpit from which sermons were to be delivered. When the reverberation time was increased, speech intelligibility was reduced significantly and more sophisticated electronic measures were needed. Providing all reinforcing sound from a single location above the head of the person speaking has several advantages, including the reinforcement's coming from an appropriate direction and arriving only slightly later than the sound coming directly from the speaker's mouth. With a long reverberation time, however, such a single powerful loudspeaker will fuel the reverberant intensity as well as the direct. To avoid increasing the reverberant intensity (the source of the problem to begin with) it is better in such cases to resort to a large number of loudspeakers located quite close to the listeners (to minimize the additional sound power added to the room), and designed to be highly directional (projecting sound only toward the listeners and not toward any reflective surfaces that would feed the reverberation). A nearly vertical array of small loudspeakers utilizes linear superposition to concentrate sound radiation in a plane perpendicular to the axis of the array. The sounds from all the loudspeakers in the array combine constructively at points on that plane, while the interference becomes increasingly destructive as distance from the plane is increased. An additional advantage of such arrays is that they are relatively unobtrusive visually when mounted on gothic columns. In order to make the reinforcing sound acoustically as well as visually unobtrusive, the signal to each array can be delayed just enough to make its sound reach its listeners slightly after the true direct sound reaches them. Such a "phased delay" arrangement was installed in the Chapel when the reverberation was increased, initially using a magnetic tape loop with a single recording head and multiple playback heads to introduce appropriate delays. Subsequent upgrades of the Chapel sound system have achieved the delays using solid state electronics. A switch allows the phased delay feature to be defeated when, for instance, the person speaking is doing so from the rear of the Chapel.
Another class of problems associated with long reverberation times involves parts of the choral repertoire. Imagine a choral work with intricate rhythms, a rapid tempo, and lyrics that must be conveyed distinctly to an audience. The Chapel's acoustics pose special difficulties for the performance of such works. On occasion, such works have benefitted from positioning the singers on a platform set up on the main axis of the Chapel, with stage shell sections (borrowed from Page Auditorium) providing a reflecting surface behind the chorus. The reasoning behind such an arrangement is analogous to that discussed above in connection with locating an organ on a gallery at the rear of the nave. An advantage of a choir's singing from the choir stalls, on the other hand, is that the reflecting walls behind them on both sides help the singers hear each other well. Such choir stalls in great European gothic churches typically are made of thick, solid, acoustically reflective wood. The paneling on the walls behind the Duke Chapel stalls, however, is relatively thin and flexible and thus absorbs considerable sound at low frequencies.
In selecting instrumental as well as choral works for performance in the Chapel it is important to keep in mind such consequences of a long reverberation time as the impossibility of sudden dramatic silences (there are limits, even, on sudden dramatic reductions in dynamic) and the danger of inner voices being lost in a general reverberant blur. [In a smaller room, not only is the overall amount of reverberant sound less, but there also are brief transient disturbances at the beginning of each note, as the reverberant sound energy is distributed among the more widely spaced available normal modes of the room. Such disturbances can make inner voices easier to recognize.] Some ranks of organ pipes are designed to include brief attack noises ("chiff") that make the movement of inner voices much easier to hear in highly reverberant conditions. Sometimes an adjustment in tempo can help.
Finally, musicians performing in the Chapel have to deal with the fact that people sitting in various locations will experience quite different balances between direct and reverberant sound.
(6) Long reverberation times also can present some special opportunities. The Chapel is a truly great place to perform a substantial part of the organ repertoire and some types of vocal music (liturgical plain chant, for instance). It is a rare resource, a room made truly optimal for the performance of certain types of music, rather than being compromized for all uses in an effort to achieve a "multipurpose" room.
http://webhome.phy.duke.edu/~dtl/136126/36hj_chl.html
