The Look of Sound: Acoustic Cancellation in Architecture

Abstract: 

Because of the propagation and interference of sound waves in a fluidic medium, acoustic cancellation due to architecture will often occur where it is least desired, such as in classrooms, churches, or presentation rooms. This dampening of sound may occur when evenly spaced structures are positioned at an interval roughly equivalent to half the wavelength of the sound being cancelled. Through the modeled and structural observance of this phenomenon, a theoretical model has been developed that can provide a means by which to determine the frequencies of sound that will be filtered out by a structure’s inherent arrangement.

Table of Contents: 

    Introduction

    Perhaps the fundamental quality of sound is its ability to echo; we can hear sound only because it can echo. However, because sound acts as a wave, it can interfere with itself, causing areas of varying intensity1 that can be louder or softer than what is needed for proper communication.2 Just as in other fields, repeated architectural structures filter sound and cause a greater amount of interference than would normally occur. This acoustic filtration can lead to the entire cancellation of sound, or cause no sound to be heard.

    Current information on architectural acoustics pertains to the theories thereof or processes by which its properties may be manipulated. The experimental data on the subject are quite limited. With the advent of modern high-speed personal computers, information has been and is being gathered with respect to sound’s waves, the surrounding architecture, and the perceived quality of said sound.3 The study of these three factors leads to a fundamental knowledge of the nature of sound.4 In the literature review following, research on architectural acoustics will be evaluated with respect to these sound characteristics. The research methodology and data seek to measure various acoustic phenomena and create a theoretical model for the distribution of architecture.

    Background

    Waveform Analysis

    The human voice originates from the vocal folds vibrating in an air column in the windpipe that in turn is amplified due to the echoing properties of the throat.5 Although the creation of voice is remarkably simple, the nature of a resonating cavity to produce overtones and interference patterns can greatly increase the complexity of a frequency analysis.6

    Waves are understood to be usually of the sine or cosine nature, or to start at the wave’s zero or its maximum, respectively. A common algorithm uses simple inverse transforms, or inversion of the wave, to place several waves on top of each other.7 Then with several mathematical transforms that are already widely used, the data create a “sparse matrix” in which data are sparsely populated between many zeros.8 Modern computers can inherently reduce these matrices and create smaller files and speed up the processing time required to reproduce the recorded or simulated sound.

    In most circumstances, the relationship between file size and signal processing time is related directly, and not inversely as with this case.9 This relationship shows the importance of an effective and efficient algorithm for sound analysis. Using a microphone without a sound-canceling function, computer software such as Pioneer Hill’s Spectra Plus signal analyzer, and any type of sound generator that can create specific frequencies without harmonics or generic white noise, a large sweep of all audible sound frequencies can be made.10

    Architectural Analysis

    The nature of sound is to diffuse around its surroundings, taking up any and all available space.11 Whether around a door or through small holes in a wall, sound expands into its environment. However, sound does not merely stop when it comes into contact with another medium: it is partially reflected. Just as the light from a flashlight can bounce off a mirror and onto another surface, sound can bounce into other directions.12 These two properties are what projects sound and allows it to be heard.13

    If a listener is positioned somewhere between the source and a reflective material, then an echo, or reverberation, occurs. The time difference between the time the sound travels directly from the source and when the reflected sound reaches the source is called the reverberation time.14 The usage of this measure defines how and why most rooms are created.

    From the reverberation time, several properties can be deduced—namely, the size of the room and the sound quality in the room.15 These data give a general idea of how the sound waves bounce around the room and the time it takes an echo to travel to the listener.

    When waves bounce off of a right angle, they tend to reflect back to the source and partially diffract around any object in their path.16 This property aids in both the study of sound waves and the creation of common architectural qualities. To check a created wave’s properties, the sound can be aimed at a right angle and reflected back to the source.17 For most rooms, it is undesirable for a sound source, such as a speaker, to produce sound that reflects back to it; usually the sound should be distributed throughout the room for the listeners.

    Sound Quality

    The focus in current technology research is on ensuring quality sound to the listener from any source. In some people who have lost their sense of hearing, a cochlear implant is inserted into the user’s unusable cochlea and sounds can be directly transmitted to the brain via a small microcontroller.18 The ability of people to hear with the implant hinges on the property of distinguishing between sounds, namely speech.19 Because of the mechanics of such an implant, the sound quality being heard by the person with the implant is studied not only to benefit the user but also to understand the characteristics of sound.20

    For ease of use, measurements have been taken of the sound quality of cochlear implants and simple indices created from the measurements for the comparison of sound quality between listeners and implants.21 With a few small changes, the indices can be used to model the sound in an entire room.22 This model allows for the comparison of sound not just among specific implants but among entire rooms and buildings.23

    The sound quality reflected in such measurements is greatly affected by the echoing and reverberation properties of the room being studied.24 For most circumstances, open spaces produce the desired sound that most people can functionally use and, as such, repeated structures should be used sparsely. When such repeated structures—such as columns, windows, or furniture—are used, the echoing can cause a differing sound across the room.25 This echo can result in a speaker’s voice becoming unintelligible across a room. As the distance between source and listener is increased, the distortion of sound is amplified and the sound quality is usually lowered.26

    Hypothesis

    Because of the basic and simplified model of wave cancellation in which waves of equal amplitude and opposite phase attenuate infinitely at their intersection,27 it follows that periodically placed structures will effectively cancel waves of a wavelength of double the distance between the structures.

    Research Methodology

    Overview

    For the investigation of architectural phenomena, three specific data collection methods were developed: taking measurements from preexisting structures,28 modifying or creating a structure, or building a scale model.29 The second method is the least feasible with respect to time and money, whereas the first may be the simplest but requires a sufficiently repetitive structure and the permission to make use of it. Although all will likely be implemented to some degree, the third method—creating a model—will be undertaken for the majority of the data collection. To further simplify matters, mass-produced building materials with a specific, regular cross-section and even acoustic impedance (meaning that the sound is dampened and distorted evenly across the medium) will be used.30 Polyvinyl chloride (PVC) pipe should prove to be a general, simple, and readily available medium for the measurement of acoustic events.31

    It is hypothesized that at certain intervals corresponding to half of the wavelength of a sound, evenly spaced holes act as a stop-band filter for sound passing through the medium. In the experiment, the pipe is cut at specific intervals to test various frequencies of sound.32 Sound is then generated at one end of the pipe and recorded through the opposite end using frequency analyzing software. Through the software, the characteristics of the pipe can be deduced.33

    Modular Creation

    Using the PVC pipe, an elongated form of a room can be developed that assumes most of the characteristics of modern architecture, though on a smaller scale. Because the pipe is smaller than a typical room by a factor of around 144:1, the viable sound frequencies that can be used increase by 1:144. Although the sound might be more difficult to hear, the effects are not seen on the objective use of sound recording devices and a frequency analyzing computer.34

    Like many of the modern woodwind instruments, holes will be cut into the pipe to change the reflection and damping characteristics of the air inside, thereby changing the sound that is produced from the ends.35 Using a combination of evenly spaced holes, moving joints, and hole coverings, the sound will be tested as it comes out of the pipe after originating from a discrete source.

    The source should produce precise frequencies at any given point in time, allowing for a full-range frequency sweep of the pipe. At each specific frequency, the sound’s distortion and intensity will be recorded. If the sound becomes distorted, specific qualities of the current spacing of the holes on the pipe can be deduced. If the sound is significantly less intense as the origination source, the spacing can be seen to block (to some degree) the specific frequency that is passed. It will likely be found that each particular spacing behaves as a band-gap or stop-band filter.36 These filters block only a certain range of frequencies but permit all others to pass unhindered through the medium.

    Data Collection and Analysis

    Using Pioneer Hill’s Spectra Plus signal analyzer37 and a generic computer microphone, all of the data can be saved and analyzed. The specific tests can be done with the software, verifying or disproving the validity of the original argument. In addition, the pipe’s filtering characteristics can be translated into the frequency domain, thereby alleviating most of the hand calculations involved.38

    By viewing the pipe’s damping characteristics in the frequency domain, a magnitude plot can be created that immediately describes the intensity of the exiting frequencies. Without any other calculations by the computer, the breadth of the data comes from these plots.39

    In this instance, a 2-inch SCH40 PVC pipe of 1 meter in length and 10 centimeters between holes (see Figure 1) and a sampling frequency of 48 kHz are used. The pipe’s dimensions allow for fundamental frequencies between 343 Hz and 3.43 kHz, or approximately the “voice band” of the audio spectrum (see Equation 1). The sampling rate of 48 kHz allows for adequate sampling without aliasing for frequencies up to approximately 24 kHz (see Equation 2). This rate is adequate for the frequency range of human hearing from approximately 20 Hz to 20 kHz.

    Results

    During the trials (see Figure 3 through Figure 14), holes were closed and opened according to arbitrary but ordered patterns (see Table 1) to discern changes in the frequency spectrum of the pipe when white noise was used as an input. Each change of the hole openings created a noticeable change in the perceived pitch.

    Due to the non-ideal characteristics of the sound generator–microphone setup, a calibration curve (see Figure 2) was first calculated using the microphone and speakers without a pipe. This curve yields a baseline from which to calculate the data using the pipe.

    The wavelengths corresponding to the distance between holes were indeed passed and less attenuated than their nearby counterparts, but a slight error in the length of the pipe was quickly found (see Table 2). Given these corrections, the frequencies and their harmonics derived from the distances between the open holes were passed in relation to their half-frequencies (or doubled wavelengths).

    Conclusions

    As verified by the data, in a periodically placed structure in an enclosed environment, the frequency of sound with a wavelength of twice the distance between structures will indeed be attenuated significantly. The reverse of this scenario would also be true: the frequency of sound with a wavelength equal to the distance between the structures will occur at a greater intensity than its surrounding frequencies.

    For the application of this property, structures should therefore be designed so that the minimum distance between columns, archways, or any periodic protuberance is 62.5 centimeters in length. This spacing would allow any fundamental band-gaps of frequencies of sound due to elements of the structure to occur at a center frequency of less than 275 Hz. Because human speech occurs primarily in the range of 300 Hz to 3 kHz, this configuration would allow vocal communication to be unhindered by filtering effects.

    Notes

    1. Frederick A White, Our Acoustic Environment, ed. Robert L. Metcalf, James N. Pitts, Jr., and Werner Stumm (New York: John Wiley & Sons, 1975), Environmental Science and Technology, 373.
    2. White, 380–396.
    3. Masayuki Otani, Yoshinobu Kajikawa, and Yasuo Nomura, “An acoustic echo cancellation using subadaptive filter,” Electronics & Communications in Japan, Part 3: Fundamental Electronic Science 90, no. 2 (February 2007): 9. Academic Search Complete, EBSCOhost (accessed October 16, 2007).
    4. Yi-ping Chang and Qian-Jie Fu, “Effects of Talker Variability on Vowel Recognition in Cochlear Implants,” Journal of Speech, Language & Hearing Research 49, no. 6 (December 2006): 1331–1332. Academic Search Complete, EBSCOhost (accessed October 16, 2007).
    5. Chang, 1332.
    6. White, 370–373.
    7. Vladimir Britanak and K.R. Rao, “A new fast algorithm for the unified forward and inverse MDCT/MDST computation,” Signal Processing 82, no. 3 (2002): 433, Academic Search Premier, EBSCOhost (accessed September 20, 2007).
    8. Britanak, 434–436.
    9. Yan Qing Zeng, Qing Huo Liu, and Gang Zhao, “Multidomain Pseudospectral Time-Domain (PSTD) Method for Acoustic Waves in Lossy Media,” Journal of Computational Acoustics 12, no. 3 (September 2004): 277–278. Computer Source, EBSCOhost (accessed October 2, 2007).
    10. Samuel Matteson, interview by Cameron McCord, Acoustics Research Methodology (April 16, 2007).
    11. White, 373.
    12. Matteson.
    13. Chang, 1331–1332.
    14. Larm Petra and Valtteri Hongisto, “Experimental Comparison Between Speech Transmission Index Rapid Speech Transmission Index and Speech Intelligibility Index,” Journal of the Acoustical Society of North America 119, no. 2 (2006): 1106.
    15. Antonio P. O. Carvalho and Anabela P. B. Carvalho, “Acoustic Characterization of Historic Cloisters in Portugal” (Baltimore, MD: Proceedings of the NoiseCon04, 2004). National Conference of Noise Control Engineering, 2.
    16. Liu Lanbo and Donald G. Albert, “Acoustic pulse propagation near a right-angle wall,” Journal of the Acoustical Society of America 119, no. 4 (April 2006): 2073–2080, Academic Search Complete, EBSCOhost (accessed October 6, 2007).
    17. Lanbo, 2073–2074.
    18. Chang, 1331.
    19. Chang, 1332.
    20. Chang, 1338–1340.
    21. Petra, 1106–1108.
    22. Chang, 1331–1338.
    23. Petra, 1106.
    24. Petra, 1106–1107.
    25. White, 262–263.
    26. Petra, 1106–1108.
    27. I. A. Andreev, “Single crystals of the langasite family: An intriguing combination of properties promising for acoustoelectronics,” Technical Physics 51, no. 6 (June 2006): 758, Academic Search Complete, EBSCOhost (accessed October 8, 2007).
    28. Carvalho, 5–7.
    29. Matteson.
    30. White, 373.
    31. Matteson.
    32. Carvalho, 2.
    33. Matteson.
    34. Matteson.
    35. White, 375.
    36. Otani, 9.
    37. Spectra Plus Signal Analyzer, Pioneer Hill Software, Poulsbo, WA.
    38. Zeng, 277–278.
    39. Matteson.

    References

    • Andreev, I. A. “Single Crystals of the Langasite Family: An Intriguing Combination of Properties Promising for Acoustoelectronics.” Technical Physics 51, no. 6 (June 2006): 758–764. Academic Search Complete, EBSCOhost (accessed October 8, 2007).
    • Britanak, Vladimir, and Rao, K. R. “A New Fast Algorithm for the Unified Forward and Inverse MDCT/MDST Computation.” Signal Processing 82, no. 3 (2002): 433–459. Academic Search Premier, EBSCOhost (accessed September 20, 2007).
    • Carvalho, Antonio P. O., and Carvalho, Anabela P. B. “Acoustic Characterization of Historic Cloisters in Portugal.” Proceedings of the NoiseCon04. Baltimore, MD: National Conference of Noise Control Engineering, 2004.
    • Chang, Yi-ping and Fu, Qian-Jie. “Effects of Talker Variability on Vowel Recognition in Cochlear Implants.” Journal of Speech, Language & Hearing Research 49, no. 6 (December 2006): 1331–1341. Academic Search Complete, EBSCOhost (accessed October 16, 2007).
    • Lanbo, Liu, and Albert, Donald G. “Acoustic Pulse Propagation Near a Right-Angle Wall.” Journal of the Acoustical Society of America 119, no. 4 (April 2006): 2073–2083. Academic Search Complete, EBSCOhost (accessed October 6, 2007).
    • Matteson, Samuel. Interview by Cameron McCord. Acoustics Research Methodology (October 18, 2007).
    • Otani, Masayuki, Kajikawa, Yoshinobu, and Nomura, Yasuo. “An Acoustic Echo Cancellation Using Subadaptive Filter.” Electronics & Communications in Japan, Part 3: Fundamental Electronic Science 90, no. 2 (February 2007): 9–21. Academic Search Complete, EBSCOhost (accessed October 16, 2007).
    • Petra, Larm, and Hongisto, Valtteri. “Experimental Comparison Between Speech Transmission Index Rapid Speech Transmission Index and Speech Intelligibility Index.” Journal of the Acoustical Society of North America, 2006: 1106–1117.
    • Spectra Plus Signal Analyzer, Pioneer Hill Software, Poulsbo, WA.
    • White, Frederick A. Our Acoustic Environment. Environmental Science and Technology. Edited by Robert L. Metcalf, Jr., James N. Pitts and Werner Stumm. New York: John Wiley & Sons, 1975.
    • Zeng, Yan Qing, Liu, Qing Huo, and Zhao, Gang. “Multidomain Pseudospectral Time-Domain (PSTD) Method for Acoustic Waves in Lossy Media.” Journal of Computational Acoustics 12, no. 3 (September 2004): 277–299. Computer Source, EBSCOhost (accessed October 2, 2007).

    Table 1: Hole Closings by Trial

    Trial # Holes (0 = open, 1 = closed) Figure #
    1 1 1 1 1 1 1 1 1 1 Figure 3
    2 0 0 0 0 0 0 0 0 0 Figure 4
    3 0 0 0 0 0 0 0 0 1 Figure 5
    4 1 1 1 1 1 1 1 1 0 Figure 6
    5 0 0 1 0 1 1 0 1 1 Figure 7
    6 1 1 0 0 0 0 0 1 1 Figure 8
    7 1 0 1 0 1 0 1 0 1 Figure 9
    8 1 1 1 1 0 1 1 1 1 Figure 10
    9 1 1 1 0 0 0 1 1 1 Figure 11
    10 1 1 1 1 1 0 0 0 0 Figure 12
    11 1 1 0 1 1 0 1 1 0 Figure 13
    11 1 0 0 0 0 0 0 0 1 Figure 14

     

    Table 2: Distances Between Holes and According Frequencies of Sound

    Distance Between
    Hole Closings
    .1 m .2 m .3 m .4 m .5 m .6 m .7 m .8 m .9 m 1.0 m
    Corrected Distance
    Between Hole
    Closings (±.001 m)
    .0996 .1991 .2987 .3983 .4978 .5974 .6970 .7965 .8961 .9956
    Fundamental
    Frequency (Hz)
    3445 1723 1148 861 689 574 492 430 383 345

     

    Equation 1: Wavelength-Frequency Relationship at Room Temperature and Pressure

     

    Equation 2: Maximum Allowed Frequency Due to Sampling Rate

    Figure 1: PVC Pipe Used in Experiment

    Figure 2: Amplitude of Calibration Curve

    Figure 3: Relative Amplitude – All Holes Closed

    Figure 4: Relative Amplitude – All Holes Open

    Figure 5: Relative Amplitude – Hole 7 Closed, All Others Open

    Figure 6: Relative Amplitude – Hole 7 Open, All Others Closed

    Figure 7: Relative Amplitude – Holes 1, 2, 4, 7 Open, All Others Closed

    Figure 8: Relative Amplitude – Holes 3, 4, 5, 6, 7 Open, All Others Closed

    Figure 9: Relative Amplitude – Holes 2, 4, 6, 8 Open, All Others Closed

    Figure 10: Relative Amplitude – Hole 5 Open, All Others Closed

    Figure 11: Relative Amplitude – Holes 4, 5, 6 Open, All Others Closed

    Figure 12: Relative Amplitude – Holes 6, 7, 8, 9 Open, All Others Closed

    Figure 13: Relative Amplitude – Holes 3, 6, 9 Open, All Others Closed

    Figure 14: Relative Amplitude – Holes 2, 3, 4, 5, 6, 7, 8 Open, All Others Closed