Architecture and Sound

From UBC Wiki

Sound waves can be either be deterred or absorbed by the barriers that surround them.[1] Much of the effect is determined by the characteristics of the barriers.[2] Hence, deterrence and absorption can be manipulated by setting up specific types of barriers around the sound waves.[3] Different barriers might be ideal depending on the types of sound waves they are interacting with, and the result that is wanted.[4] Upon reaching a barrier, sound waves can change direction by being reflected, and this reflection is correlated with accumulation of sound.[5] Most barriers, however, only reflect part of the wave. Part of the non-reflected wave is absorbed at a ratio called the absorption coefficient.[6]

Barrier Materials and Characteristics

The phenomenon of absorption is caused by the sound wave making the barrier vibrate. Variation in absorption coefficients between different barrier materials is caused by mass of the material, because this informs how significantly the sound wave can make the barrier vibrate. Higher flexibility (lower mass, easier vibration) is correlated with higher absorption. Higher mass (lower flexibility, harder vibration) is correlated with lower absorption.[7]

It is observed that flooring materials such as tile absorb an infinitesimal amount; whereas flooring materials such as carpet absorb on a larger scale.[8] The high mass and low flexibility of tile cause reflectivity, because sound waves cannot make it vibrate significantly.[9] The low mass and high flexibility of carpet causes absorption, because sound waves can make it vibrate significantly. Carpet absorbs effectively for a second reason, too. Carpet integrally contains air (between the loops), which is a low density “barrier” with complete absorption.[10] Thus, carpet mixes flexible material with low density material.[11]

In architecture, air must be considered a barrier.[12]

Absorption Coefficients and Hall Absorption (α)[13]

The absorption in the hall involves both the dimensions of each barrier, and the absorption coefficients of each barrier. If the coefficients of each barrier are multiplied by area, the absorption coefficient of the barrier can be determined (White and White call this the “total absorbing area”).[13][14] White and White formulate this as:

S = S1α1 + S2α2 + S3α3 + … where Sn = the absorption area of a given barrier, and α = the absorption coefficient of the barrier’s material.[15]

As an example, the formula will be applied to a model (cardboard U-Haul box).[16] The declared dimensions of the box are (l x w x h): 16.375” x 12.625” x 12.625”. Two sides contain holes that are about 3.5” long and 1” tall (rounded to the nearest 0.5”). Therefore, the area of each barrier is:[17][18]

Floor and Ceiling (Bottom and Top): 206.73 in2 each
Longitudinal Walls (Sides): 206.73 in2 – 1” x 3” hole = 203.73 in2 each
Open Windows (Holes in Longitudinal Sides): 3 in2 each
Lateral Walls (Sides): 159.39 in2 each

The cardboard box will be analyzed as if it was made up of barrier materials as follows (material coefficients in brackets):[19]

Ceiling: “Mineral wool tiles, 180mm airspace” (α = 0.76)
Floor (A): “Smooth marble or terrazzo slabs” (α = 0.013)
Floor (B): “9mm pile carpet, tufted on felt underlay 9mm” (α = 0.44)
Longitudinal and Lateral Walls: “Painted plaster surface on masonry wall” (α = 0.02)
Open Windows: Air (α = 1.00)

The absorption coefficient for each barrier is Sn x αn:

Ceiling: 206.73 x  0.76 = 157.11 in2
Floor (A): 206.73 x 0.013 = 2.69 in2
Floor (B): 206.73 x 0.44 = 90.96 in2
Longitudinal Walls: 203.73 x 0.02 = 4.07 in2
Open Windows (Holes in Longitudinal Sides): 3.00 x 1.00 = 3.00 in2
Lateral Walls (Sides): 159.39 x 0.02 = 3.19 in2

The absorption coefficient of the room is:

S = Sceilingαceiling + Sfloorαfloor + (Slongitudinal wallαlongitudinal wall)*2 + (Sopen windowαopen window)*2 + (Slateral wallαlateral wall)*2

With Floor (A): 157.11 + 2.69 + 4.07*2 + 3.00*2 + 3.19*2 = 180.32 in2
With Floor (B): 157.11 + 90.96 + 4.07*2 + 3.00*2 + 3.19*2 = 268.59 in2

The absorption coefficient of Floor A (marble/terrazzo, α =2.69) is a monumentally smaller number than the absorption coefficient of Floor B (carpet, α = 60.96). It is observed that the resulting "total absorbing area" of Floor (A) is also smaller than the "total absorbing area" of Floor (B).[20]

Absorption with a Noise-Maker

An attempt to demonstrate this variation in absorption is demonstrated with a noise-maker installed inside the cardboard box. A metal lid is taped to the inside ceiling of the box. The lid has a hole in it, and a string runs from outside the box, through the lid, down into the box. The end of the string inside the box is tied to a metal ring. To make a noise, the outside end of the string (tied to another ring for practical reasons) is pulled vertically till the inside ring hits the lid.[21]

An iPhone earbud microphone is hung inside the box and connected to a laptop with Audacity running, which recorded the audio for Floor (A) and Floor (B).[22][23]

Fig. 1: Noise-Maker without Towel (own work)
Audio 1: Recording of Noise-Maker, Floor (A) (own work)
Fig. 3: Noise-Maker with Towel (own work)
Audio 2: Recording of Noise-Maker, Floor (B) (own work)
  1. White, Harvey E. and Donald H. White. Physics and Music: The Science of Musical Sound. Dover Publications: Mineola, New York (2014). 352-3 Note: “transmission” is the third option listed by White and White, and "diffraction" is a fourth (42). The term "barrier" is from White and White. Also, likely Pritchard, Robert. Musc 119 lecture(s)/slide(s)/lab(s) (and coursepack?)
  2. As described by Harvey E. White and Donald H. White, Physics and Music: The Science of Musical Sound, Dover Publications: Mineola, New York (2014), the characteristic of the sound wave also has an effect (353-4). Also, likely, Pritchard, Robert. Musc 119 lecture(s)/slide(s)/lab(s) (and coursepack?)
  3. White, Harvey E. and Donald H. White. Physics and Music: The Science of Musical Sound. Dover Publications: Mineola, New York (2014). 351-7. Also, likely, Pritchard, Robert. Musc 119 lecture(s)/slide(s)/lab(s) (and coursepack?)
  4. White, Harvey E. and Donald H. White. Physics and Music: The Science of Musical Sound. Dover Publications: Mineola, New York (2014). 353-4, 356, 363-5, 368-9, 370, 377-8. Also, possibly, Pritchard, Robert. Musc 119 lecture(s)/slide(s)/lab(s) (and coursepack?)
  5. White, Harvey E. and Donald H. White. Physics and Music: The Science of Musical Sound. Dover Publications: Mineola, New York (2014). 41-3, 352, 355, 360, 363-4, 370 Also, likely, Pritchard, Robert. Musc 119 lecture(s)/slide(s)/lab(s) (and coursepack?)
  6. White, Harvey E. and Donald H. White. Physics and Music: The Science of Musical Sound. Dover Publications: Mineola, New York (2014). 352-3, 355-7. Pritchard, Robert. Musc 119 lecture(s)/slide(s)/lab(s) (and coursepack?) included a discussion of absorption, possibly also coefficients.
  7. White, Harvey E. and Donald H. White. Physics and Music: The Science of Musical Sound. Dover Publications: Mineola, New York (2014). 352-6 Also, possibly, Waltham, Chriss. PHYS 341 lecture(s)/slide(s).
  8. White, Harvey E. and Donald H. White. Physics and Music: The Science of Musical Sound. Dover Publications: Mineola, New York (2014). 352, 355, 357. Also, possibly, Pritchard, Robert. MUSC 119 lecture(s)/slide(s)/lab(s) (and coursepack?)
  9. White, Harvey E. and Donald H. White. Physics and Music: The Science of Musical Sound. Dover Publications: Mineola, New York (2014). 352-3.
  10. White, Harvey E. and Donald H. White. Physics and Music: The Science of Musical Sound. Dover Publications: Mineola, New York (2014). (352-3) 354-7 White and White also describe another, more complex function of air when it is part of (rather than replaces) the absorption mechanism: "resonating cavities" (355-7). See also the absorption coefficient of carpet versus other flooring, in Acoustic Materials & Technologies Ltd. “Absorption Coefficients.” www.acoustic.ua/st/web_absorption_data_eng.pdf. Accessed April 6, 2020. Absorption coefficients calculated by averaging coefficients of all given frequencies (range: 125-4000 Hz) for each material, which are given in the above article. Also, possibly, Pritchard, Robert. MUSC 119 lecture(s)/slide(s)/lab(s) (and coursepack?).
  11. White, Harvey E. and Donald H. White. Physics and Music: The Science of Musical Sound. Dover Publications: Mineola, New York (2014). (352-3) 354-7 White and White also describe another, more complex function of air when it is part of (rather than replaces) the absorption mechanism: "resonating cavities" (355-7). See also the absorption coefficient of carpet versus other flooring, in Acoustic Materials & Technologies Ltd. “Absorption Coefficients.” www.acoustic.ua/st/web_absorption_data_eng.pdf. Accessed April 6, 2020. Absorption coefficients calculated by averaging coefficients of all given frequencies (range: 125-4000 Hz) for each material, which are given in the above article.
  12. White, Harvey E. and Donald H. White. Physics and Music: The Science of Musical Sound. Dover Publications: Mineola, New York (2014). 352, 366-7, 368, (373-4). lecture Also, according to White and White, air temperature involves another process: refraction. Also discussed by both Waltham, Chris in PHYS 341 lecture (and slides?) and White & White mostly regarding antinodes in pipes with an open end. Air in relation to sound waves and absorption may have been discussed by Pritchard, Robert. MUSC 119 lecture(s)/slide(s)/lab(s) (and coursepack?).
  13. 13.0 13.1 "absorbtivity" is synonymous with "absorption coefficient," according to White and White (356).
  14. White, Harvey E. and Donald H. White. Physics and Music: The Science of Musical Sound. Dover Publications: Mineola, New York (2014). 365-8. May have also been discussed by Pritchard, Robert in MUSC 119 lecture(s)/slide(s)/lab(s) (and coursepack?).
  15. Formula copied from: White, Harvey E. and Donald H. White. Physics and Music: The Science of Musical Sound. Dover Publications: Mineola, New York (2014). 365-8. May have also been discussed by Pritchard, Robert in MUSC 119 lecture(s)/slide(s)/lab(s) (and coursepack?), but not sure about this formula.
  16. For further reading, view this article, which discusses cardboard and sound: Berardi, Umberto and Gino Iannace. Acoustic characterization of natural fibers for sound absorption applications. Building and Environment, Vol. 94, Pt. 2. December 2015. 840-52. www.sciencedirect.com/science/article/abs/pii/S036013231530007X#!
  17. White, Harvey E. and Donald H. White. Physics and Music: The Science of Musical Sound. Dover Publications: Mineola, New York (2014). 352, 366-7, 368, (373-4), 366, explanation in figure 27-2. The list of items to include in the calculation was taken from 365-6. Possibly also Pritchard, Robert. MUSC 119 lecture(s)/slide(s)/lab(s). Possibly also Waltham, Chris. PHYS 341 lecture(s)/slide(s).
  18. White and White (2014) describe the use of either Sabins (square feet) or square meters (365). Here, S is in square inches.
  19. Names of materials quoted from: Acoustic Materials & Technologies Ltd. “Absorption Coefficients.” www.acoustic.ua/st/web_absorption_data_eng.pdf. Accessed April 6, 2020. Absorption coefficients calculated by averaging coefficients of all given frequencies (range: 125-4000 Hz) for each material, which are given in the above article. I feel like I may have gotten the multiplication approach from somewhere, but I'm not sure where. Possibly Chris Waltham, or another skill.
  20. White, Harvey E. and Donald H. White. Physics and Music: The Science of Musical Sound. Dover Publications: Mineola, New York (2014). 365-8, also see discussion and references above. Materials and coefficients draw from Acoustic Materials & Technologies Ltd. “Absorption Coefficients.” www.acoustic.ua/st/web_absorption_data_eng.pdf. Accessed April 6, 2020. Absorption coefficients calculated by averaging coefficients of all given frequencies (range: 125-4000 Hz) for each material, which are given in the above article.
  21. The idea for this contraption may be somewhat inspired by designs in White, Harvey E. and Donald H. White. Physics and Music: The Science of Musical Sound. Dover Publications: Mineola, New York (2014). For example, the component of suspension in a project on pg. 36. However, the purpose in my contraption is different than on pg. 36.
  22. The proportional thickness of Floor (B) was not replicated precisely in this demonstration. This rough simulation may actually be exaggerated. Floor (B) is simulated by a towel installed on the bottom of the cardboard box.
  23. c.f. the relationship between these two concepts: "reflection" and "reverberation" discussed in White, Harvey E. and Donald H. White. Physics and Music: The Science of Musical Sound. Dover Publications: Mineola, New York (2014). 357, 360, 363, 364, 370. Also, Waltham, Chris. PHYS 341 lecture(s)/slides/ Also, possibly, Pritchard, Robert. MUSC 119 lecture(s)/slide(s)/lab(s) (and coursepack?). AND "Decay" in Waltham, Chris. PHYS 341 lecture(s)/slides (incl.16-19 (partly citing White and White, 2014, see below)) c.f. White, Harvey E. and Donald H. White. Physics and Music: The Science of Musical Sound. Dover Publications: Mineola, New York (2014). 15 Also, Pritchard, Robert. MUSC 119 lecture(s)/slide(s)/lab(s) (and coursepack?).