# Improving Acoustics in a Church’s Multipurpose Room

This is a slightly polished-up version of a quick report I wrote for a local church, recommending ways to improve the noisy acoustics of a room used for post-service conversation and snacks.  It’s not meant to be slick or a masterpiece of writing. This is just a text dump, formatting ignored.

Improvement to Acoustics in a Multipurpose Room at a Local Church United
2016-Oct-16
Daren Scot Wilson, B.S. Physics
720-253-2646
darenw@darenscotwilson.com

PROBLEM SUMMARY after the 2nd service, when the crowd filtered out of the sanctuary and headed for coffee and conversation, the room with the round tables, known as Fellowship Hall, became quite noisy. At a table of three, one fine fellow said that it was hard to hear the other person and myself only 3 feet away. I have heard similar comments during past Sundays. There is plenty of reverb. A cacophony of conversation arises during peak snack time. I imagine the acoustics of that room could be a problem anytime the room is used for any purpose except pantomime classes (were the church to do such a thing.)

Main observations on the problem:
* Mostly human voice frequencies
* Bass frequencies are not much of a problem
* The room’s N wall, and the S side consisting mostly of closed closet doors, are a parallel pair of flat hard surfaces. Parallel walls are a common cause of “slap echo” which interferes with conversation.
* The W and N walls are fairly hard, reflecting more sound than desired.
* The ceiling slopes join at close to 45 degrees, making a partial corner reflector. Anyone sitting anywhere but the centerline of the room will hear, more clearly than usual, sounds originating from certain other parts of the room, typically people not involved in the same conversation.
This is work for a Physicist! Or at least for a physicist to make some initial observations and recommendations to consider and inspire owners and leaders to ask an experienced building acoustics professional.

“Architectural acoustics did not exist on a scientific basis until a young professor of physics at Harvard University in 1895 corrected the abominable acoustics of the newly constructed Fogg Lecture Hall.” [small edit for grammar] – Ar. Mukunda K.S, Dean of School of Architecture, some school in Bangalore

THREE MAIN ASPECTS FOR A SOLUTION
* Absorbers: complex objects, holes, cloth, foam, fiber, bass trap. These reduce the overall sound power filling the room.
* Diffusers: complex objects, beams, columns, boxes, panels. These scatter the sound, breaking up hard echoes, defocusing sound from each specific source.
* Reflectors: at crazy angles, to escort unwanted sound out of the room or into holes or absorbers. Likely not useful for this situation, but may play some role.

I should also mention blocking – thick walls, steel plates and such – but this is a special case of absorbing and reflecting. Walls are of architectural nature, and not really practical for fixing the acoustics of an existing room. Also, great distances will make any noise quiet, but not relevant for solving a problem within a room.
Fellowship Hall needs mostly absorption. My best guess is that a mere -5dB reduction of all noise received at any typical point, from an average source anywhere else in the room, would help greatly. People *do* converse, and mostly *do* understand each other, most of the time, but often it’s right at the edge of becoming unclear. There’s only about 5dB difference in SNR between the best of difficult conversation muddled by echos, and acceptable quality conversation. Another 5dB or more will allow easy clear conversation.

We should aim for -4dB to -8dB reduction in total power received anywhere in the room from all sources, in the frequency range 200 to 3500 Hz. We don’t need more than that. A little more, okay. Too much reduction will make the room “dead” or “flat” which, ironically, also makes conversation less pleasant. Absorbers are best, but some scatterers will help reduce impulse slap, to “de-color” the reverb.

Note that this report is about sound generated and reverberating within one room. Not relevant are other acoustics problems such as outside noises (from elsewhere in the building or from outdoors) intruding into a quiet room, and preventing loud noises within the room from escaping to annoy surrounding areas.

PROPOSED EASY SOLUTIONS – Inexpensive and Good Enough
1. Foam/fibery panels or thick objects on walls. Cover 1/3 or more of total wall area of W, N walls, with object at least 6 inches thick, and ideally of irregular shapes. If rectangular, aim for different sizes and varying spacings between them.
2 Drapes for windows. Can be effective even when open, if not bunched up real tight.
3. Hang some new lighting fixtures, and/or some sort of banner/flag/sign from ceiling.
4. If some large object or two could be placed in the corner, or somewhere, not interfering with traffic or vital coffee supply operations, even if acoustically reflective, would help scatter the sound, softening any sources “seen” through corner reflectors or large flat walls.
5. We do use tablecloths on all the tables, don’t we? Cheap and easy, except someone has to put them through laundry regularly. It’s not the softness of cloth compared to the hard table tops that matters, but the overhang of soft cloth from tabletop to near the floor. Low frequency “boominess” will be reduced slightly.

LIST OF MORE GENERAL GENERAL SOLUTIONS:
* Decorative fully 3D objects on ceiling, wall. Candle-holders, large thick cross, sculptures…
– Intricate elements, irregular patterns.
– Any material, but better with absorbers = fibery material, glass wool
– Thick, though even an ordinary painting against the wall will help a little.
* Cloth hangings, curtains/drapes, towels on hooks… anything soft anywhere in sufficient amounts
* Foam, slabs of glass fiber, or “egg-carton” boards on wall.
– Rockwool is popular brand.
– 1/2″ thick will do for us. Is not a recording studio.
– make several pieces 1ft square to 2x3ft or so. arrange artistically on wall.
– standoffs about 2″ or so help reduce frequencies not directly snuffed by panel.
– foam fins in strategic places, corners, foam “stairs”
– for a room intended for kids, painted literal egg cartons are cheap and effective.
* Latticework room dividers or against wall a few inches away. Dividers can interfere with traffic, however.
* Add shelves with random objects, with gaps between vases/books
* Remodeling to avoid parallel surfaces.
– Remove last 2 of the 3 closets, or the first of the three.
– Add decorative semi-columns to N, W walls.
– Fill in corners w diagonal surface, about 3ft across
– probably the most expensive way to fix acoustics
* Chandelier or pendant lighting fixtures
* Rectangles of cloth, or boards of wood or plastic, hanging from the ceiling. Qualcomm does this to scatter, block and reduce talking noise in their open cubicle farms.
* Fuzzier carpet (but much is hidden under tables, has little effect)
* Tablecloths act as bass traps.
– not much needed in this situation. Bass is not the problem.
* Look for existing flat surfaces of brick, linoleum, glass, thick wood. Obscure them.

– Cost.
– Cleaning. We don’t want high-efficiency dust-catchers.
– Fire safety.
– Installation effort, skill, materials, disruption to normal activities.

CAUTIONS
* Do not overdamp. Room will feel “dead”
* Do something to reduce/control high frequencies, do something else for mid-range, and do something for bass. Unlikely one treatment will fix all of the problem at once.
* Ignore articles aimed at home/amateur music studios, audiophile setups, auditoriums, concert halls. We’re not putting on pricey concerts with the finest opera singers during coffee & fellowship time, are we?

FACTOIDS from various source, not necessarily consistent or verified
* 1 KHz = 1 foot wavelength. 200Hz = 5 ft.
* Human voice power is mostly in frequency range 300 to 3500 Hz.
* Fundamental of Human voice is within 90 to 250 Hz. Male 85-180, fem 165-255. For practical easy math use 100 – 300 Hz. But most of our phoneme-distinguishing ability depends more on presence and variations of higher harmonics than on the fundamental.
* Architectural elements and furniture/object details on a scale of around 5 inches, up to 10ft, are important to human voice acoustics. Actually, there’s no upper limit, but that’s the longest wavelength we need to be concerned with.
* Indoors, in a typical room: only about 1/10th to 1/1000th of what you hear is directly from the source. The rest is bounced off wall, ceiling, and objects.

SOURCES, REFERENCES, INFO ON ACOUSTIC, PRODUCTS
in no particular order

Church Acoustics Articles Aimed at churches! This is right on topic for us, but the physics applies just as well to conference rooms or homes. Well-written, educational, does not require existing engineering knowledge. Acoustic Sciences Corp. in Eugene – did work for St Thomas Episcopal (somewhere in Oregon).
http://www.church-acoustics.com/articles/auditorium-acoustics-101/
http://www.church-acoustics.com/articles/auditorium-acoustics-102/
http://www.church-acoustics.com/articles/auditorium-acoustics-103/

Layman’s Introduction to Room Acoustics. Aimed at audiophiles, but physics is the same for everyone. http://www.6moons.com/audioreviews/theroom/3.html

“How to Remove Echo From a Tall Ceiling”
http://homeguides.sfgate.com/remove-echo-tall-ceiling-27539.html
– more oriented for interior decoration, large rooms in fancy houses

http://www.fohonline.com/current-issue/28-theory-and-practice/6969-acoustics-101.html
also has advice on audio mixing, PA systems, live music

http://www.soundonsound.com/techniques/room-improvement

Auralex
http://www.auralex.com/ custom room analysis, kits, sells all kinds of absorbers, diffusors, and serious sound isolation.

– “Roominator” kits for small rooms up to 400 sqft or larger

RealTraps
http://realtraps.com/ aimed at home theater, recording studio, sells  fixes.
but has solutions for other places such as churches and bars.
educational videos:
Diffusors: http://realtraps.com/video_diffusors.htm or https://youtu.be/vb30CICG68c
Absorbers:

Kirei USA

23 Decorative Acoustic Panel Ideas

– see about 1/3 way down: “5. Get Sticky with It and Lower Sound in Style”
– sticky foam pieces attached to wall could be ½ our solution!
– See also plenty of other ideas of ceiling and wall tiles, hanging absorbers.

Church Leaders article – Intro to Acoustics in Churches

Church Acoustics 101

Kinetics Noise Control, Inc.
http://www.kineticsnoise.com/interiors/
products for noise control in all kinds of indoor places. Outdoors, too.

This link goes straight to a PDF paper on noise reduction and acoustics for schools, which have much in common with churches. It’s from the United Kingdom, so if you find yourself in conversation with one of the authors, be sure to say “decibel” with a British accent. http://www.ioa.org.uk/sites/default/files/Acoustics%20of%20Schools%20-%20a%20design%20guide%20November%202015_1.pdf Covers construction methods, floors, absorbers, “Speech Transmission Index” for quantifying clarity of conversation hampered by noise and echo.

A More Thorough Education on Acoustics (online slideshow)
Have spare time and desire to educate yourself on architectural acoustics? Not scared of “decibels” and wavelengths? Try this slide show:

by Ar. Mukunda K.S, Dean School of Architecture, Dayanand Sagar Acadamy of Technology & Management Bangalore

BOOK: Sound Studio Audio techniques for Radio, Television, Film and Recording, 7th Edition
by Alec Nisbett https://www.amazon.com/Sound-Studio-techniques-Television-Recording/dp/0240519116
For reducing external noise, a good article is: http://www.today.com/home/neighbors-too-loud-indoor-noise-solutions-t81876

DISCLAIMER
I, Daren Scot Wilson, am not a professional architectural acoustics expert, just a physicist with some knowledge of waves and sound, and modest experience in music recording. No one should start sawing load-bearing beams in half or permanently gluing stuff to walls due to anything I said here. Consult a proper professional architect or engineer with a PE license, or at least find a better quality self-appointed expert.
UNRELATED but interesting reading for those with too much leisure time

* Acoustic tricks for reduction of toilet flush noise

# One-Tilde: A New Symbol for Wavy Math

For years I’ve been using a symbol in any math involving waves.  Normally, in physics we use radians for angles, and for describing the phase of a wave along time or space.  A typical equation involving vibrations or waves will contain bits like this:

$e ^ {i \omega t}$

and this:

$e ^ { i k x}$

Omega is the angular frequency in radians per second. Angular frequency is great for differential equations, and summing infinite series for numerical computations.

In electronics engineering, radio, music, signal processing, and almost all areas of applied mathematics, we like to count cycles. Hertz, which is cycles per second. Wavelengths, the size of one full cycle.  Convert according to $\omega=2\pi f$.  We write plenty of things like this:

$e ^ {2 \pi i f t}$

and

$latex e ^ {2 \pi i x \lambda}$

You find $2\pi i$ factors all over the place.   Frequency in cycles is much easier for everyday application, for measurement, and for labeling electronic parts.

Sometimes I want to stick with cycle frequency, but prefer not to write $2\pi i$ over and over.   So I invented:

${\rlap {1}{\sim}} = e^{2\pi i}$

Here it is, as an image in case my LaTeX markup doesn’t work right:

We all know that

$e^{2\pi i} = 1$

so maybe I could use just a plain one?  No, because $1^p = 1$; unity to any power doesn’t do anything interesting. The tilde over the one means that, for noninteger $p$, don’t take the principal value but the “next” value.  It works like this:

${{\rlap {1}{\sim}}}^{f t} = (e^{2\pi i})^{f t} = e^{(2\pi if t)} = e^{i\omega t}$

We can write a Fourier transform like this:

$S(t) = \int_{-\infty}^{\infty} A(f){\rlap {1}{\sim}}^{ft} dt$

and reverse it as:

$A(t) = \int_{-\infty}^\infty S(f) {{\rlap {1}{\sim}}}^{-ft} dt$

I find it nice that there’s no $2\pi$ factors appearing anywhere.

When adding waves in the study of X-ray diffraction in crystals, or understanding image formation from radio dish arrays, or toying with harmonics in audio processing, the one-tilde keeps things neat and clean.

## One-Tilde in LaTeX

This works, allows for some adjusting, but leaves out some fine points of good typography.

\newcommand\onetilde{{%
\ooalign{\raisebox{.2ex}{$\sim$}\cr
\hidewidth$1$\hidewidth}}}

$\psi(t) = \onetilde^{ft}$



This is simple, but ugly since there’s no kerning for good taste:

{\rlap {1}{\sim}}

## One-Tilde in Lout

I don’t know yet….