The document discusses architectural acoustics, the science of sound in buildings, focusing on reverberation, absorption coefficients, and the differences between live and dead rooms. It highlights the health impacts of good versus poor acoustics and provides formulas for calculating reverberation time, notably Sabine's and Eyring's formulas. Effective design of spaces like auditoriums can enhance sound quality and audience experience.

1. Architectural Acoustics

2. Contents
• Acoustic and Architectural Acoustic
• Reverberation and Reverberation Time
• Absorption co-efficient
• Live room and Dead room
• Sabines Formula
• Eyring’s Formula
• Eyring’s Formula To Sabine’s Formula

3. 3
Acoustics
• Acoustics is actually a branch of physics that focuses on studying
sound, how it’s produced, transmitted, controlled, and received, and the
effects of this process.
• There are a few sub-discipline of Acoustics
• Architectural acoustics
• Bioacoustics
• Electroacoustics
• Musical acoustics and more.
In next few slide I will discuss about Architectural Acoustics.

4. 4
Architectural Acoustics
• Architectural acoustics (also known as building
acoustics) is the science and engineering of
achieving a good sound within a building and is a
branch of Acoustical Engineering.
• The first application of modern scientific methods
to architectural acoustics was carried out by the
American physicist Wallace Sabine in the Fogg
Museum lecture room. He applied his newfound
knowledge to the design of Symphony Hall,
Boston. Wallace Clement Sabine

5. 5
Architectural Acoustics
• Architectural acoustics, fundamentally, is the relationship between
a sound produced in a space and its listeners. But it can be so much
more than that!
• Positive architectural acoustics can benefit people’s health,
wellbeing and overall quality of life whereas poor acoustics and
noise disturbance can negatively impact our life.
• For example, The World Health Organisation (WHO) reports that
excessive overnight noise disturbs sleep, raises blood pressure and
can even increase the incidence of heart disease.

6. 6
Reverberation
• Reverberation is when sound waves continue to vibrates after
the original source of the sound has stopped emitting sound.
• Sound produced in a room will repeatedly bounce off
reflective surfaces such as the floor, walls, ceiling, windows or
tables while gradually losing energy. When these reflections
mix with each other, the phenomena known as reverberation is
created. So, that define Reverberation as a collection of
many reflections of sound.

7. 7
Reverberation Time
Reverberation time is a measure of the time required for reflecting
sound to "fade away" in an enclosed area after the source of the
sound has stopped.
Reverberation time T =
0.163 V
Σ S α
sec/m [M.K.S]
Where:
S = Surface area of material
α = Absorption coefficient of the material of the wall
V = Volume of the room

8. 8
Reverberation Time
Carnegie Hall in New
York City: 1.7
seconds
Boston Symphony
Hall: 1.8 seconds

9. 9
Absorption Co-efficient
s
• There is a way to quantify how much
sound is reflected or absorbed in a room
by using a metric called the absorption
coefficient. In a nutshell, an Absorption
Coefficient is a measure of how much
sound is absorbed, and NOT reflected.
• The absorption coefficient ranges
between zero and one, one meaning no
sound energy is reflected and the sound
is either absorbed or transmitted. An
effective absorber will have a sound
absorption coefficient greater than .75
Table 1: The absorption coefficients of the materials
used in the auditorium

10. 10
Live Room And Dead Room
Live room:
A room where the absorption co-efficient is less than 0.4 which is
very small and the reverberation time will be large such a room is known as
live room.
Dead room:
A room where the absorption co-efficient is greater than 0.4 which
is very small and the reverberation time will be lowered such a room is
known as live room.

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Live Room And Dead Room
Live room Dead room
Having absorption ci-efficient less than
0.4
Having absorption ci-efficient greater
than 0.4
Reverberation time is larger Reverberation time is larger
Clarity of sound is adequate Clarity of sound is maximum
Intensity is high Intensity of sound is minimum
Not suitable for public addressing
system.
Best suited for speaking and concerts
Difference between Live room and Dead room:

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12
Live Room And Dead Room
Which room is good for auditorium?
Because of maximum sound clarity, minimum intensity and having a
larger absorption co-efficient than live room, Dead room is more
suitable for speaking and concerts. That’s why dead room are used
for designing modern auditorium and music hall.

13. 13
SABINES FORMULA
Sabines Formula:
T =
𝟎.𝟏𝟔𝟑 𝐕
𝐀
[M.K.S]
Where,
V = the volume of the enclosed area
A = the total absorption of the enclosed area
Again, if velocity of sound C = 1116ft, then
Reverberation time t =
𝟎.𝟎𝟓 𝐕
𝐀
[F.P.S]

14. 14
Eyring’s Formula
Eyring’s formula
T =
𝟎.𝟏𝟔𝟑 𝐕
−𝑺 log𝒆(𝟏−𝜶)
Where,
S = Total area of the four walls of the room
V = Volume
𝜶 = Absorption co-efficient

15. 15
Eyring’s Formula To Sabine’s Formula
We know that,
Eyring’s formula for the reverberation time of a dead room is
denoted as
T =
𝟎.𝟏𝟔𝟑 𝐕
−𝑺 log𝒆(𝟏−𝜶)
(1)
Now,
log𝒆(𝟏 − 𝜶) = - 𝜶-
𝜶𝟐
𝟐
-
𝜶𝟑
𝟑
- ……
Since 𝜶 is very small, therefore higher derivatives will be
negligible.

16. 16
Eyring’s Formula To Sabine’s Formula
So ,
log𝒆(𝟏 − 𝜶) = - 𝜶
From (1) ,
T =
𝟎.𝟏𝟔𝟑 𝐕
−𝑺 (− 𝜶 )
=
𝟎.𝟏𝟔𝟑 𝐕
𝑺 𝜶
So, Reverberation time,
T =
𝟎.𝟏𝟔𝟑 𝐕
𝐀
where [A = 𝑺 𝜶 ]

17. THANK YOU
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