Room acoustics

Sound can propagate through compressible media such as air, water and
solids as longitudinal waves and also as a transverse waves in solids
Longitudinal sound waves are waves of alternating pressure deviations
from the equilibrium pressure, causing local regions of
compression and rarefaction.
Transverse waves (in solids) are waves of alternating shear stress at right
angle to the direction of propagation.
the velocity of sound is constant with reference to space and time. For air,
its magnitude is
c = (331.4+0.6 θ) m/s
where θ is the temperature in degrees centigrade.

A sound ‘unit’ is any acoustic unit of sound measurement.
dB - decibel - noise of sound measurement is called decibels
(dB).
Sone - A unit of perceived loudness equal to the loudness of a
1000 hertz tone at 40 dB above threshold, starting with 1
sone.
Phon - A unit of subjective loudness.
Hz - Hertz = unit of sound frequency is called hertz (Hz)

Hertz
The hertz (symbol Hz) is the unit of frequency in
the International System of Units (SI) and is defined as
one cycle per second.
Speed of sound = Frequency x Wavelength
c = fl
c = Speed of sound
F = Frequency (Hz)
l = Wavelength

Ex 1 If the sound has a frequency of 20 Hz
and travels at a speed of 340m/s, what is the
wavelength of it.

Room Acoustics
 In room acoustics we are mainly concerned with three types of
sound source:
• Human Voice
• Musical Instruments
• Technical and Other miscellaneous noise sources
 At 10 kHz and above the attenuation in air is so dominant that
the influence of a room on the propagation of high-frequency
sound components can safely be neglected.
 At frequencies lower than 50 Hz geometrical considerations are
almost useless because of the large wavelengths of the sounds;
furthermore, at these frequencies it is almost impossible to
assess correctly the sound absorption by vibrating panels or
walls and hence to control the reverberation.

 On the whole, it can be stated that the frequency range relevant to room
acoustics reaches from 50 to 10 000 Hz, the most important part being
between 100 and 5000 Hz.
 The most important sounds we hear every day are in the 250 to 6,000 Hz
range.
Speech includes a mix of low and high frequency sounds:
• Vowel sounds like a short “o” as in the word “hot,” have low frequencies (250
to 1,000 Hz) and are usually easier to hear.
• Consonants like “s,” “h,” and “f,” have higher frequencies (1,500 to 6,000 Hz)
and are harder to hear. Consonants convey most of the meaning of what we
say. Someone who cannot hear high-frequency sounds will have a hard time
understanding speech and language.

• An important property of the human voice and musical instruments is
their directionality, i.e. the fact that they do not emit sound with equal
intensity in all directions.
• In speech this is because of the ‘sound shadow’ cast by the head.

Sound reflection
Hard, rigid and flan surfaces, such as concrete, plaster,
glass, etc., will reflect almost all incident sound energy
striking these surfaces.
This phenomenon of sound reflection is quite similar to
the well known reflection of light.
• The incident and the reflected sound rays lie in the same
plane.
• The angle of the incident sound wave will equal the
angle of reflection (law of reflection).

The behaviour of sound in an enclosed space.
1 incident sound
2 direct wave front
3 reflected sound
4 reflected wave front
5 sound transmitted through enclosure
6 sound absorbed at wall surface
7 sound absorbed in the air
8 sound energy dissipated within the structure
9 structure-borne sound conducted to other parts of the building
10 sound radiated by flexural vibration of the Enclosure
11 acoustic shadow
12 diffraction of sound through opening
13 multiple sound reflection contributing to reverberation
14 diffused sound due to surface irregularities

• It must be remembered, however, that the wavelengths of sound
waves are much larger than those of the light rays, and the law of
sound reflection is valid only if the wave-lengths of the sound
waves are small compared to the dimensions of the reflecting
surfaces.
• Application of this law must be very critically considered for low
frequency sounds and for small rooms.
• Concave reflecting surfaces will tend to concentrate while convex
surfaces will disperse the reflected sou7d waves in the rooms.

Diffraction
Diffraction is the acoustical phenomenon which causes the sound waves
to be bent and scattered around obstacles( corners, piers, columns, walls,
beams, etc.
Less pronounced for low frequency sounds than for high frequency
sounds.
This repeatedly proves that the laws of geometric acoustics are in
adequate to predict precisely the behaviour of sound in enclosed spaces
because the obstacles usually encountered in room acoustics are too
small compared to the wave-lengths of the audible sound waves.
Geometric acoustics, a useful approach in the problems related to high
frequency sounds

Hardly applicable to frequencies below 250 cps, in other words, low
frequency sounds (of long wavelengths) will not respect the laws of
geometric acoustics if they encounter architectural elements of small
dimensions; in particular -
(a) They will not travel in "rectilinear" directions through an opening
(b) They will not diffract, or be scattered by small scale architectural
elements such as beams, coffers, pilasters, cornices, etc. of small
dimensions

Sound absorption AND Absorption coefficient
Change of sound energy into some other form, usually heat, in passing
through a material or on striking a surface. The amount of heat produced
by the conversion of sound energy into heat energy is extremely small.
This phenomenon is called SOUND ABSORPTION.
All the building materials absorb sound in some degree
Effective sound control of buildings will re--quire the application of
materials which are efficient sound absorbents, often termed
"acoustical" materials.

In the various types of Auditoria, the following elements contribute to the
overall sound absorption of the room:
 The surface treatments of the room enclosures, such as walls, floor,
ceiling
 Room contents, such as the audience, seats, draperies, carpets, flowers,
etc.
 The air of the room

The efficiency of the sound absorption of a material at a
specified frequency is rated by the SOUND ABSORPTION
COEFFICIENT
The Sound Absorption Coefficient of a surface is the ratio of the
sound intensity absorbed or otherwise not reflected by the surface
to that of the Initial sound intensity.
It is denoted by the Greek letter alpha α
0 < α < 1α = Ia / Ii
Ia = sound intensity absorbed (W/m2)
Ii = incident sound intensity (W/m2)

FOR EXAMPLE
If at 500 cps an acoustical material absorbs 65 % of the incident sound
energy and reflects 35% of it, then the sound absorption coefficient of
this particular material is 0.65.
• The sound absorption coefficient varies with the angle at which the
sound wave impinges on the material and also with the frequency.
• The sound absorption of a surface is measured in Sabins having the
dimensions of ft2 (in the metric system: m2).

Diffusion
If the sound pressure is the same in all parts of a room and it is probable that
sound waves are traveling in all directions, the sound is said to be homogenous
i.e. Sound Diffusion prevails in that room.
• Adequate sound diffusion is an important acoustical characteristic of certain
types of Auditoria because it promotes a uniform distribution of sound.
• It accentuates the natural qualities of speech and music, and prevents the rise
of various acoustical defects.

Diffusion of sound can be created in several ways:
• By the generous application of surface irregularities and scattering
elements; such as, pilasters, piers, exposed beams, coffered ceilings,
serrated enclosures, etc.
• By the alternate application of sound reflective and sound absorptive
surface treatments.
• By the irregular and random distribution of the sound absorptive
treatments.

Reverberation
 When the source of the sound has stopped, a notice-able time will
elapse before the sound will die away (decay) to inaudibility.
 This prolongation of sound as a result of successive reflections it an
enclosed space after the source of sound is "turned of “ is called
REVERBERATION.
 Reverberation has a distinct effect on the hearing conditions of
Auditoria because its presence will modify the perception of
transient sounds.
 It is an important goal in the reverberation control to secure the
highest intelligibility of speech and the full enjoyment of music.
 The importance of reverberation control in the acoustical design of
Auditoria has necessitated the introduction of a relevant standard
of measure: The Reverberation Time

Time for the sound pressure level in a room to decrease by 60 dB after
the source of the sound is stopped is called REVERBERATION
TIME.
R.T. = 0.16𝑉/𝐴
R.T. is the reverberation time in seconds.
0.16 is a constant
V is the volume of the room in m3
A is the total absorption in m2 units.
Reverberation time

The absorption of a surface is found by multiplying its area by its
absorption coefficient, and the total absorption "A“ is obtained by the
addition of these products with the inclusion of the absorption provided
by the audience and other room contents (seats, furnishings, etc.).
• where S1 …. Sn are the individual areas in m2
• α1 …. αn are their respective absorption
coefficients.

Room acoustics

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