Frequency (f) is the time rate of a periodic
signal. The unit is Hz (Hertz). Pure tone or sine wave has a single
frequency. Sound and noise usually are not pure tones. Fourier
Transform shows that the complex signal can be synthesized from sine
signals (or pure tones) of different frequencies, different
amplitudes and different time delays or (phases). Using this
transform sound can be described as pure tones with defined
amplitudes (or intensities). We can hear sounds with frequencies 16
Hz to 20,000 Hz. The human hearing system (the ears and related
perception system in the brain) is more sensitive to frequencies
around 1000 Hz to 4000 Hz.
The following drawing illustrates
frequency ranges of few sounds:
The wave has frequency therefore it must has what is called
wavelength, which is the distance the sound travels in one cycle
time. The higher the frequency the shorter the wavelength.
These terms are related to the amplitude of
the signal. The absolute value of the sound intensity (I) can be
described in Watts per square meter or W/m², and 10 log (relative
intensities) is the sound level in dB. In sound application the
reference value is 20 µPa for sound pressure or 10E-12 W/m² for
sound intensity. The sound level of the reference values is 0 dB.
This level represents the human threshold of hearing (the lowest
level of sound that one can perceive). The threshold of pain or
feeling (the level that causes pain in the ears) is about 120 dB.
Decibel values cannot be added to obtain the value of the resulting
sound. Instead the combined levels are turned into intensities,
added together and then turned back into decibel values.
Sound absorption coefficient
describes the efficiency of the material or the surface to absorb
sound. The ratio between the absorbed sound energy and the incident
energy is the sound absorption coefficient.
The most common way
to measure sound absorption coefficient is to lay a piece of the
material in the reverberant room (a room which has very long
Reverberation Time) then measure RT so that the coefficient can be
derived from Sabin equation (the original version of RT
calculation). There is a standard that details this procedure. The
value of the coefficient for the same material varies with the type
of the mounting in the test room. Mounting types that are frequently
given in manufacturer's data sheets of the acoustical panels are
illustrated in the following drawing:
Noise reduction coefficient NRC is the arithmetic average,
rounded off to the nearest multiple of 0.05, of the sound absorption
coefficients at 250, 500, 1000, and 2000 Hz.
Acoustical simulation is a technique that
assists the acoustical consultants in the evaluation of the room
acoustics or the performance of the sound systems. In addition to
these studies, acoustical simulation can simulate the sound as it
would be heard after the project is built. This simulation is called
The physical data of the room is entered into the
acoustical program, or the AutoCAD file can be used to transfer the
data. The data entry includes surface materials, background noise,
and the seating layout.
Several acoustical simulation programs
are in use, the popular programs are EASE and CATT.
Some of the
acoustical factors that can be studied in such programs are:
reverberation time, intelligibility, echo, sound levels over the
seating areas, and many othrers. The animation shows ray tracing
from a loudspeaker in a simple room.
The Time-Energy-Frequency (TEF) measurements
and analysis is a technology that uses a swept sinewave test signal.
The TEF device is controlled by a personal computer. The available
domains in TEF measurements include energy-frequency, energy-time,
frequency-time, and energy-frequency-time.
An example of the
energy-time domain is the reverberation time measurement as shown in
the following figure:
Sound in an enclosure can be described as a
diffused sound if the intensity of the sound energy is equal in any
location of the room, or the sound energy flows equally in every
direction. Many different factors can enhance the diffused sound.
These include: geometrical irregularities, absent of focusing
surfaces, absorptive and reflective elements randomly scattered
throughout the space, and the existence of diffusing objects
(furniture) or panels (diffusers).
Diffusing panels scatter sound
in defined directions depending on their type and the geometrical
Reverberation time is the time required for the
sound level in the room to decay 60 dB, or in other words, it is the
time needed for a loud sound to be inaudible after turning off the
sound source. This concept is shown in the following drawing:
of reverberation time using the Sabin equation assumes that the
sound in the room be diffused. In practice, RT equations are good
enough to describe the sound build up and attenuation in the room.
In the case where the sound in the room is not diffused enough, such
as rooms with good absorption surfaces in certain areas, or with an
unusual shape (long and narrow, very low ceiling, or has many
different focusing surfaces), the RT calculation is not accurate.
There is Fitzroy equation to correct the RT calculation for rooms
with good absorptive surfaces on certain axes of the room.
optimum reverberation time for different rooms depends on the volume
of the space, the type of the room, and the frequency of the sound.
In general terms, the optimum RT for rooms with speech programs is
less then the optimum RT for rooms with music performance.
Noise paths in a building are illustrated in the
The human hearing system has different
sensitivities at different frequencies. This means that the
perception of noise is not equal at all frequencies. Noise with
significant measured levels (in dB) at high or low frequencies will
not be as annoying as it would be when its energy is mainly in the
middle frequencies. In other words, the measured noise levels in dB
will not reflect the actual human perception about the loudness of a
noise. A specific circuit is added to the sound level meter to
correct its reading. This reading is the noise level in dBA. The
letter A is added to indicate the correction that was made in the
The following table displays A-weighted sound levels
for some common noises:
||Car 65 mph at 25'
||Light traffic at 100'
||Quiet residential (daytime)
||Quiet residential (nighttime)
||Sewing machines at 3'|
TL, STC and
The transmission loss (TL) for a partition is defined
as the difference in decibels between the sound intensities on two
sides of the barrier.
Sound transmission class (STC) is a single
number used to characterize the air-borne isolation properties of a
partition. The STC is determined from the TL measured at different
frequencies. These measured values are then compared with a family
of STC reference contours. Simple rules apply in choosing the
appropriate contour. For example: STC for painted concrete block
depends on its weight, but will be in the range of 45-48 for 8", and
of 47-51 for 12".
The STC of the composite structure (wall and
window for example) is not the sum of the STC of its components. We
have first to calculate the TL for the composite wall (taking into
account the surface area of the components) then find the STC
Impact isolation class (IIC), like STC, is another
single-number rating system for a solid-borne noise (floor-ceiling
structure). The higher the IIC rating, the more efficient the
construction will be in attenuating the impact sound within the
frequency range of the IIC. For example: 6" reinforced concrete slab
(75 lb/sq ft) has IIC 34, and more then 54 when carpet with pad
cover the floor.