Introduction to Acoustics

found from
�
LW = Lp + 10 log A
+ 4.34
A0
A
S
�
+ 10 log 1 + Sc
�
8Vf
� �
427 273
−25 log
400 273 + θ
� �
B
− 6
B0
dB re 10 −12 W , (23.31)
where LW is the band sound power level of the sound
source under test, Lp is the band space-averaged sound
pressure level of the sound source under test, A is the
equivalent absorption area of the room, given by:
A = 55.26
� �
V
,
c Trev
V is the room volume, Trev is the reverberation time for
the particular band, A0 is the reference absorption area,
S is the total surface area of the room, f is the midband
frequency of the measurement, c is the speed of sound
at temperature θ in ◦C, B is the atmospheric pressure,
with B0 = 1.013 × 105 Pa, V0 = 1m3 , T0 = 1s.
Diffuse sound fields can be obtained in laboratory
reverberation rooms. Sufficiently close engineering
approximations to diffuse-field conditions can be obtained
in rooms that are fairly reverberant and irregularly
shaped. When these environments are not available or
when it is not possible to move the noise source under
test, other techniques valid for the in situ determination
of sound power level may be used and are described later
in this section.
Non-steady and impulsive noises are difficult to measure
under reverberant-field conditions. Measurements
on such noise sources should be made under free-field
conditions.
Sound Power Determination
in an Ordinary Room
The sound pressure field in an ordinary room such as
an office or laboratory space that has not been designed
for acoustical measurements is neither a free-field nor
a diffuse field. Here the relationship between the sound
intensity and the mean-square pressure is more complicated.
Instead of measuring the mean-square pressure,
it is usually more advantageous to use a sound intensity
analyzer that measures the sound intensity directly
(Sect. 23.1.8). By sampling the sound intensity at defined
locations in the vicinity of the source, the sound
power level of the source can be determined. A standard
for the in situ determination of sound power is also
available, and is described below.
Noise 23.2 Noise Sources 973
Source Directivity
Most sources of sound [23.15, 16] of practical interest
are directional to some degree. If one measures the sound
pressure level in a given frequency band a fixed distance
away from the source, different levels will generally be
found for different directions. A plot of these levels in
polar fashion at the angles for which they were obtained
is called the directivity pattern of the source.
The directivity factor Qθ is defined as the ratio of the
mean-square sound pressure, p2 θ , at angle θ and distance
r from an actual source radiating W and the mean-square
sound pressure p2 S at the same distance from a nondirectional
source radiating the same acoustic power W.
Alternatively, Qθ is defined as the ratio of the intensity
in the direction of propagation W/m2 at angle θ and distance
r from an actual source to the intensity at the same
distance from a nondirectional source, both sources radiating
the same sound power W. It must be assumed
that the directivity factor is independent of distance from
the source.
The directivity index DIθ of a sound source on a rigid
plane (radiating into hemispherical space) at angle θ and
for a given frequency band is computed from
DIθ = Lpθ −〈Lp〉H + 3dB, (23.32)
where Lpθ is the sound pressure level measured a distance
r and angle θ from the source, and 〈Lp〉H is the
sound pressure level of the space-averaged mean-square
pressure averaged over a test hemisphere of radius r (and
area 2πr 2 ) centered on and surrounding the source.
The 3 dB in this equation is added to 〈Lp〉H because
the measurement was made over a hemisphere
instead of a full sphere. The reason for this is that the
intensity at radius r is twice as large if a source radiates
into a hemisphere as compared to a sphere. That
is, if a nondirectional source were to radiate uniformly
into hemispherical space, DIθ = DI = 3 dB. Equations
are available for sound radiation into a sphere and into
a quarter sphere [23.15, 16].
23.2.2 International Standards for the
Determination of Sound Power
The International Organization for Standardization
(ISO) has published a series of international standards,
the ISO 3740 series [23.17], which describes several
methods for determining the sound power levels of noise
sources. Table 23.3 summarizes the applicability of each
of the basic standards of the ISO 3740 series. The most
important factor in selecting an appropriate noise mea-
Part G 23.2