Handbook for Sound Engineers

218 Chapter 9

where,
m is called the decay index, and it takes into account the
temperature and the humidity of the air as a function
of the frequency of the sound.

The value of m has been determined both analyti-
cally and experimentally for various conditions of
temperature and humidity over a range of frequencies
extending from 100 Hz to 100 kHz and an examination
of the data shows that the absorption of air increases
with increased frequencies and that for a given
frequency the maximum absorption takes place for
higher relative humidity.
Since the distance x traveled by sound waves in a
physical model are scaled down in a linear fashion (i.e.,
by the scale factor), one cannot expect the attenuation of
the waves inside the model to accurately reflect the
absorption of the air since the loss factor K follows an
exponential decay that is dependent upon the term m
that is itself affected by the physical properties of the
medium. In a scaled physical model this discrepancy is
taken into account by either totally drying the air inside
the model or achieving conditions of 100% relative
humidity; in either case, the approach yields a simpler
relation for m that becomes solely dependent on temper-
ature and frequency. For example, in the case of totally
dry air the decay index becomes

(9-5)

and under these conditions, it is clear that the dominant
term that dictates the loss of energy in the sound wave is
the frequency f since m is proportional to f 2 and varies
only slightly with the temperature T.
Another available option to account for the differ-
ences in the air absorption between a scaled physical
model and its full-size representation is to use a
different transmission medium in the model. Replacing
the air inside the model with a simple molecular gas like
nitrogen will yield a decay index similar to that of Eq.
9-5 up to frequencies of 100 kHz but this is a cumber-
some technique that limits the usability of the scale
model.

9.2.1.4 Source and Receiver Considerations in Physical
Models

To account for the primary phenomena (defined in
Table 9-1) that take place over a range of frequencies
from 40 Hz to 15 kHz inside a full-size room, one needs
to generate acoustic waves with frequencies extending
from 400 Hz to 150 kHz if a 1:10 model is used, and the

required range of test frequencies becomes 800 Hz to

300 kHz in the case of a 1:20 scale model. The difficul-

ties associated with creating efficient and linear trans-

ducers of acoustical energy over such frequency ranges

are a major issue associated with the use of physical

scale models in acoustics.

Transducers of acoustical energy that can generate

continuous or steady-state waves over the desired range

of frequencies and that can also radiate the acoustical

energy in a point-source fashion are difficult to design,

thus physical scale models often use impulse sources for

excitation; in these instances the frequency information

is derived from application of transform functions to the

time-domain results. One commonly used source of

impulse is a spark generator as shown in Fig. 9-4 where

a high voltage of short duration (typically ranging from

less than 20μs to 150μs) is applied across two conduc-

tors separated by a short distance. A spark bridges the

air gap and the resulting noise contains substantial

high-frequency energy that radiates over an adequately

spherical pattern.

Although the typical spark impulse may contain

sufficient energy beyond 30 kHz, the frequency

response of a spark generator is far from being regular

and narrowing of the bandwidth of the received data is

required in order to yield the most useful information.

The bandwidth of the impulse 'f impulse and its duration

Wimpulse are related by the uncertainty principle

(9-6)

When dealing with impulses created with a spark

generator, the received data must be processed via a

bandpass filter of order to eliminate distortion associ-

ated with the nonlinearity of the spark explosion, but the

m 33 +0.2T 10

12–

f

2

=

Figure 9-4. A spark generator used in scale physical

models. Courtesy Kirkegaard Associates.

'fimpulsetimpulse 1=