TM 5-805-4/AFJMAN 32-1090
In addition vibration can be measured with three
by using an area weighted intensity or by logarith-
different quantities, these are, acceleration, veloc-
mically combining individual Lw's.
ity and displacement. Unless otherwise stated the
e. Determination of Sound intensity. Although
vibration levels used in this manual are in terms
sound intensity cannot be measured directly, a
o f acceleration and are called "acceleration
reasonable approximation can be made if the
direction of the energy flow can be determined.
levels". For simple harmonic vibration at a single
frequency the velocity and displacement can be
Under free field conditions where the energy flow
direction is predictable (outdoors for example) the
related to acceleration by:
magnitude of the sound pressure level (Lp) is
=
velocity
equivalent to the magnitude of the intensity level
(Li). This results because, under these conditions,
=
displacement
the intensity (I) is directly proportional to the
square of the sound pressure (p2). This is the key
Where f is the frequency of the vibration in hertz
to the relationship between sound pressure level
(cycles per second). For narrow bands and octave
and sound power level. This is also the reason that
bands, the same relationship is approximately true
when two sounds combine the resulting sound
where f is the band center frequency in hertz.
level is proportional to the log of the sum of the
b. Definition, reference vibration. In this man-
squared pressures (i.e. the sum of the p2's) not the
ual, the acceleration level, expressed in decibels, is
sum of the pressures (i.e. not the sum of the p's).
the logarithmic ratio of acceleration magnitudes
That is, when two sounds combine it is the
where the reference acceleration is 1 micro G
intensities that add, not the pressures. Recent
(10-6), where G is the acceleration of gravity
advances in measurement and computational tech-
(32.16 ft/sec2 or 9.80 m/s2). It should be noted that
niques have resulted in equipment that determine
other reference acceleration levels are in common
sound intensity directly, both magnitude and di-
use, these include, 1 micro m/s2,10 micro m/s2
rection. Using this instrumentation sound inten-
(approximately equal to 1 micro G) and 1 G.
sity measurements can be conducted in more
Therefore when stating an acceleration level it is
complicated environments, where fee field condi-
customary to state the reference level, such as "60
tions do not exist and the relationship between
dB relative to 1 micro G".
intensity and pressure is not as direct.
c. Abbreviations. The abbreviation VAL is some-
times used to represent vibration acceleration
B-6. Vibration Levels
level, and the notation La is normally used in
Vibration levels are analogous to sound pressure
equations, both in this manual and in the general
levels.
acoustics literature.
a. Definition, vibration level. The vibration level
B-7. Frequency.
(in decibels) is defined by:
Frequency is analogous to "pitch." The normal
frequency range of hearing for most people extends
from a low frequency of about 20 to 50 Hz (a
(eq B-13)
"rumbling" sound) up to a high frequency of about
10,000 to 15,000 Hz (a "hissy" sound) or even
higher for some people. Frequency characteristics
Where a is the absolute level of the vibration and
are important for the following four reasons: People
aref is the reference vibration. In the past differ-
have different hearing sensitivity to different fre-
ent measures of the vibration amplitude have been
quencies of sound (generally, people hear better in
utilized, these include, peak-to-peak (p-p), peak (p),
the upper frequency region of about 500-5000 Hz
average and root mean square (rms) amplitude.
and are therefore more annoyed by loud sounds in
Unless otherwise stated the vibration amplitude,
this frequency region); high-frequency sounds of
a, is the root mean square (rms). For simple
high intensity and long duration contribute to
harmonic motion these amplitudes can be related
hearing loss; different pieces of electrical and me-
by:
chanical equipment produce different amounts of
=
low-, middle-, and high-frequency noise; and noise
rms value
0.707 x peak
control materials and treatments vary in their
=
average value
0.637 x peak
effectiveness as a function of frequency (usually,
=
rms value
1.11 x average
low frequency noise is more difficult to control;
=
most treatments perform better at high frequency).
peak-to peak
2 x peak
B-4
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