Page 614 - Instrumentation Reference Book 3E

25 Noise measurement

J. KUEHN

25.1 Sound and sound fields sound pressures as small as 2 x pascals. It
can also pick up sound pressures as high as 20 or
25.1.1 The nature of sound even 100 pascals. When dealing with such a wide
dynamic range (pressure range of 10 million to 1)
If any elastic medium, whether it be gaseous, it is inconvenient to express sound pressures in
liquid, or solid, is disturbed, then this disturbance terms of pascals and so a logarithmic scale is
will travel away from the point of origin and be used. Such a scale is the decibel scale. This is
propagated through the medium. The way in defined as ten times the logarithm to the base 10
which the disturbance is propagated and its speed of the ratio of two powers. When applying this
will depend upon the nature and extent of the scale to the measurement of sound pressure it is
medium, its elasticity, and density. assumed that sound power is related to the square
In the case of air, these disturbances are char-
acterized by very small fluctuations in the density of the sound pressure. Thus
(and hence atmospheric pressure) of the air and
by movements of the air molecules. Provided Sound pressure level = 10loglo (g)
these fluctuations in pressure take place at a rate
(frequency) between about 20 Hz and 16 kHz,
then they can give rise to the sensation of audible
sound in the human ear. The great sensitivity of
the ear to pressure fluctuations is well illustrated
by the fact that a peak-to-peak fluctuation of less
than 1 part in lo9 of the atmospheric pressure
will, at frequencies around 3 kHz, be heard as where P is the sound pressure being measured
audible sound. At this frequency and pressure and Po is a “reference” sound pressure (standard-
the oscillating molecular movement of the air is ized at 2 x pascals).
less than lo-’ of a millimeter. It should be noted that the use of the expres-
The magnitude of the sound pressure at any sion “sound-pressure level” always denotes that
point in a sound field is usually expressed in terms the value is expressed in decibels. The reference
of the rms (root-mean-square) value of the pres- pressure will, of course, be the 0 dB value on the
sure fluctuations in the atmospheric pressure. This decibel scale. The use of a reference pressure close
value is given by to that representing the threshold of hearing at
the frequencies where the ear is most sensitive
means that most levels of interest will be positive.
(25.1) (A different reference pressure is used for under-
water acoustics and for the OdB level on audio-
grams.) A good example of the use of the decibel
where P(t) is the instantaneous sound pressure at scale of sound-pressure level and of the compli-
time t and Tis a time period long compared with cated response of the human ear to pure tones is
the periodic time of the lowest frequency present given in Figure 25.1, showing equal loudness con-
in the sound. tours for pure tones presented under binaural,
The SI unit for sound pressure is Newton/m2 free-field listening conditions.
(N/m2), which is now termed pascal, that is, The equal loudness level contours of Figure
1Newton/m2 = 1 pascal. Atmospheric pressure is, 25.1 (labelled in Phons) are assigned numerical
of course. normally expressed in bars (lbar = lo5 values equal to that of the sound-pressure level at
pascal). 1 kHz through which they pass. This use of 1 kHz
The great sensitivity of the human hearing as a “reference” frequency is standardized in
mechanism, already mentioned, is such that at acoustics. It is the frequency from which the
frequencies where it is most sensitive it can detect audible frequency range is “divided up” when