Because most sound are complex,
fluctuating in amplitude and frequency content, the relationships between sound energy
level and frequency are required for meaningful analysis (data so plotted are called sound
spectrum).
Figure 3 Sound Spectrum of an
Air-Compressor
For most engineering applications, the
greatest interest lies in the frequency range from 20 to 20,000 Hz. Although it is
possible to analyse a source on a frequency by frequency basis, this is both impractical
and time-consuming. For this reason, a scale of octave bands and one-third
octave bands has been developed. Each band covers a specific range of frequencies
and excludes all others. The word "octave" is borrowed from musical nomenclature
where it refers to a span of eight notes, i.e. 
to . The ratio of the frequency of the highest note to the lowest
note in an octave is 2:1.
If fn
is the lower cutoff frequency and fn+1 is the upper
cutoff frequency, the ratio of band limits is given by :
(8)
where k = 1 for full octave bands and
k = 
for one-third octave bands.
An octave has a centre frequency that
is 
times the lower cutoff frequency
and has an upper cutoff frequency that is twice the lower cutoff frequency. Therefore,
where f1 =
lower cutoff frequency
f2 =
upper cutoff frequency
