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 *f**1* =
lower cutoff frequency

*f2* =
upper cutoff frequency

*fo*
= centre frequency

*bw* = band width