Spectrum and Octave Band
Home Up Nature of Sound Waves Simple Harmonic Motion Characteristics of Sound Spectrum and Octave Band Strength of Sound Sound Pressure Level Sound Power Level Sound Intensity Level Free Field Manipulation with Decibels


4. Spectrum and Octave Band

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 :


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

fo = centre frequency

bw = band width


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