Engineering Acoustics. Malcolm J. Crocker

      The center frequency (or geometric mean) is . Thus f_U/f_L = 2.

      The bandwidth Δf is given by

      so Δf ≈ 70% (f_C).

       b) One‐Third‐Octave Bands

      For one‐third‐octave bands, the cutoff frequencies, f_L and f_U, are defined as follows:

      The center frequency (geometric mean) is given by . Thus f_U/f_L = 2^1/3.

      The bandwidth Δf is given by

      so Δf ≈ 23% (f_C).

We thus see clearly why the filter bands we have just discussed are called constant percentage. This is because the bandwidth is a constant percentage of the filter center frequency f_C. Of course, the filter bandwidth does not have to be defined in terms of a fraction of an octave but can be defined simply in terms of the percentage of the center frequency. Since it is impracticable to make measurements at a large number of fixed frequencies, noise measurements are made at a selected number of standardized frequencies called preferred center frequencies. Standard one-octave and one-third-octave band specifications take advantage of the fact that 2^10/3 ≈ 10. The ISO recommendation values for preferred center frequencies are given in Table 1.1 [15]. Specifications for octave‐band and fractional‐octave‐band filters are defined by the IEC 1260:1995 and the ANSI S1.11:2004 standards [16, 17].

Table 1.1 Preferred center frequencies for noise measurements according to ISO R 266 [15].

Preferredfrequencies, Hz	1/1oct.	1/3oct.	Preferredfrequencies, Hz	1/1oct.	1/3oct.	Preferredfrequencies, Hz	1/1oct.	1/3oct.
16	×	×	200		×	2500		×
20		×	250	×	×	3150		×
25		×	315		×	4000	×	×
31.5	×	×	400		×	5000		×
40		×	500	×	×	6300		×
50		×	630		×	8000	×	×
63	×	×	800		×	10 000		×
80		×	1000	×	×	12 500		×
100		×	1250		×	16 000	×	×
125	×	×	1600		×
160		×	2000	×	×

      Note that:

      1 The center frequencies of one‐octave bands are related by 2, and 10 frequency bands are used to cover the human hearing range. They have center frequencies of 31.5, 63, 125, 250, 500, 1000, 2000, 4000, 8000, 16 000 Hz.

      2 The center frequencies of one‐third octave bands are related by 21/3 and 10 cover a decade of frequency, and thus 30 frequency bands are used to cover the human hearing range: 20, 25, 31.5, 40, 50, 63, 80, 100, 125, 160, …, 16 000 Hz.

Thus we note that at high frequencies a constant bandwidth analyzer will obviously have a narrower bandwidth than the constant percentage filter. Figure 1.11 shows a comparison of the bandwidths of constant percentage and constant band filters at the same frequencies.

      Example 1.5

      Determine the