2.9 OCTAVE BANDS

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The human ear is sensitive to sounds having frequencies in the range from

about 16Hz to 16 kHz. Because it is not practical to measure the sound level

at each of the 15,984 frequencies in this range, acoustic measuring instruments

generally measure the acoustic energy included in a range of frequencies.

The human ear also responds more to frequency ratios than to

frequency differences, so the frequency ranges generally have terminal frequencies

(upper and lower frequencies of the range) that are related by the

same ratio.

The frequency interval over which measurements are made is called

the bandwidth. The bandwidth may be described by the lower frequency of

the interval р f1Ю and the upper frequency of the interval р f2Ю. In acoustics,

the bandwidths are often specified in terms of octaves, where an octave is a

frequency interval such that the upper frequency is twice the lower frequency

(Table 2-3). For an octave,

f2 ј 2f1 or f2=f1 ј 2

In some cases, a more refined division of the frequency range is used in

measurement, such as 1/3-octave bands, in which р f2=f1Ю ј 21=3 ј 1:260:

Basics of Acoustics 33

TABLE 2-2 Handheld Calculator Routine for Combining Levelsa

Keystroke entry Key pressed Display results

Initial level value divided by 10 Ѕ10x_ I1=Iref , for example

(none) [STO] (value stored in memory)

Next level value divided by 10 Ѕ10x_ I2=Iref , for example

(none) [SUM] (value added to memory)

(Repeat for the remaining levels

(none) [RCL] Itotal=Iref , for example

(none) [log] Level/10

(none) [_]

10 [ј] Total level

Example

8.0 [10x]; [STO] 100000000

8.5 [10x]; [SUM] 316227766

[RCL] 416227766

[log]; [_] 8.619331048

10 [ј] 86.19331048

a The notation is that used for most ‘‘scientific’’ handheld calculators; however, there

may be some variation for different calculator models.

Copyright © 2003 Marcel Dekker, Inc.

The center frequency of the band р f0Ю is defined as the geometric mean

of the upper and lower frequencies for the interval:

f0 ј рf1 f2Ю1=2 (2-44)

For an octave band, the upper and lower frequencies are related to the

center frequency by:

f1 ј f0=21=2 and f2 ј 21=2 f0;

For 1/3-octave bands,

f1 ј f0=21=6 and f2 ј 21=6 f0

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