THE SCIENCE AND APPLICATIONS OF ACOUSTICS - H. H. Arnold ...

46 3. Sound Wave Propagation and CharacteristicsTable 3.1. Octave Bands.Lower Band Limit Center Frequency Upper Band Limitf L f C f U22.4 Hz 31.5 Hz 45 Hz45 63 9090 125 180180 250 355355 500 710710 1 kHz 1.4 kHz1.4 kHz 2 2.82.8 4 5.65.6 8 11.211.2 16 22.4each octave band are given byBecausef L = f C√2f U = √ 2 f C (3.14)f C = √ f L f U (3.15)we see that the center frequency f C constitutes the geometric mean of the upperband limit f U and lower band limit f L . The bandwidth BW for full octaves isdefined by( ) √2 1BW = f U − f L = f C − √2 = f C√ (3.16)2and thus the ratio BW/f C is shown to constitute a constant. In order to avoid theuse of irrational numbers the octave bands have been standardized in the field ofacoustics, according to Table 3.1.One-third octave bands are formed by subdividing each octave band intothree parts. The successive center frequencies increase in intervals by cube rootof 2, and the upper and lower frequencies are related to the center frequency asfollows:f L = f C6√2, f U = 6 √2 fC , f C = √ f L f U (3.17)From Equations (3.16) and (3.17), the ratio BW/f C is also a constant for the thirdoctavebands,BW √−6√= 6 2 − 2 (3.18)f CTable 3.2 lists the standardized one-third octave limits and center frequencies.