Page 83 - The Master Handbook Of Acoustics

58 CHAPTER THREE

has a loudness level of 60 phons and a loudness of 4 sones. The 160-
Hz bandwidth has the same loudness, but something mysterious
happens as the bandwidth is increased beyond 160 Hz. The loud-
ness of the noise of 200-Hz bandwidth is louder, and from 160 Hz or
up, increasing bandwidth increases loudness. Why the sharp change
at 160 Hz?
It turns out that 160 Hz is the width of the ear’s critical band at
1,000 Hz. If a 1,000-Hz tone is presented to a listener along with ran-
dom noise, only the noise in a band 160 Hz wide is effective in
masking the tone. In other words, the ear acts like an analyzer com-
posed of a set of bandpass filters stretching throughout the audible
spectrum. This filter set is nothing like that found in the electronics
1
laboratory. The common ⁄3-octave filter set may have 28 adjacent fil-
ters overlapping at the –3 dB points. The set of critical band filters is
continuous; that is, no matter where you might choose to set the sig-
nal generator dial, there is a critical band centered on that fre-
quency.
Many years of research on this problem has yielded a modicum of
agreement on how the width of the critical-band filters varies with fre-
quency. This classical bandwidth function is shown in the graph of
Fig. 3-11. There has been some question as to the accuracy of this
graph below about 500 Hz that has led to other methods of measuring
the bandwidth. Out of this has come the concept of the equivalent rec-
tangular bandwidth (ERB) that applies to young listeners at moderate
11
sound levels. This approach is based on mathematical methods and
offers the convenience of being able to calculate the ERB from the
equation given in Fig. 3-11.
One-third-octave filter sets have been justified in certain mea-
surements because the filter bandwidths approach those of the criti-
cal bands of the ear. For comparison, a plot of one-third-octave
bandwidths is included in Fig. 3-11. One-third-octave bands are 23.2
percent of the center frequency. The classical critical-band function
is about 17 percent of the center frequency. It is interesting to note
that the ERB function (12 percent) is very close to that of one-sixth-
octave bands (11.6 percent). This suggests the possibility of one-
sixth-octave filter sets playing a larger role in sound measurements
of the future.