Читать книгу Engineering Acoustics - Malcolm J. Crocker - Страница 163

Another important factor is the way that the ear analyzes the frequency of sounds. The critical band concept already discussed in Section 4.3.5 is important here as well. It appears that the human hearing mechanism analyzes sound like a group of parallel frequency filters. Figure 4.18 shows the bandwidth of these filters as a function of their center frequency. These filters are often called critical bands and the bandwidth each possesses is known as its critical bandwidth. As a band of noise of a constant sound pressure level increases in bandwidth, its loudness does not increase until the critical bandwidth is exceeded, after which the loudness continually increases. Thus the critical band may be considered to be that bandwidth at which subjective responses abruptly change [28]. It is observed that up to 500 Hz the critical bandwidth is about 100 Hz and is independent of frequency, while above that frequency it is about 21% of the center frequency and is thus almost the same as one‐third octave band filters, which have a bandwidth of 23% of the center frequency shown by the solid line. This fact is also of practical importance in sound quality considerations since it explains some of the masking phenomena observed.

Figure 4.18 Critical bandwidth, critical ratio, and equivalent rectangular bandwidth as a function of frequency. (○) Critical bandwidth from Zwicker [41] is compared to the equivalent rectangular bandwidths according to a cochlear map function (‐ ‐ ‐) (dashed line).

(Source: Based in part on Ref. [42].)

The critical ratio shown in Figure 4.18 originates from the early work of Fletcher and Munson in 1937 [28]. They conducted studies on the masking effects of wide‐band noise on pure tones at different frequencies. They concluded that a pure tone is only masked by a narrow critical band of frequencies surrounding the tone, and that the power (mean‐square sound pressure) in this band is equal to the power (mean‐square sound pressure) in the tone [28]. The critical band can easily be calculated. From these assumptions, the critical bandwidth (in hertz) is defined to be the ratio of the sound pressure level of the tone to sound pressure level in a 1‐Hz band (i.e. the spectral density) of the masking noise. This ratio is called the critical ratio to distinguish it from the directly measured critical band [28]. A good correspondence can be obtained between the critical band and the critical ratio by multiplying the critical ratio by a factor of 2.5. The critical ratio is given in decibels in Figure 4.18 and is shown by the broken line.