Читать книгу Engineering Acoustics - Malcolm J. Crocker - Страница 153

1 The loudness level in phons of each tone is found from Figure 4.6 and the corresponding loudness in sones is found from Eq. (4.1). Then we have that100 Hz @ 60 dB has P = 50 phons and S = 2 sones200 Hz @ 70 dB has P = 70 phons and S = 8 sones1000 Hz @ 80 dB has P = 80 phons and S = 16 sonesTherefore, the total loudness of these three pure tones is 2 + 8 + 16 = 26 sones.

2 The total loudness of the combined tones (26 sones) corresponds to a loudness level of P = 10log2(26) + 40. Since log2(26) = ln(26)/ln(2) = 4.7, then P = 87 phons.Now, from Figure 4.6 we observe that a pure tone of 2000 Hz and loudness level of 87 phons has a sound pressure level of 82 dB.

So far we have discussed the loudness of pure tones. However, many of the noises we experience, although they may contain pure tones, are predominantly broadband. Similar loudness rating schemes have been worked out for broadband noise. In 1958–1960, Zwicker [12], taking into account masking effects (see later discussion in Section 4.3.3), devised a graphical method to compute the loudness of a broadband noise. It should be noted that Zwicker's method can be used both for diffuse and free field conditions and for broadband noise even when pronounced pure tones are present. However, the method is somewhat time‐consuming and involves measuring the area under a curve. It has been well described elsewhere [13].

Stevens [14] at about the same time (1957–1961) developed quite different procedures for calculating loudness. Stevens' method, which he named Mark VI, is simpler than Zwicker's method but is only designed to be used for diffuse sound fields and when the spectrum is relatively flat and does not contain any prominent pure tones.

The procedure used in the Stevens Mark VI method is to plot the noise spectrum in either octave or one‐third‐octave bands onto the loudness index contours. The loudness index (in sones) is determined for each octave (or one‐third‐octave) band and the total loudness S is then given by

(4.2)

where S_max is the maximum loudness index and ∑S is the sum of all the loudness indices. The 0.3 constant (used for octave bands) in Eq. (4.2) is replaced by 0.15 for one‐third‐octave bands. The Zwicker method is based on the critical band concept and, although more complicated than the Stevens method, can be used either with diffuse or frontal sound fields. Complete details of the procedures are given in the ISO standard [15] and Kryter [16] has discussed the critical band concept in his book.