Engineering Acoustics. Malcolm J. Crocker

level to become effective, the amount of masking attained is a linear function of the masker level. This means, for instance, that a 10‐dB increase in the masker level causes a 10‐dB increase in the masked threshold of the signal being masked. It was found that this effect is independent of the frequency of the tone being masked and applies both to the masking of pure tones and speech [19, 20].

Figure 4.10 Masking of tones by noise at different frequencies and sound pressure levels [20].

      Source: Reprinted with permission from [20], American Institute of Physics.

Figure 4.11 shows the masking effect of a narrow‐band noise of bandwidth 160 Hz centered at 1000 Hz. The curves in Figure 4.11 join the sound pressure levels of test tones that are just masked by the 1000‐Hz narrow‐band noise at the sound pressure level shown on each curve. It is observed that the curves are symmetric around 1000 Hz for low levels of the narrow‐band noise, while for high levels, the curves become asymmetric. It is seen that high levels of the narrow band of noise mask high‐frequency tones much better than low‐frequency tones. Figures 4.9 and 4.11 show that using either white noise or narrow‐band noise it is more difficult to mask low‐frequency than high‐frequency sounds. This fact is of some importance in evaluating the sound quality of a product since it is of no use to reduce or change the noise in one frequency range if it is masked by the noise at another frequency. There are other masking effects that are not normally as important for sound quality evaluations as the frequency effects discussed so far but still need to be described [16–19, 21–30].

Figure 4.11 Masking effect of a narrow‐band noise of bandwidth 160 Hz centered at 1000 Hz. The contours join sound pressure levels of pure tones that are just masked by the 1000‐Hz narrow‐band noise at the sound pressure level shown on each contour [17, 18].

When a masking noise stops, the human hearing system is unable to hear the primary sound signal immediately. This effect is known as postmasking (and is sometimes also known as forward masking.) The time it takes for the primary sound to be heard (normally called the delay time, t_d) depends both upon the sound pressure level of the masking noise and its duration. Figure 4.12 shows how the primary sound is affected by different sound pressure levels of the masking noise. Also shown in Figure 4.12 are dashed lines that correspond to an exponential decay in level with a time constant τ of 10 ms. It is observed that the human hearing mechanism decay is not exponential, but rather that it is nonlinear and that the decay process is complete after a decay time of about 200 ms. This fact is of practical importance since some vehicle and machinery noise is quite impulsive in character such as caused by diesel engines, automobile door closings, brake squeal, warning signals, or impacts that may mask the sounds of speech or other wanted sounds. Figure 4.13 shows how sounds are affected by different durations of the masking noise. Figure 4.13 presents the level of a just‐audible 2‐kHz test tone as a function of delay time.

Figure 4.12 Postmasking at different masker sound pressure levels [17].

Figure 4.13 Postmasking of 5‐ms, 2‐kHz tones preceded by bursts of uniform masking noise are plotted as a function of the delay between masker and signal offsets. The parameter is masking duration T_m as indicated. The symbols are data from Zwicker [31].

      Source: Reprinted with permission from [31], American Institute of Physics.

      4.3.4 Pitch

Like loudness (Section 4.3.2), pitch is another subjective aspect of hearing. Just as people have invented scales to express loudness, others have invented scales for pitch. Stevens et al. [32] were the first to produce a scale in mels. A pure tone of 1000 Hz at a sound pressure level of 40 dB has a pitch of 1000 mels. As a result of subjective experiments, the pitch scale is found to be approximately linear with frequency below 1000 Hz, but approximately logarithmic above 1000 Hz. It has been suggested by some that noise measurements should be made in bands of equal mels (mel was named after the musical term, melody). However, this suggestion has not been adopted. A formula to convert frequency, f (in hertz) into mel, m, is [33]

(4.3)

      Masking noise may change the pitch of a tone. If the masking noise is of a higher frequency, the pitch of the masked tone is reduced slightly; if the masking noise is of a lower frequency the pitch is increased slightly. This can be explained [34, 35] by a signal/noise ratio argument. The locus of the position on the basilar membrane at which the tone is normally perceived could be changed by the masking noise [34].

      Example 4.4

      What is the equivalent frequency of 2595 mel?

      Solution

We take the inverse of Eq. (4.3): f = 700(10 ^m/2595 − 1) = 700 (10 − 1) = 6300 Hz.

      4.3.5 Weighted Sound Pressure Levels

      Figure 4.6 in this chapter shows that the ear is most sensitive to sounds in the mid‐frequency range around 1000–4000 Hz. It has a particularly poor response to sound at low frequency. It became apparent to scientists in the 1930s that electrical filters could be designed and constructed with a frequency response approximately equal to the inverse of these equal loudness curves. Thus A‐, B‐, and C‐weighting filters were constructed to approximate the inverse of the 40‐, 70‐, and 90‐phon contours (i.e. for low‐level, moderate, and intense sounds), respectively (see Figure 4.6). In principle, then, these filters, if placed between the microphone and the meter display of an instrument such as a sound level meter, should give some indication