Handbook for Sound Engineers

52 Chapter 3

quencies, on average, it is a good estimate of a mini-
mum audible limit. The tones louder than the curve of
120 phons will cause pain and hearing damage.

The equal loudness contours also show that human
hearing is most sensitive around 4 kHz (which is where
the hearing damage due to loud soundsfirst happens),
less sensitive to high frequencies, and much less
sensitive for very low frequencies (which is why a
subwoofer has to be very powerful to produce strong
bass, the price of which is the masking of mid-and
high-frequencies and potential hearing damage). A
study of this family of curves tells us why treble and
bass frequencies seem to be missing or down in level
when favorite recordings are played back at low
levels.^26

One might notice that for high frequencies above
10 kHz, the curves are nonmonotonic for low levels.
This is due to the second resonant mode of the ear
canal. Moreover, at low frequencies below 100 Hz, the
curves are close to each other, and the change of a few
dB can give you the feeling of more than 10 dB of
dynamic change at 1 kHz. Furthermore, the curves are
much flatter at high levels, which unfortunately encour-
aged many to listen to reproduced music at abnormally
high levels, again causing hearing damage. Actually,
even if one wanted to have flat or linear hearing,
listening at abnormally high levels might not be wise,
because the frequency selectivity of our auditory system
will be much poorer, leading to much greater interaction

between various frequencies. Of course, one limitation

of listening at a lower level is that, if some frequency

components fall below the hearing threshold, then they

are not audible. This problem is especially important for

people who have already lost some acuity at a certain

frequency, where his or her hearing threshold is much

higher than normal. However, in order to avoid further

damage of hearing, and in order to avoid unnecessary

masking effect, one still might consider listening at

moderate levels.

The loudness level considers the frequency response

of our auditory system, and therefore is a better scale

than the sound pressure level to account for loudness.

However, just like the sound pressure level is not a scale

for loudness, the loudness level does not directly repre-

sent loudness, either. It simply references the sound

pressure level of pure tones at other frequencies to that

of a 1 kHz pure tone. Moreover, the equal loudness

contours were achieved with pure tones only, without

consideration of the interaction between frequency

components—e.g., the compression within each audi-

tory filter. One should be aware of this limit when

dealing with broadband signals, such as music.

3.8.2 Level Measurements with A-, B-, and

C-Weightings

Although psychoacoustical experiments give better

results on loudness, practically, level measurement is

more convenient. Because the equal loudness contours

are flatter at high levels, in order to make level measure-

ments somewhat representing our loudness perception,

it is necessary to weight frequencies differently for mea-

surements at different levels. Fig. 3-14 shows the three

widely used weighting functions.^27 The A-weighting

level is similar to our hearing at 40 dB, and is used at

low levels; the B-weighting level represents our hear-

ing at about 70 dB; and the C-weighting level is more

flat, representing our hearing at 100 dB, and thus is used

at high levels. For concerns on hearing loss, the

A-weighting level is a good indicator, although hearing

loss often happens at high levels.

3.8.3 Loudness in Sones

Our hearing for loudness is definitely a compressed

function (less sensitive for higher levels), giving us both

sensitivity for weak sounds and large dynamic range for

loud sounds. However, unlike the logarithmic scale (dB)

that is widely used in sound pressure level, experimen-

tal evidence shows that loudness is actually a power law

function of intensity and pressure as shown in Eq. 3-3.

Figure 3-13. Equal loudness contours for pure tones in a
frontal sound field for humans of average hearing acuity
determined by Robinson and Dadson. The loudness levels
in phons correspond to the sound pressure levels at
1000 Hz. (ISO Recommendation 226).

120

100

80

60

40

20

0

50 100 300 500 1k 3k 5k 10k 20k

Minimum

audible

Sound pressure level–dB

Frequency–Hz

Loudness level–phons