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D. Rocchesso: Sound Processing
standing wave
Fletcher-Munson curves
equal-loudness curves
loudness level
phons
loudness
sones
standardized loudness scale
I
IL
×1.26
+1
×2
+3
×10
+10
Table C.1: Relation between factors in the linear intensity scale and shifts in
the dB intensity-level scale
where p
0,max
and p
0,RM S
are the peak and RMS pressure values at the threshold
of hearing. For a propagating wave, we have that IL = SP L. For a standing
wave, since there is no power transfer and since IL is a power-based measure,
the SPL is more appropriate.
Given a reference tone with a certain value of IL at 1kHz, we can ask a
subject to adjust the intensity of a probe tone at a different frequency until
it matches the reference loudness perceptually. What we would obtain are the
Fletcher-Munson curves, or equal-loudness curves, sketched in figure 3. Each
curve is parameterized on a value of loudness level (LL), measured in phons.
The loudness level is coincident with the intensity level at 1kHz.
0
20
40
60
80
100
120
100
1000
IL [dB]
frequency [Hz]
Equal-loudness curves
Thresholds
90 phons
60 phons
20 phons
Figure 3: Equal-loudness curves. The parameters express values of loudness level
in phons.
Even though the Fletcher-Munson curves are obtained by averaging the re-
sponses of human subjects, the LL is still a physical quantity, because it refers
to the physical quantity IL and it does not represent the perceived loudness in
absolute terms. In other words, doubling the loudness level does not mean dou-
bling the perceived loudness. A genuine psychophysic measure is the loudness in
sones, which can be obtained as a function of LL by asking listeners to compare
sounds and decide when one sound is "twice as loud" as another. Somewhat ar-
bitrarily, a LL of 40 phons is set equal to 1 sone. Figure 4 represents a possible
average curve that may emerge from an experiment. The standardized loudness
scale (ISO) uses the straight line approximation of figure 4, that corresponds