Page 49 - The Master Handbook Of Acoustics

24 CHAPTER TWO

When the sound pressure is increased until it sounds twice as loud,
the level dial reads 10 units. This completes observation A. For obser-
vation B, the source pressure is increased to 10,000 units. To double
the loudness, you find that the sound pressure must be increased from
10,000 to 100,000 units. The results of this experiment can now be
summarized as follows:

Ratio of Two
Observations Two Pressures Pressures
A 10 – 1 10: 1
B 100,000 – 10,000 10: 1

Observations A and B accomplish the same doubling of per-
ceived loudness. In observation A, this was accomplished by an
increase in sound pressure of only 9 units, where in observation B it
took 90,000 units. Ratios of pressures seem to describe loudness
changes better than differences in pressure. Ernst Weber (1834),
Gustaf Fechner (1860), Hermann von Helmholtz (1873), and other
early researchers pointed out the importance of ratios, which we
know apply equally well to sensations of vision, hearing, vibration,
or even electric shock.
Many years ago, a friend working in a university research labora-
tory demonstrated his experiment on the hearing of cats, which in
many ways is similar to that of humans. A tone of 250 Hz, radiated
from a nearby loudspeaker, was picked up by the ears of an anes-
thetized cat, a portion of whose brain was temporarily exposed. A
delicate probe picked up the 250-Hz signal at a highly localized spot
on the auditory cortex, displaying it on a cathode-ray oscilloscope.
When the tone was shifted to 500 Hz, the signal was picked up at
another spot on the cortex. Tones of 1,000 and 2,000 Hz were detected
at other specific spots. The fascinating point here is that changing the
tone an octave resulted in the signal appearing on the auditory cortex
at discrete, equally spaced points. Frequencies in the ratio of 2 to 1
(an octave) seem to have a linear positional relationship in the cat’s
brain. This indicates a logarithmic response to frequency. Ratios of
stimuli come closer to matching up with human perception than do
differences of stimuli. This matching is not perfect, but close enough
to make a strong case for the use of levels in decibels.