Page 94 - The Master Handbook Of Acoustics

69
THE EAR AND THE PERCEPTION OF SOUND

are feeding their respective channels, one at 24 kHz and the other at 23
kHz, a distinct 1,000-Hz tone is heard if the tweeters are good enough
and you are standing in the right place.
The 1,000-Hz tone is the difference between 24,000 and 23,000 Hz.
The sum, or 47,000 Hz, which even the dog may not hear even if it
were radiated, is another sideband. Such sum and difference side-
bands are generated whenever two pure tones are mixed in a nonlin-
ear element. The nonlinear element in the above experiment is the
middle and inner ear. In addition to the intermodulation products dis-
cussed earlier, the nonlinearity of the ear generates new harmonics
that are not present in the sound falling on the eardrum.

Aural Harmonics: Experiment #2

The distortion introduced by the auditory system cannot be measured
by ordinary instruments. It is a subjective effect requiring a different
approach. Another demonstration of distortion in the ear can be
accomplished by the following method with the same equipment used
above, with the addition of a pair of headphones.
First, a 150-Hz tone is applied to the left earphone channel. If the
hearing mechanism were perfectly linear, no aural harmonics would
be heard as the exploratory tone is swept near the frequencies of the
second, third, and other harmonics. If it is nonlinear, the presence of
aural harmonics is indicated by the generation of beats. When 150 Hz
is applied to the left ear, and the exploratory tone of the right ear is
slowly varied about 300 Hz, the second harmonic is indicated by the
presence of beats between the two. If you change the exploratory oscil-
lator to a frequency around 450 Hz, the presence of a third harmonic
will be revealed by beats.
Experts have even estimated the magnitude of the harmonics by the
strength of such beats. The amount of distortion produced in the ear is
modest at lower levels but becomes appreciable at high levels. Run-
ning the above experiment with tones of a higher level will make the
presence of aural harmonics even more obvious.

The Missing Fundamental
If tones such as 1,000, 1,200, and 1,400 Hz are reproduced together, a
pitch of 200 Hz is heard. This can be interpreted as the fundamental
with 1,000 Hz as the 5th harmonic, 1,200 Hz as the 6th harmonic, etc.