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Where does the audble 1 kHz come from?

Hi list

A trivial question for you.  A colleague here recently described (from
a text book) a phenomenon that we neither anticipated nor can explain
and I wondered if anyone had the answer...

Apparently if you play a 22 kHz and 23 kHz tone over two loudspeakers
in the sound field to normally hearing listeners they report hearing a 1
kHz tone, the detectibility of which depends on the location.  Is this
so and why?

Our immediate thoughts were:

(A) Its beats - but to hear the beats (1) the spectral components must
be audible (and the beat frequency isn't in the spectrum) which is
unlikely at such high frequencies; (2) if they are audible they must go
unresolved in the auditory system - possible; (3) the modulation
frequency must be represented in the auditory system which is unlikely
to be the case given the low-pass nature of normals' TMTFs.  We think
that even if these were the case (and we seriously doubt it from
consideration 1 and 3), listeners would not hear a sound with a clear
pitch sensation let alone a pitch of 1 kHz with only 2 spectral

(B) Distortion product i.e. a 1 kHz spectral component comes from
somewhere.  As the two signals are delivered from two independent
channels in the instrumentation, this can't be distortion from the
equipment.  We can't imagine that the DP arises in the air / room
acoustics.  So that leaves the cochlear.  We have doubted this because
(1) very little energy would be transmitted through the middle ear into
the cochlea; (2) even if a f2-f1 DP was generated in the cochlea, I
can't image that this would be sufficiently intense to be audible and;
(3) I thought that any cochlear DPs other than 2f1-f2 were exteremly
hard if not impossible to hear.  However, I know little about the
perception of cochlear DPs.

Any thoughts?  (Note, we have not attemtped to try and replicate the


Daniel Rowan MSc
Research Student
Institute of Sound and Vibration Research
University of Southampton
University Road
Southampton SO17 1BJ
England, UK
Tel: 023 80594968
Email: dr@isvr.soton.ac.uk