[Phys-L] Re: sound frequency in helium

[John Denker <jsd@AV8N.COM>]

On 04/17/05 21:56, Julie Quah wrote:

> Dear experts, pleasse help me out with this issue of sound pitch in
> helium gas. When one breath helium gas, and speak, it is found that the
> pitch increases. How do we explain this? But if we compare the water
> wave travelling through deep to shallow water, its speed changes without
> frequency chage, as the source (motor frequncy) is the same.

Well, for starters we need to discuss the concept
of OTBE (other things being equal) ... the problem
is, of course, only rarely do you find that other
things are in fact equal.

In response to a change of wave speed:
  -- If you keep the frequency constant (motor),
   you get a different wavelength.
  -- If you keep the wavelength constant (organ
   pipe), you get a different frequency.

The human voice complicated:  the vocal cords
are to a first approximation like a motor, while
the formants result from acoustic resonances
corresponding to a somewhat funky organ pipe.

The formants are fixed-wavelength critters, i.e.
they have a wavelength that "just fits" in the
vocal tract.  So, to answer the specific question,
if you change the wave speed, the formants change
their frequency in proportion.

(The vocal cord frequency is also affected in
principle, since that depends partly on acoustic
impedance, but the acoustic effect is swamped by
the effect of muscle tension and muscle mass, and
in any case there is lots of high-level feedback
on the muscle tension, so the frequency ends up
pretty much being an independently-controlled
variable.)

At the next level of detail:  The signal coming
out of the vocal cords is a train of sharp clicks,
having a definite fundamental frequency plus a
huge number of higher harmonics.  It is a Dirac
comb in realtime space, and its Fourier transform
is a Dirac comb in frequency space.  The signal
then gets convolved with the formants.  The vocal
cords determine whether you are singing F# or G,
while the formants determine whether you are
singing aaaah or ooooh.

For further detail, you might try
   http://www.google.com/search?q=formants+helium
which leads to things like
   http://www.phys.unsw.edu.au/~jw/speechmodel.html
which has some pictures.
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