Klarinet Archive - Posting 000235.txt from 1994/05

From: John Belz <BELZ@-----.BITNET>
Subj: Re: Pitch and gases
Date: Thu, 12 May 1994 18:03:53 -0400

I've been lurking on this list for a month or so. I'm a new player (about a
year and a half) so I've been content to listen to the opinions of the
experts. Since I happen to have a freshman physics book and a CRC Handbook
on the bookshelf next to my desk, however, I thought I might be able to
contribute to the discussion on gases and pitch.

First, the relationship between density and frequency: The frequency of
sound in a gas for a given wavelength is inversely proportional to the
square root of the gas's density. So in general an increase in density
will result in a (lesser) decrease in frequency. The question is, can gas
densities change enough so that you can actually hear the frequency change?

Clark asked about the pitch when the clarinet was warm vs. cold. Cold air
is denser than warm air, but only slightly. At 20 degrees C (68 F) dry air
has a density of 1.205 grams/liter. At 10 C (50 F) the density increases
to 1.247 g/l, about a 3.5% change. This corresponds to a 1.7% decrease in
the frequency, so an A440 would change to 432 Hz. This change is about 1/4
of a half-step which might well be audible.

Clark's other question was about whether changes in oxygen/carbon dioxide
ratios in your breath cause pitch to drop the longer you blow. Here I
have to estimate a little, but I think I know the answer. The density of
CO2 (1.977 g/l) is indeed greater than that of O2 (1.429 g/l) and air.
But 78% of what we breathe in is nitrogen. Oxygen (20%) accounts for most of
the remainder. A question for any medical-types is: what fraction of the
oxygen that we breathe in is converted to CO2? If I guess 10%, then the
total change in air density due to O2 -> CO2 conversion is only about 0.8%.
This corresponds to a 0.4% change in frequency or A440 -> 438, 1/15th of
a half-step. I'm less sure that this difference would be audible. I've
neglected the addition of moisture to the air in this calculation.

Now, a coke burp would be almost all CO2. So I think this really would
change the sound. I'm going to try this when I get home.

- John Belz