Author: NorbertTheParrot
Date: 2008-03-19 18:43
Mark C wrote:
"Depends on your idea of significance."
My idea of significance is what is significant to a musical performance. 1% is the difference between A=440 and A=444, and is significant. 0.1% is not.
"Density - and the local speed of sound, ergo the resonant frequency of a vibrating air column - is dependent on pressure, temperature, and humidity."
This statement is true in a literal sense, but is deeply misleading.
The speed of sound in a gas does indeed vary with pressure so long as the density is kept constant. The speed of sound does indeed vary with density so long as the pressure is kept constant. But, for a given chemical composition of the gas, at a given temperature, density and pressure are in direct proportion to one another, and their respective effects exactly cancel out.
It is an observable fact that a given orchestra is able to play both at sea-level and at altitude using the same instruments. If different instruments were affected in different ways by pressure, then there would be a big problem. We have to conclude that:
1. Either all instruments are affected, but to the same extent. This is manifestly absurd.
2. Or, no instrument is affected (significantly) at all.
We can see this must be true without even bothering to go to altitude. At a given location, atmospheric pressure can vary by 10% or even more as the weather changes. Given constant temperature and humidity (as in an air-conditioned room) this has no effect on the pitch of our clarinets.
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The Clarinet BBoard
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