On 3 Apr 2009, at 19:20, Anthony W. Youngman wrote:
1.311 transposing instrument
..., the speed of sound in air is 343m/s,...
This is only true at about 19.6℃ (degrees Celsius):
The temperature of the air in the human blown instrument is higher,
clearly. If I quickly measure my flute with an IR-thermometer (and it
can be hard to know exactly what it measures), I got 30-32℃ at the
head-joint alone, and 24-26℃ at the lower end. The actual air
temperature may be higher. A trick one can do on a flute to raise the
air temperature before playing, is to close all finger holes and blow
directly into the mouth-piece hole.
The speed of sound in gases is (roughly) proportional to the square-
root of the absolute temperature. Figures used the speed of sound v_0
in air at 0℃ varies a bit in the range from 331.2 to 331.8 m/s
perhaps. This gives the formula at absolute temperature T
v = sqrt(T/273.15)*v_0 m/s
For example, if the temperature of the air is 28℃, then T = 273.15+28
= 301.15 K (Kelvin). If v_0 is set to 331.5 m/s, then at 28℃, v =
sqrt(301.15/273.15)*331.5 = 348.1 m/s. Translated into pitches, this
is a change of 25.4 cents relative the speed 343 m*/s given above, or
a difference in tuning of about 6-7 Hz, or enough to hear the
instrument go out of tune. (But the temperature of the air varies
throughout the instrument - I just took a value to show how to
calculate v.)
Hans
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