I assume (perhaps wrong), that the fundamental frequency of brass instruments can be calculated with the wave equation:
c = lambda * f,
- c = the speed of sound. I calculated this to be 349 m/s at 30 degrees C (temperature of a warm instrument). I think this is right because two control conditions (0C and 20C) gave me correct answers (331 and 343 m/s).
- f = Fundamental frequency of the instrument.
- lambda = length of the instrument.
Given the fundamental frequency of 87.31 Hz (F2) the length of this F-tuba should be 4.0m.
However, Wikipedia's article on tubas says an Eb-tuba is 4.0m and an F-tuba is 3.7m. I took a tape measure and measured my F-tuba along the center of the bore to the edge of the bell, and I measured 3.72m. It seems Wikipedia is right!
Did I use an incorrect equation to calculate the length of a brass tuba or was there another problem?
My guess is that there's a problem in the boundry condition at the bell.
c=Lf applies to a non-flared pipe like a Didgeridoo and the flare of the bell effectvely lengthens the instrument. In the sketch below, I measured the long-dashed line to the
X where I should have measured to the
?. But is there a way to know the distance between those two marks?
I don't think the problem is related to the speed of sound. If I use the known 331 m/s at 0 deg.C, the F tuba is 3.79m, still longer than my measured 3.72.
My mouth-piece is not 30cm long, so that also doesn't account for it.
Another thing it could be is the extra length added when reflecting from wall to wall as the sound travels around curves. A straight tuba without curves could be closer to the theoretical length I calculated. But I don't know if this is true. Any ideas would be welcome.