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Postby iiipopes » Mon Sep 17, 2007 1:20 pm

Hmm. I always thought that with the larger volume of a larger bore & taper, that the actual length would be slightly shorter.
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Postby Rick Denney » Mon Sep 17, 2007 2:41 pm

I've read in the past about the "bell effect". The effective length of the bugle is longer than the physical length by something like 2/3rds of the bell diameter. Since organ pipes are cylindrical, this effect would be visible along the whole length. I suspect, however, that the bell effect is a rule of thumb that works only for conical bugles with wide flares like tubas have.

The narrower the narrow tubing, the more effect on the "velocity factor", I would suspect. In radio frequencies, the velocity factor of the transmission wire affects its electrical length, and the velocity factor is directly related to its conductivity. Friction along the walls of the tubing would drag the traveling pressure fronts back. Because of that, a bugle with narrow tubing would need to be shorter to resonate on the same frequency. This might be the effect that is at least partly described (perhaps incorrectly) by "bell effect".

A lot of what we normally assume about acoustics goes out the window with conical bugles, however. The resonance of the bugle varies with frequency in very significant ways depending on the taper design. It's possible to make a realistic looking bugle that resonates on the odd harmonics, and another that resonates more on the even harmonics. Fletcher and Rossing (The Physics of Musical Instruments) makes really good reading on this topic.

I have this feeling that because of the vagaries of taper design, instrument makers arrive at the correct length by experiment rather than by calculation.

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Postby eupher61 » Mon Sep 17, 2007 9:58 pm

Rick Denney wrote:/snip It's possible to make a realistic looking bugle that resonates on the odd harmonics, and another that resonates more on the even harmonics. Fletcher and Rossing (The Physics of Musical Instruments) makes really good reading on this topic.
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Postby iiipopes » Tue Sep 18, 2007 12:45 am

Hey Robert -- thanks.
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Postby DonShirer » Tue Sep 18, 2007 8:45 am

As usual, Rick is a fount of wisdom, however if you are looking this up in a textbook, it is usually found under "end effect" rather than "bell effect", and the figure usually given for cylindrical organ pipes is to add about 0.6 the diameter to the effective length of the pipe, but is often more for non-cylindrical ends (such as open holes in woodwinds).

The velocity of sound does change when pipes change diameter and the varying impedance of the bell flare affects the higher frequencies differently than the lower ones. The departure of the bell from a conic shape may be an effort by the manufacturer to bring the harmonic resonances into better tune with the fundamental pitch.
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Postby windshieldbug » Tue Sep 18, 2007 11:33 am

Carl Kleinsteuber on modifying an Eb tuba to F: http://home.planet.nl/~tubaness/How2.htm

"The speed of sound is 343.5 meters per second, assuming relatively normal barometric pressure and a temperature of 20 degrees centigrade. (Higher temperatures require longer wavelengths, and at lower temperatures wavelengths will be somewhat shorter. As can be imagined, when figuring wavelengths for brass instrument construction, one must take into account the warmth of the player's breath. For a temperature of 28 degrees centigrade as compared to 20 degrees C, one must add an additional 1% to the length of the instrument, corresponding to a revised speed of sound of 347 meters per second.) The equal-tempered frequency of FF (F1, or "pedal F") is 43.654 cycles per second, so the length of the wave that produces pedal F is 7.8687 meters long. However, brass instruments act acoustically as "closed pipes", so only half this length is required to produce this note, thus 3.93435 meters. This is further complicated by the fact that a conical pipe contains more air than a comparable cylindrical pipe; it has greater volume. A physicist would say "The pitch produced by a vibrating medium (air!) depends on its weight per unit length." That's why the tubing of a euphonium is shorter than the tubing of a trombone. Yet another factor to consider when planning the correct length of a brass instrument: the diameter of the bell rim. During playing, the acoustical standing waves produced inside a brass instrument actually extend beyond the end of the bell. This effect varies with frequency and the width of the bell. For almost all common purposes, this effect can be expressed thusly:

effective tube length = actual tube length + (0.6 * bell diameter)

In the case of my F tuba, whose bell diameter is 39 centimeters, this means 23.4 centimeters of tubing must be left out of the body of the horn in order for it to come out in the desired pitch. Not an insignificant figure!

By informed guesswork, I determined I needed 92 centimeters (for the 2nd and 3rd branches), flaring from an interior bore diameter of 20.5 mm to 37 mm. Elementary school geometry told me that the following rule applies:

circumference = diameter * 3.1416 "

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