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Re: [Phys-l] [PTSOS] Musical Instrument Project [1 Attachment]


On 2011, Sep 05, , at 16:43, Bob Bessin wrote:

Here is mine Robert. It is pretty straightforward, but I have gotten some great instruments over the years.
Best,
Bob


Bob, I highly recommend you either drop from your references the first one (The Physics Classroom) or add a correction.

Not wishing facial egg, I posted as "Bad Physics" on the phys-l list the excerpt (copy below) of the resonance of the air column in the hollow tube. I thought it highly unlikely a significant resonance would occur, as the ratio of the longitudinal vibrations waves speeds differ by a factor of approximately 19. This means that the 18th overtone would be the nearest match to the tube's fundamental. Not only that, the coupling between the two is likely very weak. The four replies [so far] agreed.

One even wrote, referring to "The Physics Classroom",

"Ouch. That was painful to read."


The frequency difference between the modes near the 18th are approximately 170 Hz. I calculated (including the end effect, which is for a one cm radius tube about 0.012m) the mismatch is approximately 10Hz to the closest mode. For a reduction of the response of 1/sqrt(2) the Q of the air column is ~ 320 [3.2kHz / 10 Hz]



"Another common physics demonstration that serves as an excellent model of resonance is the famous "singing rod" demonstration. A long hollow aluminum rod is held at its center. Being a trained musician, teacher reaches in a rosin bag to prepare for the event. Then with great enthusiasm, he/she slowly slides her hand across the length of the aluminum rod, causing it to sound out with a loud sound. This is an example of resonance. As the hand slides across the surface of the aluminum rod, slip-stick frictionbetween the hand and the rod produces vibrations of the aluminum. The vibrations of the aluminum force the air column inside of the rod to vibrate at its natural frequency. The match between the vibrations of the air column and one of the natural frequencies of the singing rod causes resonance. The result of resonance is always a big vibration - that is, a loud sound."


bc thinks this required "way" too much time.

p.s. f = c*n / 2*L for both the air column and the tube ~ respective c's ~ 343 m/s and 6420

c*n / 2(L + 0.012) = c*n / 2L L= 1m n (Al tube) = 1

3210Hz = n(air) 171.5 n ~= 18.7 19*171.5 = 3.2585kHz and 18.7*171.5 = 3.2482kHz difference = 10.3Hz

Note: Q of a tuning fork is ~ 1k. The coupling to the air of the column is the area of the two ends v. ~ the same as a typical fork. So I expect the Q abut the same unless the internal losses of Al and air differ much.