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Re: [Phys-l] Glencoe physics: music




22. A clarinet sounds the same note as in the previous problem,
370 Hz. It, however, produces harmonics that are only odd
multiples of the fundamental frequency. What are the frequencies
of the lowest three harmonics produced by the clarinet?

Furthermore 370 Hz is waaaay above the fundamental for an ordinary clarinet.
The instrument isn't anything like a simple tube at this frequency. I'll
betcha there is plenty of energy at even-numbered multiples of 370 Hz.

I agree with all you said (and I deleted :-) about conical vs cylindrical bores. I suppose the author could get away with saying the sax "acts" like a tube open on both ends, but that is still strecthing the truth considerably.

But for the 370 Hz, it doesn't say this is the fundamental for the lowest note of the clarinet. The player could well have many fingers up so that the fundamental _of_the_note_being_played is 370 Hz. The allowed harmonics of that note would be 3x and 5x.


2. When you blow across the top of a soda bottle, a puff of air
(compression) travels downward, bounces from the bottom, and
travels back to the opening. When it arrives (in less than
a millisecond), it disturbs the flow of air that you are
still producing across the top. This causes a slightly
bigger puff of air to start again on its way down the bottle.
This happens repeatedly until a very large and loud vibration
is built up that you hear as sound. The pitch depends on the
time taken for the back and forth trip. What happens to the
pitch as liquid is added to the bottle?

Uhhh, does it really take only 1 ms for air to make a round-trip in a
soda bottle? That must be a really small soda bottle. For that matter,
why mention this number at all?

Actually, soda bottles act mostly like Helmholtz resonators. The critical dimension is the VOLUME of the bottle, not the length (as well as the radius and length of the neck). The air in the body acts like a spring, while the air in the neck acts like a plug resting on the spring. You can predict the frequency of such resonators quite well based on the dimensions listed above and the properties of air (density and gamma in particular). (The tapering shape of bottles and the "end effects" of the air in the neck complicate things a bit, but not too much.)

I've never seen a musician categorize instruments as open-pipe
instruments versus one-end-closed instruments, or as cylindrical
versus conical instruments.

True, musicians don't talk this way, but there is a noticeable difference in the sound that musicans recognize. Instruments with only the odd harmonics have a more "hollow" sound. Saxophones sound more like brass instruments that clarinets do -- and it's not because saxophones are made of brass! It's because the harmonics are more similar.

There is also the practical difference that when you go to the upper register on a sax, you go up 1 octave. On a clarinet, you go up 1.5 octaves. This has to do with the odd vs all harmonics issue, which relates back to the cylindrical vs conical issue.


Tim F