Re: [Phys-l] Glencoe physics: music

[John Denker <jsd@av8n.com>]

Folkerts, Timothy J wrote:

> But for the 370 Hz, it doesn't say this is the fundamental for the lowest note of the clarinet.

Certainly it is not the lowest note of an ordinary clarinet.

> The player could well have many fingers up so that the fundamental _of_the_note_being_played is 
> 370 Hz. 

That's the only scenario that makes sense.

>  The allowed harmonics of that note would be 3x and 5x.

Really?  How do you know?  Have you done the experiment?

> Actually, soda bottles act mostly like Helmholtz resonators. 

Yeah, I noticed that.  I thought that would be yet another horrible
problem with the Glencoe question, but upon reflection I decided it
wasn't really fatal.

>  The critical dimension is the VOLUME of the bottle, not the length 

How did volume get to be more critical than length?
I can make two different Helmholtz resonators with radically
different volume but the same frequency.  Hint:

          ||                     _||_
          ||                    |    |
          ||                    |    |
          ||                    |    |
         _||_                   |    |
        |____|                  |____|


> (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. 

The mass+spring model is OK (within limits), but doesn't connect to "VOLUME".

The funny thing is that the question that Glencoe asked is almost
model-independent:  You get the same answer whether you model the
bottle as a Helmholtz resonator or as a simple resonant tube:
adding water to the bottle raises the resonant frequency.