Re: [Phys-l] Glencoe physics: music

["Folkerts, Timothy J" <FolkertsT@bartonccc.edu>]

John,

I rarely disagree with you, but I have to object to a bit of what you wrote.


> 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.

Did I ever say one was more critical?  Both were mentioned and both are important.
See http://www.phys.unsw.edu.au/~jw/Helmholtz.html for more details, but the resonant frequency is predicted to be (give or take a few small corrections)

 f = v/2pi (A/LV)^0.5

where 
  v = speed of sound
  A = cross-sectional area of neck
  L = length of neck
  V = volume of container


>          ||                     _||_
>          ||                    |    |
>          ||                    |    |
>          ||                    |    |
>         _||_                   |    |
>        |____|                  |____|

Since you made L(1) = 5 L(2) and V(1) = 1/5 V(2), then LV is constant, and f is constant.  However, other variations like 

           ||        vs           _||_
          _||_                   |    |
         |    |                  |    |
         |    |                  |    |
         |    |                  |    |
         |____|                  |____|

would NOT produce the same frequency.

Also, containers like 

          _||_        vs          __||__
         |    |                  |      |
         |    |                  |      |
         |    |                  |      |
         |    |                  |      |
         |____|                  |______|

would have different resonant frequencies, and no length has changed.


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

Well, the equation above clearly depends on volume, and the example above clearly depends on volume, so I stand by my claim the frequency DOES connect to "VOLUME" - certainly much more than frequency connects to the overall length from top to bottom.  


Tim F