[Phys-l] Glencoe physics: music

[John Denker <jsd@av8n.com>]

Quoting from Glencoe _Physics, Principles and Problems_

Chapter 15: Sound

From page 318:
> Many musical instruments are also open-pipe resonators.  Some examples
> are the saxophone and the flute.
>
> Practice Problems 
>   9.  A bugle can be thought of as an open pipe.  If a bugle were
>       straightened out, it would be 2.65 m long.
>     a.  If the speed of sound is 343 m/s, find the lowest frequency
>         that is resonant in a bugle (ignoring end corrections).
>     b.  Find the next two higher resonant frequences in the bugle.
>  10.  A soprano saxophone is an open pipe. ....

From page 322:
> Many familiar musical instruments are open-pipe resonators.  Brass
> instruments, flutes, oboes, and saxophones are some examples.  Closed-
> pipe resonators, like the clarinet, have only the odd harmonics.

End-of-chapter Problems (page 326)
>   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?

On page 318 a saxophone was allegedly an open pipe.  Really?  I would have
thought the reed on a saxophone closed the pipe, just like the reed on a
clarinet, which is repeatedly stated to be closed.

My first hypothesis is that the author got the idea that since open pipes
produce all harmonics, anything that produces all harmonics must be an open
pipe.  Yeccchhhh.  A sax does produce all harmonics ... not because it is
open, but rather because it has a conical bore.  (The notion of conical bore
is not mentioned anywhere in the book AFAICT.)

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.

And on page 322, all brass instruments are open-pipe resonators??????  That
smashes my hypothesis into dust.  Many brasses are neither open nor conical.
Evidently the author is just making up facts willy-nilly.

By the way: A bugle in C?  Those exist, but they're rather rare.  And if
we are going to calculate the fundamental resonance, it should be mentioned
that nobody ever plays that note on a bugle.

>    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?

More generally, what is the pedagogical point of *any* of these exercises?
In question 21 they explicitly tell you to find just the odd harmonics, and
in question 22 they tell you to find all the harmonics.  All you need to know
is the definition of "odd number".

Similarly, in question 2, you can safely answer the question at the end of
the paragraph without paying attention to anything that came before.

In all these questions, AFAICT, the more you think about the physics of
what's going on, the less likely you are to get the intended answer.

The subtitle of the book is "principles and problems".  I see lots of
problems, but the principles seem to be getting short shrift.

==========

The sheer number of errors leads to the following obvious conjectures:
 a) The author never actually understood the theory, and was probably
  just parroting something from some other work.
 b) The author never did any of the experiments suggested in the text,
  such as looking at the power spectrum put out by a clarinet.
 c) The author never even so much as looked at a bugle or a saxophone.
 d) The author was confident that reviewers and readers would not
  actually know anything about the subject, and would not do any
  experiments.

Now the funny thing is that the author was probably right about point (d).
Virtually nobody does such experiments, because _they don't care_ about
the answer.  I've never seen a musician categorize instruments as open-pipe
instruments versus one-end-closed instruments, or as cylindrical versus
conical instruments.  So really the book is foisting on us a bunch of
stuff that virtually nobody cares about, masquerading as a real-world
application.  That's doubly sad, because there are lots of interesting
legitimate physics-of-music ideas that could have been discussed ... even
at the high-school level.