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# Re: [Phys-L] error in Feynman § I-50-5 : wave energy "theorem"

• From: John Denker <jsd@av8n.com>
• Date: Sun, 22 Jun 2014 09:57:44 -0700

On 06/22/2014 09:02 AM, rjensen@ualberta.ca wrote:
I believe many of us endeavor to teach in a constructivist manner.
That is, we build on the material taught in junior courses and teach
in a manner that leaves the door open for future course to build on
what we taught.

OK.

does the 'correct'
answer for the energy of all waves simplify to "energy proportional to
the wave amplitude" for the conditions in FLP?

I assume that was supposed to say "amplitude squared".

Even so, that is not a correct simplification. There
are lots of ways I can change the square of the amplitude
without a proportional change in energy, under conditions
contemplated in FLP chapter 50.

Is "energy proportional to the wave amplitude" stated
in FLP a reasonable simplification for the level of the student FLP is
endeavoring to educate?

Well, questions about the appropriate level of detail
versus simplification are matters of taste. De gustibus
non disputandum.

I reckon all the extremes are wrong: Extreme simplification
is not good, and extreme complexity is not good.

However, there is one fundamental rule we should all
agree on, namely the rule that says:
/Say what you mean, and mean what you say./

The book defines f in terms of acoustics only: air
pressure as a function of time. So far so good.
However, it almost immediately generalizes it. Just
two paragraphs later, things are arranged
so that our formula will be completely general

Secondly, in section 50-4 it says that the results
apply
for a wide class of functions, in fact for all
that are of interest to physicists
so once again, the definition of f has been generalized.

Thirdly, the heading of section 50-5 speaks of an
energy theorem
Usually theorems are completely general, unless the
restrictions are clearly stated, or obvious from
context.

Fourthly, as it says in section II-12-1 and elsewhere,
with emphasis in the original:
the same equations have the same solutions
[...]
/The equations for many different physical situations/
/have exactly the same appearance./
Of course, the symbols may be different—one letter
is substituted for another—but the mathematical
form of the equations is the same. This means that
having studied one subject, we immediately have a
great deal of direct and precise knowledge about
the solutions of the equations of another.

To summarize:
-- Section 50-1 applies to strings.
-- Section 50-2 is "completely general":
-- Section 50-4 applies to "all functions of interest
to physicists"
-- Section 50-5 speaks of a "theorem"
++ Then without warning, the key claim of section 50-5
does not apply to strings, is not completely general,
is secretly not an energy theorem, and does not apply
to all situations of interest to physicists, but is
implicitly restricted to acoustics only.

If you choose to restrict the square-law formula to
apply to acoustics only, that's fine with me ... so long
as the restriction is explicit, or at least obvious from
context.

Maybe I'm old-fashioned, but when I am serving as writer,
reviewer, or editor, I look at things from the readers'
point of view. I don't see how an ordinary mortal reader
is supposed to divine that the square-law energy formula
is the /only/ result in the whole chapter that is restricted
to acoustics.

I'm OK with simplification. I'm just not OK with deception.