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*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

so once again, the definition of f has been generalized.for a wide class of functions, in fact for all

that are of interest to physicists

Thirdly, the heading of section 50-5 speaks of an

Usually theorems are completely general, unless theenergy theorem

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.

**References**:**[Phys-L] error in Feynman § I-50-5 : wave energy "theorem"***From:*John Denker <jsd@av8n.com>

**Re: [Phys-L] error in Feynman § I-50-5 : wave energy "theorem"***From:*rjensen@ualberta.ca

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