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Math is not enough. (was Wave phase reversal ...)



It seems to me that a theorist must also be aware of the
mechanism, not only "the unwashed student". Otherwise
s/he may come to wrong conclusions, as far as physics
is concerned. Likewise a mathematician working with
economists must know what s/he is analyzing (in addition
of knowing how to analyze). Trivial? Yes. Worth saying?
I hope so. Attempts to teach "with math only" are common.

Bob Sciamanda wrote:

Yes, but what is the physical mechanism whereby the cancelling, reflected
wave is generated?
Perhaps something like: When an upward going vertical pulse on a rope
encounters a rigid wall termination, the last rope segment exerts an upward
force on the wall. The wall responds by exerting a downward pull on the
rope segment (by N3), thus starting a downward going vertical pulse on the
rope.

The mathematical argument shows how WE KNOW that some such mechanism
must be acting; only the physics (Newton's laws in the rope case) can
identify
that mechanism.

The theorist is often completely satisfied with only the mathematical
answer; the unwashed student has yet not acquired sufficiently naive faith
in mathematical models; he still requires the confirmation of a physical
mechanism.