Re: Hewitt Special Relativity Example (Long)

[John Mallinckrodt <ajm@CSUPOMONA.EDU>]

Carl E. Mungan wrote:

> John M wrote:
>
> > Everything in this argument (except, perhaps*, the conclusion)
> > applies equally well to sound waves.  So how would you explain to a
> > student why the conclusion doesn't?  I'll leave this, for now, as an
> > exercise!
> >
> > * I say "perhaps" because the conclusion is a little vague about who
> > is doing the sending and who is doing the receiving.  With
> > appropriate assignments, the conclusion *does* apply to sound waves.
>
> Neat! Okay, time's up, I'd love to hear the rest of the details. Carl

Well, O.K.  A generalized version of Hewitt's argument does prove the
following for *any* wave phenomena:

If the frequency is shifted by a factor of r when an observer moves
away from (or toward) a source at a speed v, then the frequency will
be shifted by a factor of 1/r when the source moves toward (or away
from) the observer at the same speed v.

An examination of the equations for the "normal" and relativistic
Doppler effects will show that both support this conclusion.  The
critical difference--one that needs to be made explicit to apply the
argument to Hewitt's treatment of the twin paradox in which the
observer is always "at rest"--is that, in the case of the
relativistic Doppler effect, motion of the source is
indistinguishable from motion of the observer.

--
John Mallinckrodt        mailto:ajm@csupomona.edu
Cal Poly Pomona          http://www.csupomona.edu/~ajm

This posting is the position of the writer, not that of SUNY-BSC, NAU or the AAPT.