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Re: Hewitt Special Relativity Example (Long)



My apologies for hitting the send key WAY too early. Here's what I
meant to say!

Chuck Britton wrote:

At 11:31 PM -0700 10/19/02, John Mallinckrodt wrote:

>It is interesting, however, to note that his argument might well
*seem* to apply equally well to sound waves; the reason it doesn't is
a little subtle. To his credit, he does *say* that it doesn't apply
to waves that require a medium, but he doesn't explain why.

This 'subtlety' can be cleared up by stressing the postulate
of c being constant. For waves that utilize a medium - this is not
the case.

I disagree. Especially for the target student audience, this
"explanation" won't be sufficient. (Well, it *may* be sufficient as
far as they are concerned, but it shouldn't be.) One has to explain
WHY the constancy of c is critical to Hewitt's clever argument. That
isn't so difficult to do, but it is far from trivial and it certainly
isn't obvious.

For the benefit of those who weren't able to reconstruct Hewitt's
argument from my cryptic description last night, here's what he says:

"Suppose a sender on earth emits flashes 3 min apart to a distant
observer on a planet that is at rest relative to the earth. The
observer, then, sees a flash every 3 min. Now suppose a second
observer travels in a spaceship between the earth and the planet at a
speed great enough to allow him to see the flashes half as
frequently--6 min apart. This halving of frequency occurs for a
speed of recession of 0.6 c. We can see that the frequency will
double for a 0.6 c speed of approach by supposing that the spaceship
emits its own flash every time it sees an earth flash, that is, every
6 min. How does the observer on the distant planet see these
flashes? Since the earth flashes and the spaceship flashes travel
together at the same speed c, the observer will see not only the
earth flashes every 3 min but the spaceship flashes every 3 min as
well. So although a person on the spaceship emits flashes every 6
min, the observer sees them every 3 min at twice the emitting
frequency. So for a speed of recession where frequency appears
halved, frequency appears doubled for the same speed of approach."

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!

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

* 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.

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