Re: Taylor & Wheeler:Spacetime Physics, Ex,L-5 Doppler Shift

On Thu, 28 Jun 2007 09:09:11 -0400, hetware <massless@xxxxxxxxxxxx>
wrote:

In exercise L-5 of Taylor and Wheeler's Spacetime Physics, they ask me to
show that the location x of the nth pulse of light from an emitter with
constant frequency satisfies the relation:

n=(f/c)(t-x)

Where time is given in meters. So WTH is c? They say that the wave travels
in the positive x direction with speed c, but c=1 unless we are dealing
with phase velocity or propagation through some material where the speed of
light != c. Neither of these conditions are mentioned in the statement of
the problem.

If the problem were given in conventional units, n=(f/c)(t-x) fails
dimensional analysis. f[1/T], c[L/T] t[T] x[L], f[(1/T)(T/L)(T-L). The
last term (T-L), in particular doesn't make sense. Does anybody understand
what they mean here?

You must insert c m/s for ct. c=1 is bad practice. Your query attests
to that.
f/c is commonly called the wave number K with units in cycles per
meter, So the number of cycles is given by
n = K cycles/meter * distance(ct-x)meters = cycles.
John Polasek
.

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