Natural Science Forum / Physics / Relativity / March 2005

Seems like you never heard of something called wavelength. c = lambda * nu.
Since
c is constant, if frequency changes then wavelength changes inversely.
But you know this already. Why are you trolling this group?

. > HW.

In sci.physics.relativity, H@..(Henri Wilson)
<H@>
wrote
on Wed, 30 Mar 2005 04:10:35 GMT
<799k41l6dp6bmt2uefpcr3anfb80o3kl00@4ax.com>:

In its reference frame, yes.

Or the number of wavecrests received by a receiver.

False.

No, it wouldn't.  You need to follow the bouncing Lorentz transform.

Let's give it specific figures here.

An antenna at 10.24 MHz (I pick this because AIUI it's a frequency
of a certain system that a lot of people depend on :-) ) is
centered on a coordinate system.  The moving observer has
velocity v relative to this coordinate system, and has his *own*
coordinate system.

For purposes of clarity the antenna's coordinate system I will
designate as x_A, t_A and the receiver's as x_R, t_R.  Then
Lorentz specifies the transformation between these two pairs
of coordinates as

(x_R,t_R) = ( (x_A - v * t_A) * g, (t_A - v * x_A /c^2) * g)

where g = 1/sqrt(1-v^2/c^2).

Since x_A is identically zero (the antenna is not moving in its space)
we get

(x_R,t_R) = ( ( - v * t_A) * g, t_A * g)

Since the observer is not at -v * t_A, he has to wait
an additional v * t_A * g / c seconds to get the wavecrest;
the time observed is therefore t_A * g * (1 + v/c) and
the frequency is then f_R = f_A / (g * (1 + v/c)).

At v = 3 km/s = 10^-5c and f_A = 10.24 MHz we get
f_R = 10.2398976005 MHz.  In a pure emissive theory
scenario one would get f_REmissive = f_A * (1 - v/c)
= 10.2398976000 MHz.

Note that this is a pure SR effect; GR also is a factor in
any realistic calculation involving orbiting satellites (hint hint). :-)

The result is small, but measurable.

[.sigsnip]

As I pointed out in sci.physics.relativity:

No, c + v and c - v are not valid equations. c is at right angles to
any v you can name.

c + v and c - v can be used for the Doppler effect, but there is never
linear addition of velocities because
Doppler is a *positonal* effect: with each cycle the source is closer
by z*lambda and therefore has that much less distance to go which
*simulates* a velocity change allowing you to write c + v.

Once you understand that, you will see why the Michelson Morley
experiment was a null: v + ic = v - ic. See Fig. 7 in my gravity paper
at dualspace.net.

Mr. Dual Space