Re: Fun with Majorettes


actionintegral@xxxxxxxxx wrote:
There is a long parade of majorettes, moving steadily from left to
right. To the left of you, they hold their batons fixed in such a way
that the baton orientation forms a sine wave of some wavelength.

To the right of you, the orientation of the batons also form a sine
wave, but the wavelength has doubled!

How can this be? The majorettes have not slowed, and their spacing is
the same everywhere.

http://www.majorettes.ca/images/U903837INP.jpg

If they are holding their batons *fixed*, then the only way they can do
this is to double the space between adjacent majorettes. Unfortunately,
this places an undue burden on majorettes far away from where you are
standing. The reason is pretty plain. The first majorette to the right
of you has to take some steps to increase her spacing from you from x
to 2x. The *next* majorette, who was at distance 2x from you, now has
to take twice as many steps as the first majorette, to increase from 2x
to 4x. The next majorette has to go from 3x to 6x, three times as far,
and so on. If it's a very long line, this gets tough.

However, the majorettes don't have to hold their batons fixed and march
in a line to make a wave. The can also stand in one place and move
their batons up and down, each majorette slightly out of phase from the
adjacent majorette (lagging a little in time). Now to double the
wavelength, there are two possibilities: a) raise and lower the batons
twice as slowly, b) increase the speed of the wave by halving the phase
(the lagging) between adjacent majorettes.

PD

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