[Phys-L] Re: World Jump Day

[John Denker <jsd@AV8N.COM>]

I wrote

> > It's much more impressive if the jump NON-simultaneously.
> >  a) Imagine rows of people, with successive rows jumping at successive
> >   times, phase-matched to the surface-acoustic-wave velocity.  This
> >   launches a plane wave.  Given N jumpers, the amplitude grows like N,
> >   and the energy grows like N^2.

Folkerts, Timothy J wrote:
> That doesn't seem physically reasonable.

But it is what happens, under a wide range of practical conditions.
Phenomena of this sort are exceedingly common throughout wave
mechanics;  the optical and QM analogs are well known.  My favorite
example is the proverbial mutability of clouds:  a cloud can very
quickly vanish "into thin air" yet the number of scatterers (water
molecules) is conserved.  How so?  Answer: It's the difference between
coherent and incoherent scattering.

>   The first row adds an energy E
>   The second row adds an energy 3E
>   The third row adds an energy 5E
>   ...

Yes, that's what I'm saying ... over a wide range of conditions.

Very generally: superposition of waves contributes linearly to the
amplitude, and the energy goes like the square of the amplitude.

In this case:  Coherent jumping should add linearly to the amplitude,
over a wide range of conditions.

> Each row has the same available energy but each row adds more energy =
> than the previous row.

Yes.

> With enough rows, the final row would be addi=
> ng more energy to the wave than the total energy available (i.e. the =
> potential energy of the row at its max height during the jump).

When the wave gets that big, we are outside the range where
each jumper contributes linearly to the amplitude.  This happens
only when the wave is already verrry impressively huge, so I 100%
stand by my statement that coherent jumping is "more impressive".

> So, does the rule break down at large N?

Yes ... but only for very large N.  If the earthquake's SAW is already
so large that you can't add linearly to its amplitude by jumping on
it, I'd say the jump has _already_ been a success.
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