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Re: Waves

I missed the fact that you attribute the ice example to dispersion. You
told us about this a couple of years back - no, I don't have that kind of
memory, it's just that I recently looked over an old phys-l thread on
culvert whistlers because a student wanted to do an investigation into the
phenomenon - and I took your comment then to be another example of the same
waveguide phenomenon that was under discussion.

I just mentioned the ice example again in a post in this thread.
I don't know that the dispersion of sound in ice is due to the
variation in sound velocity with frequency; you may be correct
in your inference that it is a different effect. The *group
velocity* of waves in the ice sheet varies with frequency, the
higher frequencies propagating faster than the lower frequencies.
I called that phenomenon "dispersion", but it may not relate to
the variation of group velocity of longitudinal waves in ice,
but rather to some interference phenomenon in the ice sheet. The
optical phenomenon of dispersion relates to the wave velocity
variation, not the that of the group velocity. The duration of
the ice chirp is measured in tenths of seconds, so the wave
velocity is not what is seen to produce that effect.

As I understand it, the culvert whistle is not due to dispersion, but
rather to the wavefront being multiplied by reflections from the sides of
the tube. The sound propagating in a large slab of ice, where reflections
occur from the top and bottom surfaces would presumably create the same
effect, as would the spherical shell cavity between the earth and the
ionosphere for an electromagnetic pulse.

Are those what Frank Crawford might call "corrugahorn modes"?
The components of the culvert whistler sound discrete to me,
while the ice sheet chirp sounds like it is continuously varying
in frequency.

I see by the web that François Arago measured the speed of sound
in ice back in the 19th c. It doesn't seem to say anything about
frequency dependence, however.

Leigh