Yesterday Ludwik said that transverse waves driven by tension were
relatively familiar, while those driven by other restoring forces were
relatively unfamiliar.
I suspect that another way of classifying waves gets more to the
point: some wave equations are (more or less) nondispersive, while others
are markedly dispersive.
Examples of (more or less) nondispersive waves include:
visible light in air or vacuum
audible sound in air or water
transverse waves driven by tension in a taut string
longitudinal compression/extension waves in a spring
In contrast, examples of markedly dispersive waves include:
visible light in media such as flint glass (e.g. prisms)
radio waves in the ionosphere
low-energy solutions of the Schrödinger equation
surface waves at the air/water interface
transverse waves driven by stiffness in a spring
Many high-school physics books blissfully ignore dispersion. They can get
away with this by considering only nondispersive media and/or considering
only monochromatic waves if the medium is dispersive.
You can make a good classroom demonstration of nondispersive propagation by
stringing a strong but flexible rope across the room under plenty of
tension. (I've got some nice Dacron kernmantle yacht braid that works
great.) Then smack it near one end with a bat or a hammer. This will form
a nice pulse which can be seen to retain its shape as it runs down the
rope, in accordance with the running wave solution
f(x,t) = F(x-ct)
The directly-contrasting demonstration is more difficult and less pleasing,
because it tries to demonstrate the NONexistence of such a solution -- and
it's always hard to prove a negative. Get a long metal or fiberglass rod
and clamp it at one end so it sticks across the classroom. It needs to be
stiff enough to keep itself off the floor, but floppy enough to allow
flexional waves. If you smack it with a bat, you will *not* see a
shape-preserving wave packet run to the other end. The wavespeed for the
high-frequency components is so much faster than the wavespeed for the
low-frequency components that the wave packet tears itself apart.
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A better contrast would be to measure the dispersion relation for the two
media directly, by measuring the wavelength versus frequency.
Of course this would require students to actually *do* stuff (measuring
lengths, counting and timing cycles, drawing graphs) rather than just
sitting there and watching a qualitative demonstration.