Wave Propagation in Linear Media | re-examined

1.5 Other velocity de nitions
evident that this procedure is in fact nothing but a ltering of the pulse, apt to make it
smoother and reduce the in uence of noise. Unfortunately, it fails to give a unique result
whenever the pulse is split into several parts on its passage through the medium.
Anyhow, it might be indeed more meaningful in such a case to treat the distinct parts separately
than to construe an arti cial centre of gravity, which Bloch compared drastically to
the fact that, `if the earth were blown to pieces by a thermonuclear device, the center of mass
would still serenely orbit the sun'. On the other hand, is there any good reason for treating
a pulse di erently only because it is incidentally torn apart by dispersion? After all, it is still
one single signal. These nal thoughts re ect, in essence, the nature of the entire discussion
on wave propagation velocity.
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