Look at the damped waves: http://en.wikipedia.org/wiki/Damped_wave

The damped waves pulses are simillar to AM (amplitude of oscillation
decreases/increases with time).

The decreasing/increasing may be sharp or gently.

The old damped waves " transmissions have a wide bandwidth".

Was the bandwith the distance dependent?
S*

Damped waves bear little or no similarity to AM, they are essentially
pulses with a very different spectral content.

Being pulses the spectral content is wide, tending to infinite, and yes
I suppose that the spectrum received by a distant station will vary
depending on distance; the lower level spectral lines that are spaced a
long way from the fundamental will be lost below the noise as you get
further away or the signal gets weaker due to propagation changes. The
more side-bands that you loose the slower will be the rise and fall time
of the received pulse.

AM is very different the spectrum is much more contained and only 1
side-band is required to replicate the waned signal.

Jeff