Re: Waves

[Mark Sylvester <msylvest@SPIN.IT>]

At 11:21 AM 7/3/00 -0400, John Denker wrote:
> At 09:16 AM 7/3/00 -0400, David Abineri wrote:
> >Am I correct in explaining string instruments, to say that a string
> >actually vibrates in many modes simultaneously when bowed or plucked?
> >That is, is it producing its fundamental along with several harmonics
> >all at the same time?
>
> Sure.  The fundamental alone would be musically useless.
>
> >Is it possible to show this behavior (if the notion is correct) with a
> >string vibrator or other equipment, rather than just postulating to
> >students that this does in fact occur?
>
> The vibrator is unhelpful for this purpose.

I agree that the vibrator is unhelpful for the purpose stated, but I think
the "Standing Waves on a String" lab deserves more support than it has
received in this thread. It is *not* an introductory experiment on waves,
but standing waves do need to be understood, whether for musical
instruments or quantum mechanical heuristics as someone else has pointed
out. With the vibrator run by a signal generator, the way that the string
responds to the resonant frequencies is definitely something to be
experienced.

> Set up a reasonably long string, or preferably rope.  I just tried it with
> 10 meters of 3/16" dacron yacht braid;  very nice rope, heavier than string
> but very, very flexible.
>
> Rig the rope across the room.  A foot or two from one end, give it a sharp
> whack with your finger.  Any student can see the resulting pulse.  (From
> across the room, vertical polarization is easier to see than
> horizontal.)  The pulse is quite localized, very small compared to the
> length of the rope.  It keeps its shape as it runs down the rope, reflects,
> and makes 10 or so round trips as it gradually decays.

A few years ago I was hiking in the Alps. At a refuge where we spent the
night there was a very long steel cable for hauling goods up from the
valley. It was a single span, goodness knows how long. I couldn't resist
whacking it with a piece of firewood from a stack nearby. The pulse came
back from the valley after what seemed like a very long time. The
interesting part is that for a few seconds before the main pulse arrived
the cable sang with high frequency noise.

Mark