"Jim Coleman, Sr." wrote:
>
> Hi Richard:
>
> You have jumped to the wrong conclusion about the whip ilustration. That
> may have been some one else's illustration, but it is not complete. A string
> with fixed points WILL have longitudinal modes as well as transverse modes.
>
> Tie a rope to a door knob and then pluck the rope snear your tightly held
> end. You will see the wave travel from one end to the other, back and forth.
> This quickly sets up standing transverse waves in piano strings, but the
> longitudinal mode does not go away. It is when one of the longitudinal modes
> is very close to one of the transverse modes that you will hear a very
> high sharp peak. Jim Hayes is working on additional patents beyond what the
> Baldwin Piano Co. holds which were made by Harold Conklin when he was at
> Baldwin.
>
> Yes, plain strings also have longitudinal modes. Their problems occasionaly
> show up in the Tenor section mainly, but Bass strings often show these bad
> characteristics. Incidentally, there are some good characteristics also.
I think there is some confusion here with some terms.
A wave is made up of collective vibration of particles. Ie in air, the
air
particles vibrate, but they don't go away from their place. What
propagates
(the wave), is really the phase of the particles, ie the time at which
they
reach a certain reference point in their vibration cycle.
The difference between longitudinal and traverse waves now, is the type
of
vibration the particles make. Traverse waves look like this:
o o ^
o o o o |
o o o o |
o o o o o
o o |
o o |
o v
particle motion
-------------------------->
wave motion
Ie, the particles vibrate up and down, and the wave travels in the
direction
of the arrow. Thus in a transverse wave, the motion of the particles is
perpendicular to the motion of the wave.
A longitudinal wave looks like this:
oo o o o o o o o oo o o o o o o oo o o o
o o o oo
---------------------------------->
wave motion
<----o---->
particle motion
Ie, the particles vibrate horizontally, and the wave also moves
horizontally:
in a longitudinal wave, the wave moves in parallel to the particle
motion.
The difference between travelling waves and standing waves (both exist
in the
traverse and longitudinal variant) is, that a travelling wave is a wave
in
one direction: you can see it move. A standing wave is the motion that
results
when two identical travelling waves move in opposite direction and
collide.
Here you don't see a wavefront travelling anymore (it's standing).
Looks like this: Travelling wave at three consecutive time instants:
(where X denotes the fixed ends of the string)
o o
o o o o
o o o o
Xo o o o ooooooooooooooooooooooX
o o
o o
o
o o
o o o o
o o o o
Xooooooooooo o o o oooooooooooooX
o o
o o
o
o
o
o o o
o
o o o
o
Xooooooooooooooooooooooooooooo o o
oX
o
o
o
o
o
Standing wave:
o o
o o o o
o o o o
Xo o o o oX
o o o o
o o o o
o o
This is typically what happens, when you excite a string that is fixed
at two
ends. You generate a travelling wave in the string by hitting it with a
hammer.
The wave travels to the ends of the string and reflects back there. In
this way, you get waves that travel in opposite directions, and a
standing wave
emerges...
I think, that because of the stiffnes of the string, there are no
noticable
longitudinal waves there, except at very high frequencies. (very high)
So I guess that when you speak of longitudinal waves in the string, you
really
mean some residual travelling wave motion. This could be accounted for
from the
way of excitation of the string. Ideally, in a string, there would be
only one
standing wave mode: the one that produces the tone you want to have. But
when
you excite the string using a hammer strike, what you really do, is put
a pulse
of motion on the string. As a pulse is made up of an infinity of modes
(waves
of different wave lengths) right after the pulse, waves of lots of
different
wavelengths travel through the string. In a good string, the unwanted
wavelengths
get damped quickly, and only the desired standing waves remain. But I
guess that in
some strings, some unwanted waves don't get damped quickly enough, so
that
some residual travelling waves stays there.
(Or maybe you mean something completely different? ;-)
regards,
Jos.
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