Science > Physics > Followup to magnetic lines question: standing waves
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Science > Physics |
| User: |
"TimR" |
| Date: |
27 May 2004 12:54:59 AM |
| Object: |
Followup to magnetic lines question: standing waves |
Thanks for the quick answer on magnetic lines and their continued
nonexistence.
I believe the infamous "standing wave" is similar to a magnetic line:
no real physical existence, though at times a useful concept.
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| User: "Timo Nieminen" |
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| Title: Re: Followup to magnetic lines question: standing waves |
27 May 2004 01:38:58 AM |
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On Thu, 26 May 2004, TimR wrote:
I believe the infamous "standing wave" is similar to a magnetic line:
no real physical existence, though at times a useful concept.
A guitar string tells me otherwise - its vibration is a standing wave.
Mathematically, it's the sum of two waves travelling in opposite
directions along the string.
Perhaps you could clarify what you mean by a "standing wave", if the above
does not satisfy?
--
Timo Nieminen - Home page: http://www.physics.uq.edu.au/people/nieminen/
Shrine to Spirits: http://www.users.bigpond.com/timo_nieminen/spirits.html
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| User: "TimR" |
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| Title: Re: Followup to magnetic lines question: standing waves |
27 May 2004 06:43:18 AM |
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Timo Nieminen <timo@physics.uq.edu.au> wrote in message news:<Pine.LNX.4.50.0405271636270.24123-100000@localhost>...
On Thu, 26 May 2004, TimR wrote:
I believe the infamous "standing wave" is similar to a magnetic line:
no real physical existence, though at times a useful concept.
A guitar string tells me otherwise - its vibration is a standing wave.
Mathematically, it's the sum of two waves travelling in opposite
directions along the string.
Perhaps you could clarify what you mean by a "standing wave", if the above
does not satisfy?
It should not satisfy.
I contend that standing wave is a method of visualizing a phenomenon
that more often leads to confusion than clarity.
How is a guitar string an example of a standing wave? Any
differential element of a guitar string is moving at 90 degrees to the
long axis of the string. There are no waves traveling longitudinally
from end to end as you propose. In fact the only wave shape on that
string occurs if and only if you graph the function of displacement
from center, vs time, for one point on the string.
Now a wind column can be seen differently. The pressure impulse does
travel down the tube and reflect. If tube length is chosen correctly
there should be areas of relatively constant high and low pressure.
However nothing ever stops the wave fronts from passing through each
other, right? Nothing "stands?"
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| User: "Franz Heymann" |
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| Title: Re: Followup to magnetic lines question: standing waves |
28 May 2004 01:13:21 AM |
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"TimR" <timothy42b@aol.com> wrote in message
news:87af0be7.0405270343.1a0b4a80@posting.google.com...
[snip]
How is a guitar string an example of a standing wave? Any
differential element of a guitar string is moving at 90 degrees to
the
long axis of the string.
So what? Have you never heard of transverse waves?
There are no waves traveling longitudinally
from end to end as you propose.
There are 2 transverse waves travelling in opposite directions along
the string.
In fact the only wave shape on that
string occurs if and only if you graph the function of displacement
from center, vs time, for one point on the string.
Now a wind column can be seen differently. The pressure impulse
does
travel down the tube and reflect. If tube length is chosen
correctly
there should be areas of relatively constant high and low pressure.
However nothing ever stops the wave fronts from passing through each
other, right? Nothing "stands?"
If you were to pluck a guitar string, then quickly clamp it for a
fraction of a second exactly at the middle so as to reduce the number
of harmonics you will see a standing wave with a node at the centre.
Franz
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| User: "Richard Herring" |
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| Title: Re: Followup to magnetic lines question: standing waves |
27 May 2004 10:43:00 AM |
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In message <87af0be7.0405270343.1a0b4a80@posting.google.com>, TimR
<timothy42b@aol.com> writes
Timo Nieminen <timo@physics.uq.edu.au> wrote in message
news:<Pine.LNX.4.50.0405271636270.24123-100000@localhost>...
On Thu, 26 May 2004, TimR wrote:
I believe the infamous "standing wave" is similar to a magnetic line:
no real physical existence, though at times a useful concept.
A guitar string tells me otherwise - its vibration is a standing wave.
Mathematically, it's the sum of two waves travelling in opposite
directions along the string.
Perhaps you could clarify what you mean by a "standing wave", if the above
does not satisfy?
It should not satisfy.
I contend that standing wave is a method of visualizing a phenomenon
that more often leads to confusion than clarity.
How is a guitar string an example of a standing wave? Any
differential element of a guitar string is moving at 90 degrees to the
long axis of the string. There are no waves traveling longitudinally
from end to end as you propose.
Non sequitur.
In fact the only wave shape on that
string occurs if and only if you graph the function of displacement
from center, vs time, for one point on the string.
Instead of plucking the string, strike it with a hammer at a single
point and watch what happens. _Something_ travels to all the other
points in order to produce what you see.
Now a wind column can be seen differently. The pressure impulse does
travel down the tube and reflect.
Just as the displacement impulse travels down the guitar string.
If tube length is chosen correctly
there should be areas of relatively constant high and low pressure.
However nothing ever stops the wave fronts from passing through each
other, right? Nothing "stands?"
The location of the nodes and antinodes "stands".
--
Richard Herring
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| User: "Timo Nieminen" |
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| Title: Re: Followup to magnetic lines question: standing waves |
27 May 2004 05:56:40 PM |
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Comments addressed to the OP, not the replier on whose excellent reply I
piggyback.
On Thu, 27 May 2004, Richard Herring wrote:
TimR <timothy42b@aol.com> writes
Timo Nieminen <timo@physics.uq.edu.au> wrote:
On Thu, 26 May 2004, TimR wrote:
I believe the infamous "standing wave" is similar to a magnetic line:
no real physical existence, though at times a useful concept.
A guitar string tells me otherwise - its vibration is a standing wave.
Mathematically, it's the sum of two waves travelling in opposite
directions along the string.
Perhaps you could clarify what you mean by a "standing wave", if the above
does not satisfy?
It should not satisfy.
Then perhaps you should explain clearly what you mean by a "standing
wave". Note that the vibrating guitar string is indeed a standing wave, as
the term is commonly used. The fact that you do not believe it to be a
standing wave suggests to me that you and I mean quite different things by
the term.
Note that a (simple harmonic) travelling wave has a space and time
variation of cos(kx-wt) or cos(-kx-wt) depending on the direction of
travel. Add these together and you get 2*cos(kx)*cos(wt). Note that this
describes the vibration of (a single harmonic on) a guitar string. Note
also that the "wave shape", as you call it below, does not move relative
to x.
How is a guitar string an example of a standing wave? Any
differential element of a guitar string is moving at 90 degrees to the
long axis of the string. There are no waves traveling longitudinally
from end to end as you propose.
Non sequitur.
In fact the only wave shape on that
string occurs if and only if you graph the function of displacement
from center, vs time, for one point on the string.
... or if you graph the displacement vs x, for a fixed time. For the
fundamental mode, you see a 1/2 wavelength.
Instead of plucking the string, strike it with a hammer at a single
point and watch what happens. _Something_ travels to all the other
points in order to produce what you see.
A further useful exercise is to try to excite the higher harmonics while
minimising the fundamental mode.
However nothing ever stops the wave fronts from passing through each
other, right? Nothing "stands?"
The location of the nodes and antinodes "stands".
Just so.
Note well that a standing wave is stationary in space, not in time.
--
Timo Nieminen - Home page: http://www.physics.uq.edu.au/people/nieminen/
Shrine to Spirits: http://www.users.bigpond.com/timo_nieminen/spirits.html
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| User: "Jim Deutch" |
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| Title: Re: Followup to magnetic lines question: standing waves |
27 May 2004 03:01:02 PM |
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On 27 May 2004 04:43:18 -0700, (TimR) wrote:
I contend that standing wave is a method of visualizing a phenomenon
that more often leads to confusion than clarity.
How is a guitar string an example of a standing wave? Any
differential element of a guitar string is moving at 90 degrees to the
long axis of the string. There are no waves traveling longitudinally
from end to end as you propose. In fact the only wave shape on that
string occurs if and only if you graph the function of displacement
from center, vs time, for one point on the string.
Ok, how about a bowed violin string?
The phenomenon is nearly identical, but in this case, slow-motion
photography reveals that the string is essentially in two straight
segments with a rather sharp bend at one point. The bend travels up
and down the string, reversing itself at each end-reflection.
Really, this is no different. It's just a mix of harmonics with a
particular phase relationship that causes the "bend". In both the
violin and the guitar string, there are travelling waves going both
directions, giving rise to a standing wave that oscillates in place.
You can even get the "bend" in a guitar string -- briefly -- by giving
the string an impulse near one end, for instance, by plucking it with
a pick. The bend smooths out pretty quickly, but is there initially.
Jim Deutch (Jimbo the Cat)
--
"Philosophy needs pencil and paper. Science needs pencil, paper, and
a wastebasket." - Uncleal
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| User: "TimR" |
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| Title: Re: Followup to magnetic lines question: standing waves |
28 May 2004 01:02:12 AM |
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(Jim Deutch) wrote in message news:<40b64830.199308069@news.compuserve.com>...
On 27 May 2004 04:43:18 -0700, (TimR) wrote:
I contend that standing wave is a method of visualizing a phenomenon
that more often leads to confusion than clarity.
How is a guitar string an example of a standing wave? Any
differential element of a guitar string is moving at 90 degrees to the
long axis of the string. There are no waves traveling longitudinally
from end to end as you propose. In fact the only wave shape on that
string occurs if and only if you graph the function of displacement
from center, vs time, for one point on the string.
Ok, how about a bowed violin string?
The phenomenon is nearly identical, but in this case, slow-motion
photography reveals that the string is essentially in two straight
segments with a rather sharp bend at one point. The bend travels up
and down the string, reversing itself at each end-reflection.
Really, this is no different. It's just a mix of harmonics with a
particular phase relationship that causes the "bend". In both the
violin and the guitar string, there are travelling waves going both
directions, giving rise to a standing wave that oscillates in place.
You can even get the "bend" in a guitar string -- briefly -- by giving
the string an impulse near one end, for instance, by plucking it with
a pick. The bend smooths out pretty quickly, but is there initially.
Jim Deutch (Jimbo the Cat)
You all have convinced me that even a string vibrating can be taken to
have a longitudinal component. In that case it makes sense
mathematically to treat it as a superposition of waves. So I buy your
various arguments. However I'm not sure what is gained by adding the
term standing wave at that point. If you knew how musicians use it
you would cringe.
Um, a thought. If a guitar string is slowly pulled at the center
point then released and allowed to vibrate freely in first mode, it
isn't that obvious that longitudinal waves must exist. But since they
do, a 0th order mode must have them too. Doesn't seem a particularly
useful thought, but there you have it.
Note that bowed and plucked strings have entirely different sets of
harmonics.
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| User: "Franz Heymann" |
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| Title: Re: Followup to magnetic lines question: standing waves |
28 May 2004 11:29:04 AM |
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"TimR" <> wrote in message
news:87af0be7.0405272202.594ca077@posting.google.com...
103134.3516@compuserve.com (Jim Deutch) wrote in message
news:<40b64830.199308069@news.compuserve.com>...
On 27 May 2004 04:43:18 -0700, (TimR) wrote:
I contend that standing wave is a method of visualizing a
phenomenon
that more often leads to confusion than clarity.
How is a guitar string an example of a standing wave? Any
differential element of a guitar string is moving at 90 degrees
to the
long axis of the string. There are no waves traveling
longitudinally
from end to end as you propose. In fact the only wave shape on
that
string occurs if and only if you graph the function of
displacement
from center, vs time, for one point on the string.
Ok, how about a bowed violin string?
The phenomenon is nearly identical, but in this case, slow-motion
photography reveals that the string is essentially in two straight
segments with a rather sharp bend at one point. The bend travels
up
and down the string, reversing itself at each end-reflection.
Really, this is no different. It's just a mix of harmonics with a
particular phase relationship that causes the "bend". In both the
violin and the guitar string, there are travelling waves going
both
directions, giving rise to a standing wave that oscillates in
place.
You can even get the "bend" in a guitar string -- briefly -- by
giving
the string an impulse near one end, for instance, by plucking it
with
a pick. The bend smooths out pretty quickly, but is there
initially.
Jim Deutch (Jimbo the Cat)
You all have convinced me that even a string vibrating can be taken
to
have a longitudinal component.
I think you are still missing the point. THere has been no mention of
longitudinal waves on strings in this thread. The longitudinal
natural frequencies of a string are orders of magnitude higher than
the transverse standing waves under discussion, and they are not
usually used for sound production.
In that case it makes sense
mathematically to treat it as a superposition of waves.
Transverse waves can also be superposed.
So I buy your
various arguments. However I'm not sure what is gained by adding
the
term standing wave at that point. If you knew how musicians use it
you would cringe.
Um, a thought. If a guitar string is slowly pulled at the center
point then released and allowed to vibrate freely in first mode, it
isn't that obvious that longitudinal waves must exist. But since
they
do, a 0th order mode must have them too. Doesn't seem a
particularly
useful thought, but there you have it.
You are simply confusing the issue by dragging in longitudinal modes.
Note that bowed and plucked strings have entirely different sets of
harmonics.
Franz
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| User: "" |
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| Title: Re: Followup to magnetic lines question: standing waves |
28 May 2004 01:08:15 AM |
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In article <87af0be7.0405272202.594ca077@posting.google.com>, (TimR) writes:
103134.3516@compuserve.com (Jim Deutch) wrote in message news:<40b64830.199308069@news.compuserve.com>...
On 27 May 2004 04:43:18 -0700, (TimR) wrote:
I contend that standing wave is a method of visualizing a phenomenon
that more often leads to confusion than clarity.
How is a guitar string an example of a standing wave? Any
differential element of a guitar string is moving at 90 degrees to the
long axis of the string. There are no waves traveling longitudinally
from end to end as you propose. In fact the only wave shape on that
string occurs if and only if you graph the function of displacement
from center, vs time, for one point on the string.
Ok, how about a bowed violin string?
The phenomenon is nearly identical, but in this case, slow-motion
photography reveals that the string is essentially in two straight
segments with a rather sharp bend at one point. The bend travels up
and down the string, reversing itself at each end-reflection.
Really, this is no different. It's just a mix of harmonics with a
particular phase relationship that causes the "bend". In both the
violin and the guitar string, there are travelling waves going both
directions, giving rise to a standing wave that oscillates in place.
You can even get the "bend" in a guitar string -- briefly -- by giving
the string an impulse near one end, for instance, by plucking it with
a pick. The bend smooths out pretty quickly, but is there initially.
Jim Deutch (Jimbo the Cat)
You all have convinced me that even a string vibrating can be taken to
have a longitudinal component.
You may be needlesly confusing yourself. It is a transverse wave,
propagating longitudinally.
Mati Meron | "When you argue with a fool,
meron@cars.uchicago.edu | chances are he is doing just the same"
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| User: "Sam Wormley" |
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| Title: Re: Followup to magnetic lines question: standing waves |
27 May 2004 12:59:25 AM |
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TimR wrote:
Thanks for the quick answer on magnetic lines and their continued
nonexistence.
I believe the infamous "standing wave" is similar to a magnetic line:
no real physical existence, though at times a useful concept.
Standing Wave
http://scienceworld.wolfram.com/physics/StandingWave.html
A standing wave is a wave which oscillates but does not propagate
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