After a recent physics lab on standing waves, I became curious about
the idea of producing oscillating standing waves, by which i mean,
standing waves which change in amplitude over time, much in the same
way two notes similar in frequency which are played in close proximity
to eachother produce a note which is the average of the frequencies of
the two original notes, but which changes in "loudness" over time.
So here's my question:
Is it possible, by connecting two wave generators, one to each end of
a piece of string, to produce in that string a standing wave which
oscillates in amplitude.
Please provide a diagram of the setup, and details of what settings
would be needed to achieve this (as in, what frequencies on the
generators, what kind of generators, what kind of string, etc, such
that i would be able to go out and buy said equipment and follow said
instructions to achieve intended result)
Thank you very much!
-Christopher |
Request for Question Clarification by
hedgie-ga
on
05 Jun 2003 22:31 PDT
hello soren
Your specifications: 'beats and standing ways' contradict each other
for practical systems.
standing waves requires length /lambda = n
where n is integer (or integer over small integer)
beats require close frequencies : c/lambda1 - c/lambda2 =epsilon is
small
combining two equations you see that length/c would have to be very
large
where c is speed of the wave.
The composition of the waves will be
Composite = a1* sin(k1 *x - omega1 *t) + a2* sin(k2 *x - omega2 *t
+dphase)
Try do plot that, (on the computer) and see if choice of omega.i will
produce
what you want.
Here are some examples of the plots you should get:
http://www.upscale.utoronto.ca/GeneralInterest/Harrison/Vibrations/Vibrations.html
Closest to you spec is shown on this applet
. As the movie shows, when the two waves are 180°
out-of-phase with
each other they cancel, and when they are in-phase with each other
they add
together. As the two waves pass through each other, the net result
alternates
between zero and some maximum amplitude.
http://www.kettering.edu/~drussell/Demos/superposition/superposition.html
Additional references
Beats
http://www.physics.ucla.edu/demoweb/demomanual/acoustics/effects_of_sound/beats_and_sympathetic_vibration.html
SEARCH TERM
Vibration beats standing waves
This is posted as request for clarification since it is a 'negative
answer'.
Question is: Do you want to accept this, perhaps with some
clarifications
as an answer?
hedgie
|
Clarification of Question by
soren9580-ga
on
05 Jun 2003 23:49 PDT
the information you gave me was very good, but i just would like some
more clarification. Are you saying that it is not possible to use wave
generators to produce a physical version of oscillating standing wave
at kettering.edu? Would it work to simply have two generators at the
same frequency 180 degrees out of phase as the diagram indicates?
Basically, here's what i want; i want a way to physically produce in a
string using wave generators, the diagram at the website you showed
me. How would i do that?
|
Thank you soren
Are you saying that it is not possible to use wave
generators.. ?
Not at all. I was suggesting that you do some [computer] simulation
since it is fun, easy, and quite educational. Once the computer says
XYZ can be done, the next task is to build it in the lab. Some
people
are more likely to benefit, some may skip that part and go straight
to the lab. Most of the time calculation helps. It helps to 'debug'
the
experiment if it does not 'behave' and clarify the concepts.
Instead of using computer one can 'model the waveforms'
on the osciloscope, which the school may have.
Electric, mechanical (and many other) vibrations are described
by similar equations.
One can use a generator 1 to drive a generator 2 e.g. to sweep the
frequency
or one have two generators each exciting the same physical string at
two
points.
You want to create this case:
'Two sine waves travelling in opposite directions create a standing
wave'
right?
The equation shown can be realized pysically. The actual realization
depends
on the physical setup and intruments you have. What drivers you use,
how you monitor the oscilations atd. But as a general procedure:
create one traveling wave driving at one end by generator 1, create
other wave traveling the other way using the other generator/wxciter
at the other end. Learn to control the phase delay, then activate both
generators simultaneously.
Lab setups use different exciters, pickups etc. An example of simple
setup
for exciting a beam are shown in lab 6 of this
http://www.ece.uiuc.edu/coecsl/me240/
Few more instruments (scope) are shown here
http://www.kostic.niu.edu/ScopeDemo.html
If possible, check out the programable generators,
and instruments which have GPIB interface.
http://www.educatorscorner.com/index.cgi?CONTENT_ID=3234
http://sine.ni.com/apps/we/nioc.vp?cid=1230&lang=US
http://www.inesinc.com/linux.htm
They allow wide range of configurations.
If you need more clarification, please describe
(or point to a site describing)
the setup you are using or thinking of.
Happy experimenting.
hedgie |
Request for Answer Clarification by
soren9580-ga
on
07 Jun 2003 23:42 PDT
I am still a bit confused as to whether this is possible or not.
What i want is to have two wave generators, creating changes in
amplitude at certain set frequencies on either end of a string. (one
on each end) I would like, through use of these generators to produce
a standing wave in the string, whose amplitude changes over time. What
i would like from you, very simply, is for a string of length L, mass
M, and tension T,
(Left Generator)-------------(Right Generator)
what amplitude and frequency should each generator be set to, so that
i produce in the string a wave which will go from being a standing
wave, to being a flat line, to being a standing wave, to being a flat
line, and so on till infinity. I figured this could be done by having
two different frequencies, but it seems like you were suggesting using
the same frequency for both, but just having them out of phase, which
would work, but the waves have to reflect when they reach the end of
the string, (a wave from the left generator will bounce off the right
generator and return, not simply continue as in the picture from the
link you sent me) and so thus the equations (as far as i can tell)
require more thought. I would please request that you explain whether
it is possible in a closed string, to produce a standing wave which
changes in amplitude, and with what (ideal) conditions, this could be
setup.
-Chris
|
Clarification of Answer by
hedgie-ga
on
08 Jun 2003 20:00 PDT
Soren
we are having a communication problem.
There is no way I, or anyone, can give you three numbers,
L M and T which will make your concept real. I can only
give you few pointers to accumulated store of knowledge
called physics. Physicists developed a language whiech allows us
to describe physical concepts. It is called mathematics. In our
case, case of waves, the math is simple trigonometry:
Superposition
of waves on the string can be described by adding the sine waves.
You have described your concept as 'beats' and 'standing waves' and
I pointed out to you it is sort of an oxymoron. I have said 'closest
to
what you are describing' may be case on the kettering site :
--two waves pass through each other... a case described
mathematically
by superposition of two waves with a phase delay of 180.
That mathematical representation can be realised experimentally. It
may or
may not be what you mean by your verbal, non-mathematical description
' standing wave which changes in amplitude ' . I gave you a
prescription:
first describe your concept by mathematical model. After that, you
may be
able to realize as a real experiment. People have developed many
setups
which may vibration phenomena easy to observe, Slinky is a popular
medium
Bell vibration machine is another
http://nemesis.ucsc.edu/waves/visible/visible.html#longitudinal
there are several setups here
http://www.csupomona.edu/~physics/oldsite/demo/oscillat.html#OW-A-SS
which include waves in a streached wire, which it seems is setup you
are
using. The abstract, mathematical terms, wavelength, speed of
propagation,
can be realized on any of these. The speed of propagation depends on
density and elasticity of a spring. One has to be able to measure that
speed
for specific set-up one has first. You cannot get it from some one
else,
without going to more detailed description of your physicsl system
(e.g. material of the string). To realize your concept is a process.
The physics
is in the mapping of mathematical description into physical reality.
There
is no shortcut I know of. In the experiment of two passing waves of
equal
frequencies the generators would be asctivated for few seconds only,
so
that they waves meet in the middle and effect shown will be exhibited
for
few seconds - before any reflections arrive. I do not think it can be
a
steady state. But again - if you manage to model it by sine waves
first,
model the reflections, see if you can neglect dispersion,...you may be
able to realize that in the lab. So far, you concept is described in
such
a fuzzy, inexact way, that one cannot say for sure if it can, or
cannot be realized,
hedgie
|
Request for Answer Clarification by
soren9580-ga
on
08 Jun 2003 20:37 PDT
In physics, it is very possible, to model the behavior of waves in a
closed system such as piece of string anchored at both ends. having
given you the three neccessary conditions of the system, the linear
mass density of the string (from the mass and length of the string)
and the tension T, you should be able to model this system using
simply mathematical and physical properties. What i want to know, is
using such a setup, of a string which is: in such a closed system, is
it possible to set up a standing wave which changes in amplitude over
time. There are two possible answers, Yes, it is possible, and here's
how: with two pulse generators, one on either end, and a string of
length L, mass M and tension T,
the pulse generator on the left side of the string, would generate
pulses at frequency F1 and amplitude A1, and the generator on the
right side of the string would generate pulses at frequency F2 and
amplitude A2. these pulses would travel down the string to the other
side of the string, and reflect off the wall in some predictible
manner, and through superposition would sum at any given moment, into
a standing wave of some amplitude, which would change over time, much
in the same way that a regular standing wave created by a string of
mass M length L and tension T which is anchored on one end to a pulse
generator and is fixed on the other end, will generate a standing wave
of amplitude A1 and frequency F1, when the pulse generator is set to
create pulses of amplitude A1 and Frequency F1, and when
F1=(n/2L)(SQRT(T/(M/L)), where n is any whole number. As you can see,
it is easy to mathematically determine what conditions are required
when you know the correct equations. So very simply, given T, M and L
for a string fixed at each end to a pulse generator which can generate
a pulse a at frequency F and and an amplitude A, is it possible to
creat a standing wave which changes in amplitude over time. If the
answer is yes, please give me an equation for the frequency and
amplitude of each pulse generator, and if the answer is no, please
tell me definitively that it is not possible. Otherwise, you have not
answered my question.
I am sorry for being so insistant, but I would really like a clear
answer to this question. It has been bothering me for a while, and I
do not have the knowledge of physics, nor the time, to figure it out.
I would assume that for you, an expert, it would be a rather easy
question. I know this was more work then you originally intended to do
for 5 dollars, so i'll give you an extra ten dollars (i'm a student)
if you will give me a definitive answer. If you need any more
clarification then this, i am happy to oblidge.
The source of the equations i cited is
http://romano.physics.wisc.edu/lab/manual/node24.html
And for clarification of the setup, i am speaking of a string
connected on either end to (ideal versions) the speaker in figure
three.
-Chris
|
Clarification of Answer by
hedgie-ga
on
10 Jun 2003 02:06 PDT
Hi again Soren
Re: 'I am sorry for being so insistant,
but I would really like a clear answer to this question '
It is OK to express what you want - as long as the
discussion converges to a single final question.
Clear answer has as a pre-requisite a clear question
Your clarification, particularly the link
http://www.ric.edu/ptiskus/Physical_Science/Waves_Sound_notes.htm
to the schematics of your setup was very helpful
So, in our case we are clarifing, rather then transmuting
the question- and so I will give it another try.
Let me summarize the question, as I now understand it
(assuming your place for a moment) OK?
------- final question
I am a college-level student, pre-calculus but with understanding
of trigonometry
I have:
A setup similar to the one shown, but symmetrical :
Not just left, but both ends are fixed and
there is a driver (speaker) near each end.
2) Both speakers are on continuously, with fixed parameters F1,A1
on the left and A2, F2 on the right
( i.e amplitude and frequency are constant in time,
feed TO EACH is a single harmonic wave. )
Question:
3) for the given setup, is there combination of T M L F1 A F2 A2 parameters
which will produce a single harmonic standing wave (any fixed frequency)
with A(t) an amplitude which wary with time?
I want yes or no answer, rather then tips for experimentation
or how to find out myself.
Either the parameters which will do that, and derivation
showing that it will work,
or a derivation or argument that it cannot work
for any such combination.
-------- end of question
FRFC = Final Request for Clarification
Is this a fair description of the question?
Is A(t) arbitrary function of time - or must it be a sine function?
Is that assumption above, that we seek steady state solution, correct?
Transient means that we turn the drivers off
after a short time and
observe the phenomena as disturbances are dying out.
Steady means we keeps drivers on, and after a short time,
after everything setles
down to a final steady periodic response,
we observe the periodic response.
Note, we have eliminated the ambiguous word
'pulse' which I used previously which was perhaps
too telegraphic 'shorthand' for 'steady' vs 'transient'.
hedgie
|
Clarification of Answer by
hedgie-ga
on
16 Jun 2003 09:38 PDT
soren
Seeing no corections, I assume that my formulation of
the question is consitent with the issue which, you said:
" has been bothering me for a while ..".
Answer is NO. There is no combination of two frequencies and amplitudes,
both fixed, which would produce the standing wave, harmonic or not, which
would uniformly acroos the whole string go up and down in amplitude.
It can be shown by constructing a general solution for such a case, and
show that the family of solution does not have an element with such propeties.
However, there is an easier, more conceptual wave to show this, which is based
on conservation of energy:
When a wave, let's say a wave packet of given shape, travels along the string,
energy propagates along the string. It propagates with a speed of the wave,
which is finite. In the scenario above, with whole wave amplitude going down
across the whole string, the energy would dispear. In the next phase, the
energy would have to appear again, everywhere along the string.
that would violate either the finite speed requirement or the conservstion law.
Thatnk you for an interesting question.
hedgie.
|
