When do objects Resonate?

Discussion in 'Physics' started by Mathematics!, Jul 31, 2008.

1. Mathematics! Thread Starter Senior Member

Jul 21, 2008
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I am trying to understand when a given object resonates.

For example in the case of mechanical waves when you have 2 same tuning forks and when you hit one the other resonates.
Does this depend on the distance?
Does resonation only occur when the wave is total refracted into an object?

Is their away to determine what objects resonate to what frequencies?
If so is their a difference in the formulas for resonating with mechanical waves as opposed to electromagnetic waves?

I would think the princples of resonation would depend on the energy levels of the atoms that make up the resonating object and the frequency
of the wave. In the case of electromagnetic waves I would guess that if you have a frequency of f which corosponds to an energy = f * h.

Then one of the atoms electron orbital energy state must be the same
as the energy carried by the wave. So as to bump it to another orbital level.

I am thinking that resonation can be descriped by the same means as
what frequency of light gets reflected (i.e what color you see ) as opposed to what frequencies get refracted (i.e goes into the object). Which this can be descriped by absorption spectroscpy.

But now I was think about a black body object that absorbs all frequencies (or wavelength of light ). So does black bodied objects resonate at all frequencies?

Anyway I am getting confused on how you can determine when an object resonates , when it reflects or refracts.

What I believe but could be wrong is an object reflects a wave when their is no corrosponding energy level in the atoms that make up the object so the atom doesn't absorb the photon. And if their is an energy level corrosponding to the waves energy then the atom absorbs the photon and is bumped to the next energy level. But then what contols the angle at which it is refracted. We can determine it from snells law but from an atom point of view what controls the angle that the photon is emited out of the electron at?

Thanks for any help on this question.

2. triggernum5 Active Member

May 4, 2008
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Objects resonate when a periodic driving force coincides with a natural frequency of the object.. In terms of waves, whenever periodic constructive interference is observed.. Sorry if I pointed out the obvious, you seem to be decently educated in physics.. Regarding the atomic photon emission though, the angle of refraction is actually a statistical quantity..
I'm assuming you're thinking lasers though.. This page explains that pretty well.. http://www1.union.edu/newmanj/lasers/Laser Theory/laser_theory.htm

3. studiot AAC Fanatic!

Nov 9, 2007
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This is true but not a 'why or how'

The best explanatory demonstration of resonance I have ever seen was with a hanging weight and a knotted handkerchief! The same principle applies to atoms and photons or any other resonance system.

Take a weight hanging freely and unmovingly.

Swing the hanky to hit the weight with the knot. Do this repeatedly.
You will observe the following

If you strike the weight always whilst it is moving away from you you will gradually build up pendulum motion. This effect will be maximised by always striking at the point where the weight is motionless and about to move away.

If you strike it whilst it is moving towards you, you will dampen the motion.

Thinking about the relative momenta of the knot and weight will show the best transfer and rate of striking. It will even explain harmonics.

A little consideration will tell you that this model will show all about resonance.

Last edited: Aug 1, 2008
4. triggernum5 Active Member

May 4, 2008
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Another good demo is when you're bored at a bus-stop.. Those signs can get some hefty resonant sway.. I'm not sure if thats the scope of the original question though.. The OP seems like hes already nailed the basics down.. Is it confusion with the various definitions?

5. Mathematics! Thread Starter Senior Member

Jul 21, 2008
1,022
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What I am confused about is do all objects resonate when a given wave hit's it. Or does it depend on the frequency of the wave.

In the case of Mechanical waves if you have 2 different tuning forks
then you will not see any vibrations/resonating object pairs when you hit one tuning fork on a table away from the other not on the table.

But if you have 2 of the same tuning forks then they will both vibrate when one vibrates.

So I would think objects only resonate at certain frequencies.
Maybe the key is the wave must carrier a certain energy that corrospond's to the electron orbitals of the chemical componds that make
the resonating object up. (kind of like what photon's of light get emitted or absorbed ) I Would thing resonation occur's from the part of the wave being refracted/absorbed into the object. If it is total refraction then that would be the max resonation that the object could resonate for that given wave frequency.

In the case of electromagnetic waves we have E = f h. So if we have total refraction then the wave carries E into the object.

Anyway if you physical move a stop sign back and forth with your hand.
Then you are exerting a force thus you are delivering a certain energy to the object. In some big objects you lack the energy to vibrate them.
But if you deliver an energy that vibrates an object then all energy/work that is larger would just produce a faster/greater oscilation in the object.

But it seems this is not always the case when dealing with waves.

Like in the case of an LC circuit they give the resonating frequency to be
f^2 = 1/(4 pi ) * c * L but I would think an object would resonate at this frequency or any frequency that gives a higher energy/work.
(I.E E = f h when it is greater then the so called resonating frequency the object should resonate.)
So a transmitter transmiting a 40khz wave the reciever should resonate at
40khz or higher.

I am just confused about resonation. Does all object resonate at all frequencies. Or is their some inherant property of a wave being refracted that produces a vibration.

For the stop sign example I gave above when you exert a certain
force, work,etc (transfer of energy) on a building does the building on a microscopic level resonate? If not then resonation doesn't occur always.

And what affects the frequency of vibration of the object. I would think the object would vibrate with the same frequency of the wave if the wave was total refracted. But would vibrate with less frequency if it was only partially refracted.

I still am unclear if only the refraction is the key to vibrations/resonations of the given objects. Or if their is more to the story. When an object total reflects a wave does it not resonate the object at all. I would think this is the case. So then resonation only occurs by the refraction of a wave into an object.

Thus to determine what objects resonate for a given wave. It only depends on determining the refraction component of the wave and what it carries for energy. But then I am unsure about this because then we have to take into account the angle of refraction so not all the vibration will be up and down.

Somebody said about snells law is determined by statistical mechanicas.
But if that is the case the sin/sin = v/v etc... how did they derive the snells law with their statistical quantum mechanics. Because they must be in corrospondence?

I said absorbtion spectroscopy determines what the what photons get absorbed / emitted from a given material.
So for a given object we can determine what gets pass thru an object.
(i.e refracted ) and what doesn't get thru the object (i.e reflected)

I would think the atomic spectra of the material under consideration
would tell you if the object will resonate. But I am unsure of this as well.

Why does an anntena pick up some electromagnetic waves and not pick up other electromagnetic waves. Or does it pick up all the waves even gamma level waves and it is just the fact that the tuner and op-amplifer cann't tune into those high frequency wave's. But that they are still present.

I basically want to know how given an object how can I determine what waves reflect/refracted . What waves resonate/vibrate.
From a quantum level can you do it or is it all just statistical and not fully understood.

Because using the atomic spectra of a substance you can determine a substance that you can put on a plane or car that when the car is hit by a radar (i.e microwave's usually propagate in straight lines and bounce of of metals ) the microwaves will be absorbed. Thus the radar's won't pick up your speed. This is called stealth.

It is pretty easy to come up with a chemical given the frequency of the wave and a list of the atomic spectrums for the periodic table.

Anyway this question is killing me and I have been to many physics forums
but I have not gotten a soild answer.

Because how would you explain why microwaves bounce of metal.
And why radio waves go thru metal. But visible light does not go thru metal. Visible light has the greatest frequency so it has the greatest Energy. I would think greater energy would produce the ablity to go thur / refract into the object. But then why does radio waves go thru but visible light doesn't? So then I read some stuff on spectroscopy which told me that it is the energy levels of the atom that determines what elements get absorbed/refracted or reflected/emitted.

But Then this still doesn't cover vibrations and resonations?

AHHHHHHHHHHHHHHHHHH
Any help would be great may be it cann't be determined and it is like trial and error. But I would think this question would be important in data transmission where you know if things are going to bounce of the ion-sphere or metal or ...etc etc. And what materials would block a signal?
etc ...

6. triggernum5 Active Member

May 4, 2008
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Go back to the pendulum, or the bus stop sign, or a spring.. A simple pendulum has a natural period of 2pi*sqrt(length/gravitational_acceleration).. You need to 'tune' your driving force to the natural frequency of the object..
Its a matter of simple harmonic motion, more than reflection/refraction.. Remember that in shm, the driving force alternates direction periodically.. If you apply a periodic force that always adds energy you will get resonance.. So in the case of a pendulum, or atom, or whatever, if you push it only when its moving away from you, you are adding energy, but if that push is out of sync with the motion of the object, and you're still pushing when its potential energy in the opposite direction exceeds its kinetic energy in the direction you are pushing, your push will prevent some of the potential energy from being converted back to kinetic energy in the recoil direction..

I think you'll get it if you read up on simple harmonic motion, and damped harmonic motion..

7. Mathematics! Thread Starter Senior Member

Jul 21, 2008
1,022
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Wait is resonation the same as natural frequency.
Maybe I am confused on what resonation is I thought it was just the frequency at which an object vibrates.

I get all the stuff on simple harmonic motion. I have done alot on the subject matter.

But usually when we talk about simple harmonic motion we are talking about mechanical systems. Like pendulms and we have an applied force.

I still don't get why a larger tuning fork won't vibrate a smaller one?
You have more energy so you could provide more work on displacing the object. But it seems to me (correct me if I am wrong ) that the tuning forks will not resonate unless they are the same type of tuning fork.
You would think if a bigger tuning fork is vibrating then a smaller one
would vibrate (at least if they are relativily close together)

As for electromagnetic waves these are not mechanical (they can propogate thru a vacuum which is why light reaches us) plus they don't have mass assoisate to them. They just carry energy and momentum.
However the transfer of energy = work = F * d. So the wave has the ability to do work on an object. But what controls the vibration in the object that the wave is transfering it's energy to? Remember some atom's emit the photon in different directions the net displacement would be the sum/average of all the tiny photon emission directions. Like your spring argument about loss in kinetic gain in potiential energy How would you go about explaining it with waves. Plus the material is not all one atom type.
It would seem to me that if an object vibrates then it's vibration isn't simplly back and forth such as a spring.

Plus the spring is the object that loses or gains it's potiential / kinetic energy in sinc. But the shape at which it travels is the shape of a wave.
So I think your getting the objects in simple harmonic motion mixed up with the shape they oscilate at.

(back to electromagnetic waves)
And is the amount of vibration propotional to the amount of energy being transfered or does the energy have to be equal to one of the electron orbital levels in the object.

Either way I would believe the objects chemical make up could be used to determine what enery level the object would need transfered to it in order to resonate . But then the object should resonate if it was acted upon by
a wave that carries more energy. Which I don't think is always the case.

Another thing is about absorbtion spectroscopy radio waves pass thru metal but microwaves don't. This can be explained be the atomic spectra and I get all that. But just think logically atoms are spaced out relatively far so a few waves should get thru if they have a path straight thru the object with no atoms in it's way. Is it always the case that at least one electron will be in the path.

Because then looking at the atomic spectra this only tells what definitely goes thru but their could perhaps be lucky waves that get thru here and their.

Plus what makes the object reflect a certain frequency at the same angle as it came in at. From a atomic level the electrons emit photons in an unpredictable way. So why is light always reflected at the angle it came in at?

8. triggernum5 Active Member

May 4, 2008
216
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The spring gets acted upon by a longitudinal wave regardless of what causes the periodic force.. It could be mechanical, electric, magnetic, whatever, the force can be viewed as a wave due to its periodicity..

Regarding the tuning fork, think about it.. A big one has a lower frequency, it vibrates, and it does exert a force on a smaller one, but when the smaller one's natural frequency to the force applied by the big one causes it to want to change directions, the big one is still trying to push it further.. So now we observe destructive interference, the forces cancel each other out.. You'll still get vibration, but it won't get a chance to grow over multiple periods.. Resonance is all about a gradual buildup of energy..
EM waves are resonant in space when the reflected component superimposes constructively on the incoming wave.. Standing waves do this.. Whether its refecting off a surface, or another EM force as in RLC circuits.. Actually that applies to alot more than EM waves..
Regarding the microscopic, molecules tend to resonate at MW frequencies.. Think about the pendulum eqn, and compare the force on the pendulum's mass via gravitational acceleration to the electric force on the molecule.. These act like springs.. They have a natural frequency to the electric force exerted on them, and basically when they want to reverse direction, the MW's are in agreement.. Atoms vibrate faster to electric force naturally, so they resonate at visible/UV range..
Some aspects of your question can be answered with the simple paradoxes of quantum mechanics.. Duality of light, diffraction, etc..

9. Mathematics! Thread Starter Senior Member

Jul 21, 2008
1,022
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Oh so it has to do with destructive/constructive interferance of the waves.

So then what determines if a wave is refracted into an object or
reflected off an object. (absorbtion spectroscopy)

Because I was under the impression that the vibration of an object
had to do with the displacement of the atoms inside the object provided that the wave is "transmitted thru" that object.

But can an object vibrate from a wave that does not get transmitted thru it. Say it was reflected back then it still exerted a force on the object.
And it should vibrate the same regardless of the wave going thru or reflecting from.

I guess the vibration is cause by the wave hitting the surface and transfering it's energy to the object and the object transfering the same energy back.

So does a wave that refracts give the same vibration as if the wave was reflected.

Then everything resonates at any frequency provided we don't have destructive interference?

I still think it matters about if the wave goes thru as opposed to bouncing of an object!

I guess as a wave goes thru an object it loses the energy then gains the energy back when going out of the other side of the object.
But this is if it is longitude wave and not a transversal wave.

But then electromagnetic waves are transversal waves???
So I get why the tuning fork works and why longitude wave resonates an object but transversal is applying it's force up and down not right and left.
I guess it would depend on what direction the wave is hitting the object.

10. studiot AAC Fanatic!

Nov 9, 2007
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Physics is an experimental subject.

Have you done the experiment I suggested?

When you do it, imagine the knot as a photon and the weight as a molecule. Each time you hit imagine you are modelling a photon striking a molecule. Try different frequencies of hitting the weight. Try also hitting harder and softer.

You will soon see that oscillatory systems can only accept energy at certain frequencies, no matter how hard they strike (how much incident energy they receive.)

Notice I have not said anything about waves. Only particles. This is enough to model a single oscillator.

You need waves to model coupled oscillators, but that is for the next installment.

Keep It Simple,
you seem to have swallowed a physics encyclopedia and are bringing in far too many ideas at once.

Apr 28, 2004
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12. Mathematics! Thread Starter Senior Member

Jul 21, 2008
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Ok, I was missing what resonation really is.
It is just the vibration of a given object. And vibration occur's in every object as long as you are in sync with it's natural frequencies or sometimes called harmonic frequency)

Tesla's swinging example helped clear it up.

Question in an LC circuit we can figure out the resonating frequency
by 1/2 pi sqrt(LC) but what controls the intensity of the wave.
What I mean is what controls the amplitude of the wave.
I would imagine the amount of voltage you use would control the height?

I am now trying to build a simple receiver / transmitter pair for verification of something's.
So if I create a LC circuit for the transmiter and one for the reciver using
the same L and C. Then when the transmitter vibrates the reciever should?
But what limits the distance of my reception. Is their a way to calcuate how far a wave can be transmitted before it cann't be recieved ???

Also for the LC circuit's

I know their is alot of resistance facts that could dampen the oscillation but I just want to see some indication if I plug the reciever into my audio port of my computer.

13. triggernum5 Active Member

May 4, 2008
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Voltage is analogous to height in a pendulum.. Notice the similarity between the equations for a simple pendulum, and an LC circuit.. Neither height, nor voltage affect the results of those eq'ns..
Your transmission question boils down to engineering of your receiver pickups.. In reality there will be millions of noise signals superimposed over your transmission, and the point of the LC resonance is to amplify the desired signal, without amplifying the noise..
Read up on Fourier transforms if you want to know the math..

14. Mathematics! Thread Starter Senior Member

Jul 21, 2008
1,022
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No, I already know the mathematics. I am a mathematician looking to build some simple transmitter / reciever's. So with the LC circuit we can create a certain frequency wave. By varying the voltage we get AM (amplitude modulation. But what put's the wave into the air. I would think the anntena.
An LC circuit has a capacitor and an inductor where do you connect the anntena? And for the reciever how when the wave hit's the anntena do we use the wave. Does the wave atomatically get converted into electrical charge again.

I am confused because waves only carrier momentum and energy.
But volt's is energy per charge. With a wave we don't have charge.
So how do you measure the wave on an
xy-plane I would think y-axis is joules and x-axis is time.

But I always see osciloscopes using voltage to measure wave's? Maybe I am mistaking?

Also what controls how far the wave can be pick up from. The voltage
has only to do with the amplitude but what gives the wave it's distance in

Note I am trying to get a wave to transmit to a reciever with in a 12 or less foot distance. This project is more a proof of concept.

I want to be able to plug the reciever into my mic port of my computer.
To verifiy I am picking up the waves I know I will see interference but I will probably notice the difference by when I am not transmiting the shape will look different.

Any help would be great note this is my first atempt and I am still learning.

May 4, 2008
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16. studiot AAC Fanatic!

Nov 9, 2007
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Goodness gracious me if only post #14 had been your first post.

What is you field of mathematics?

I can recommend two books to bring you up to speed

The Physics of Vibrations and Waves
by
H.J. Pain. (Wiley)

It is pretty much up to date, at university level and includes a chapter on nonlinear oscillations and chaos theory.

Secondly a much simpler book because there are evidently many gaps in you applied knowledge.

The Foundations of Wireless and Electronics
by M.G.Scroggie

Any edition will do but it contains practical and simple theoretical answers to several of you queries.

Yes there is a whole branch of engineering maths devoted to this. (Transport Phenomenon)

But waves can also carry information. Again there is a whole branch of applied mathematics devoted to this.

The radio waves that are generated by your LC circuit have a frequency many times that of that maximum audible by humans. The input circuitry of your pc will not be designed to respond directly to these frequencies.

The radio wave is often called a carrier. A usable signal is impressed onto this carrier, by a process known as modulation.
At the receiver you have to perform the reverse process - demodulation - to recover the wanted audio frequency signal.
This is the information part of the wave.

Both the transmitter and the receiver need to be 'tuned' to the same frequency. Both suffer from energy loss by a process called damping.

To answer you question about antenna, EM waves are transverse waves. As such, they can take one of two forms of wave.

Travelling Electromagnetic Waves (TEM)

Stationary Electromagnetic Waves (SEM)

The wave sent out by the transmitter is a travelling wave. The wave picked up by the antenna is a stationary wave.

A final comment, even with modulators and demodulators you cannot interface directly with your LC circuit or your antenna for circuit impedance reasons. You need suitable impedance transformation circuitry to achieve this.

So I recommend you sit down with a rounded comprehensive introduction, like Scroggie, and fill in your gaps.

Last edited: Aug 4, 2008
17. Mathematics! Thread Starter Senior Member

Jul 21, 2008
1,022
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I know everything you are saying I just want to beable to create this stuff.

I know the theory but it seems to me it is somewhat different in reality.

My thing is if I have 2 LC -circut's with the same 1/2pi sqrt(LC)

Will they both vibrate if I set one to ocsillate.

Since waves have only momentum and energy. They don't have voltage
assocated with them. Since voltage is work per charge.
But their is no charge in a wave? So I would say you would have to measure them with y-axis joules and x-axis time.

Yes I am familar with amplitude modulation and frequency modulation.
AM FM. But I don't understand in an LC circuit how you can vary the frequency. I thought your frequency is always determined by
1/2pi sqrt(LC) which is a constant unless you have varible capacitors or something.

For a demonstration purpose could I do something that turns on a led when one of the LC circuit's is switched on .

As for the distance in progation
I am going to research more about anntena theory but I still don't get
What limit's the distance of the wave. The voltage is just for the amplitude , the change in C L will effect the frequency of the wave.

But what effect's it's distance???? How do you make a wave travel farther.

Like water waves when you drop a pebble in the water the rings get smaller the farther out you go. (damped out)

But for electromagnetic waves do they never get (damped out).
Do they just propagate forever. And the only problem is destructive inteference. I think their is more to the story here.

I can do out all the theory for waves however I am finding it of little use in understanding just how to build propagating devices and receiving devices. Bare in mind I am just learning this engineering side.

So thanks for any help.

18. triggernum5 Active Member

May 4, 2008
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If you have 2 matching LC circuits, and you have antennae, then essentially you have a transmitter and reciever..
Even without antennae you do actually, and in that scenario, induced oscillation that occurs is typically considered a problem needing correction.. Antennae range drastically in price for a reason.. EM waves travel infinite didtance, and get dirtier, and dirtier with background noise as they go along (diminishing intensity according to the inverse square law).. Good antennae are better at sorting the desired signal from the noise.. A theoretical perfect design would pick it up across the universe, sorting out all noise.. Even though it would be very weak, it would build it up to usable strength via resonance..
I linked you to a page that describes how to build MacGyver style radios from scrap, so I'm not sure what your confusion is..
About the voltage, what happens when you subject charge to an energy field? Voltage is 'potential'.. It isn't exactly possessed by charge, just like gravity isn't possessed by mass.. NOT analogous to a tree falling in the woods, if there were no objects in the universe besides our sun, would the sun still create a gravitational field? And the answer is yes.. (However there would be no 'force' on anything resulting from that field)..

19. studiot AAC Fanatic!

Nov 9, 2007
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Try reading my post #16 again.

You are trying to repeat Marconi's original experiments. They do work.
But there are large gaps in your knowledge / understanding which are leading you to introduce many irrelevant matters.

Keep it simple.

20. Mathematics! Thread Starter Senior Member

Jul 21, 2008
1,022
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Yes , I remember trying something like this but it didn't work.
RadioShack doesn't sell germanium diode's . You have to buy a kit.
I would really like to do this from scratch. Do I need a germanium diode
because I have silicon and other such diode's.

Basically the diode only lets the current flow in one direction so it cut's of the negative humps of the waves.

Their is potiential energy , and potiential difference (volts).
potiential difference (volts) is by definition energy per charge.

"per charge"
F = q * E (force of the electric field)
Look at the definition PE = integral q * E * ds
(work/energy of the electric field)

PD = (integral q * E * ds) / q = integral E * ds

I understand we can define voltage as integral E * ds without charge involved but why do we measure volts as energy per charge. This would lead to a definition conflicts? Isn't the voltage measured in J/C but where is the C in electromagnetic waves.

I hope am explaining my point clearly enough.
Maybe this is some stupid thing that I am not understanding.
Any clarity on it would be great. Alot of books define volts = work per charge. Maybe this is just a special case?