# What is resonance?

1. May 7, 2015

### kapital

What exactly is resonance? I have bean reading some literature and I do not understand what precisely it is saying. But since that is very unspecific question, I will to ask some question that are puzzling me, to try to show more specific what I do not understand.
1. What exactly can resonate? Articles on resonance usually put weight on spring for the first example of resonance. But than they say glasses, springs, solids, electric circuits, ... can also resonate. What do all types of resonance have in common?
2. Co-lapsing bridge is often shown as example of harmful resonance? What exactly is resonating there?
3. What is glass's own frequency? Does every solid has "own frequency" and what "own frequency"does it mean?
4. Is some kind of oscillation always need for resonance?
5. When block is oscilating on pendulum with some frequency, the frequency is calculated by equation oscillation divided with time. If we want to calculate resonant frequency, frequency of what wold that be?
6. On Wikipedia resonance is defined as: In physics, resonance is a phenomenon that consists of a given system being driven by another vibrating system or by external forces to osccilate with greater amplitude at some preferential frequencies. What is the reason, that this happens?

2. May 7, 2015

### rumborak

The simplest example of resonance is the "kid on a swing" one: If you just randomly push the kid with no regard where it is on the motion, the kid will never swing meaningfully. If however you time the push exactly right that you are pushing at the apex of the kid's swinging, you are constantly adding to the motion and the swing gets bigger and bigger (with possibly disastrous results). That is resonance.

What can resonate? Any system that you can put energy into, which after a certain delay will return it.

3. May 8, 2015

### gleem

Most real rigid bodies are elastic to some extent. And as such can be set into a vibration or oscillation by striking it or interacting with it in some other way like a bell. This vibration is characteristic of the shape and material of the object. When you interact with an object and you distort it even slightly you do work and transfer energy to the body. The body being elastic will rebound and vibrate some more but real bodies have a characteristic like an internal friction which causes the vibration to dissipate with time and usually quickly. If you reapply this interaction before the vibration dissipates the vibration can be sustained. If the interaction applied is in tune with the characteristic frequency of the bodies vibration ( has the same frequency) the vibration will increase in intensity and the body will accumulate more energy before it can be dissipated. The build up in energy can continue until the dissipation of the energy equals to the energy input or the vibrations become so large as to distort the object to the extent that it exceeds the elastic limit of the material of the object. An example is a singer holding a tone equal to the characteristic frequency of a wine glass to cause it to eventually break. The "singing" of stretched cable in a high wind is another example of resonance where the energy builds up to a certain level and dissipates additional energy as it is introduced. A guitar or other string instrument has a body designed to accumulate the vibrational energy of the strings thus amplifying it. The pianos sounding board, an annoying rattle in a car at a certain speed. All examples of resonance and its application.

There are analogies in other areas of physics as in AC circuit theory. All we need is a periodically varying force applied to a body or structure with a vibrational component equal to that structures characteristic frequency and long enough for sufficient energy to accumulate. In mechanical systems this can cause visual movement sometimes with destructive affect.

Google the" Tacoma Narrows Bridge" for a famous example. With regards to this bridge the wind passing through the bridges steel girders is the energy "catcher" for the bridge. Wind is usually not very steady but gusty and can be rhythmic. This oscillatory excitation of the bridge structure could and was in tune with the bridge decks characteristic frequency which accumulated so much energy in its vibrational mode that it self destructed like the wine glass. Another example is the collapse years ago of a hotels suspended floor when a crowd of dancers where able to excite a characteristic vibration in that floor.

4. May 8, 2015

### UncertaintyAjay

Everything around you vibrates. You can't see most of these vibrations because of their frequency, and because their amplitudes are small. But if you provide energy , you can amplify these vibrations and that's when you get resonance. For example think if those funny things in movies where fat opera singers let out a high pitched shriek and break glass. This actually does happen. What happens is that they sing at a frequency that almost corresponds with the natural frequency of glass. The glass resonates and the amplitude if the vibrations gets so large that the structure breaks. Youtube this, there are some amazing videos of it.

5. May 8, 2015

### rumborak

That is a really dangerous thing to say, because it is a standard phrase for New Age hippies, and leads to a lot of wrong conclusions about physical reality.
If you mean vibration because of heat, sure, that's true, but you will never see resonance in heat vibration, since by its very nature it is chaotic.

6. May 8, 2015

### UncertaintyAjay

Yeah, no I did mean heat vibration. Not the new age hippy thing lol. So what is responsible for resonance in glass ?

7. May 8, 2015

### UncertaintyAjay

In the sense that what vibrations are being strengthened?

8. May 8, 2015

### rumborak

The glass is like a very stiff spring really. It gets deformed by the incoming sound wave.
See here:

9. May 12, 2015

### kapital

Is it possible to calculate(or approximate) the resonance of glass for example? Which information would we need to do so if it is possible?
Is resonance connected with geometry of objects? Does a metal(for example copper or iron) in shape of cube also have own frequency and can resonate?
In the glass video the resonance of glass is achieved using sound, would it also be possible to cause resonance with other sources?

10. May 12, 2015

### Merlin3189

The body of the instrument (except for modern electric instruments) has no energy source and cannot add to the energy of the string. So it cannot amplify the sound in the traditional sense.
If it accumulated energy from the string and later released it suddenly, I don't think the amplitude characteristic would be as it is. There would need to be a silent (or at least, quite) period while the energy was accumulated by the body, then a relatively short duration loud sound when this was released. I think guitar sounds at least have a very fast attack with a long slow decay, as one would expect from a plucked string itself. I accept that bowed instruments do have a much slower attack, but I think this can be accounted for by the increasing amplitude of the vibration of the string itself.

I can only offer an uninformed guess as to why the sound board is effective. I think it acts as an impedance matching device, allowing the string to transfer its energy more effectively to the air. I would suspect that a good body design actually seeks to avoid resonances, so that no one note sounds louder than others.

I guess the glass breaks because its amplitude of vibration becomes so large that the restorative forces at peaks become sufficient to cause rapid crack propagation. Its vibration is increasing because it is receiving energy at the vibration frequency from the sound. If you provided energy at that frequency by another means, that would have the same effect. Vibrating the table is the obvious alternative, since air and the table are the only things in contact with the glass. (Some people, such as me, might argue that a vibrating table is just sound by another name, though!)
Maybe you could provide energy at the right frequency electromagnetically? If you had a strong enough electric field alternating at the right frequency and essentially put the glass between the plates of a capacitor? Maybe one could use a magnetic field, but I think the diamagnetism of glass is too small for this too be possible?
Maybe you could modulate the intensity of an intense beam of light and generate vibration by modulated thermal expansion of the glass? I think the thermal inertia of the glass would be too great though - like having a low pass filter damping the thermal variation.
You could always hit the glass with a hammer! It would then ring at its resonant frequency. If you hit it hard enough, the initial peak of vibration might be enough to initiate failure.

11. May 12, 2015

### gleem

I previously said "A guitar or other string instrument has a body designed to accumulate the vibrational energy of the strings thus amplifying it"

(Disclaimer: I am not an acoustical science expert)

THBS The reason for this "amplification" or enhanced sound intensity ( as I understand it) is the body of a guitar or violin to which a string is mechanically coupled is able to accept the energy of imparted to the string and more efficiently transfer it to the air which then carries the sound to our ears. A vibrating string by itself having little surface area is poorly coupled to the atmosphere an thus slowly transfers its energy to the air directly. Consequently the sound intensity is weak. Remember the high school demo, take a tuning fork strike it and note the sound intensity. Now place it in contact on a wooden box. Note the increase in intensity.

12. May 12, 2015

### Merlin3189

Gleem - Yes. I agree: that is what I understand by impedance matching in this context.. Perhaps I took "amplification" differently from you.

I also disliked the accumulation of energy idea as I understood it, but I can see that you meant that differently now.
Immediately the string starts vibrating, it is passing energy to the body and that is immediately passing it to the air. The body starts with no vibration, so is accepting lots of energy from the string and passing little to the air. This imbalance causes the vibration of the body to increase in amplitude until it is passing energy to the air as fast as it is receiving it from the string. Up to that point it is accumulating energy.
I would not say this accumulation is the cause of increased loudness of sound, just an incidental transient feature of the coupling mechanism. Once the body has reached equilibrium and is transmitting energy to the air as fast as it receives it from the string, the sound is still louder than the string alone would be without this impedance matching.

13. May 13, 2015

Resonance is basically a phenomenon which occurs when the frequency of the forced vibration matches with the natural frequency of the vibrating system which results in a rapid shoot...
For example consider a very simple case of spring mass system.. If you give the block an initial displacement and left it to vibrates on its own then the frequency at which it will vibrate or oscillate will be its natural frequency. Now on the other hand if you make an arrangement which can pull the block and then push it back and forth with different sets of frequencies then you will find that when the forced frequency matches with the natural frequency of the spring mass system , the block will vibrate abruptly. This is resonance.
I hope it would be somewhat helpful for you...

14. May 14, 2015

### Merlin3189

I think we may have neglected some aspects of the OP's Q. Though I'm no expert here, I'll kick off a few comments.
1-I guess, anything that oscillates, aka vibrates. Mechanical ones are characterised by an inertial element (mass m) and a springy elastic element (k). A block and spring is just a simple system that can be easily modelled and analysed to find a natural frequency of linear vibration f = 1/(2π√(k/m)) A circular object and a torsion spring can have a natural frequency of torsional oscillation.
A pendulum gives a similar result, f=1/(2π√(L/g))
A string (as in violin, etc) has a density (μ), length (L) providing inertia and tension (T) providing springiness to get f= 1/(2L√(T/μ)) for a fundamental frequency, but having the possibility of higher frequency overtones or harmonics.
A hollow container with a neck (eg. bottle) can resonate because the mass of air in the neck (inertia) can move in and out compressing the air in the container (spring). This is known as Helholtz resonance. I think most wind instruments have resonant frequencies based on a different idea, standing waves dependent on dimensions and speed of sound.
For two and three dimensional objects it becomes more difficult, but they have mass (albeit distributed rather than a single block) and springiness which allows a similar mass-spring behaviour. They will have multiple modes in which they can vibrate, giving multiple possibilities for resonance. For eg. a rectangular sheet could flex about its short axis (like bending a ruler) but also about its long axis. It could also vibrate by twisting ....

Wow! In looking for an illustration for this, I found a fantastic site from Prof. Daniel Russell at Penn State.This has super animations and far better explanations than I could ever give. Just take a look - you'll be there all day! I think you may find answers to 2 & 3 as well.

4 - Yes! That's what resonance is (except in Eng. Lit., Art Appreciation, Psychbabble, etc.) Resonance occurs when an oscillation at some special frequency has a much greater amplitude than at others.

5 - f = 1/T T= 1/F A simple pendulum has one natural frequency and that is the one that it will resonate.

6 - I think the simplest example to use here is the child on a swing. The swing is a pendulum with a natural frequency. If you keep giving it a push at the right frequency and phase (ie at the natural pendulum frequency, pushing when the swing is stationary or moving away from you) the amplitude of the swing increases. If you try giving a push out of phase - pushing when the swing is coming towards you - then it slows or stops. If the timing of pushes is unrelated to the natural swing frequency, then sometimes you will be helping and sometimes you will hinder, so the swing amplitude will vary, but not continuously increase.
If you take firm hold and push & pull forcibly, the swing will move according to your push/pulls: this is forced vibration. It will require considerable continuing effort to make it keep moving in this way. If you choose to push/pull strictly at the rate of natural swing, then it will be much easier and you can even rest for a while and only push occasionally (as long as you do it at the right time) - that's resonance.

15. May 22, 2015

### kapital

What about geometry? Would a cube of glass resonate just as a wineglass? And is it possible to calculate resonant frequency(or approximate)?