You get the same phenomenon with sound, too. If you hum a perfect E, then you can actually see the string on a guitar start to vibrate at the same frequency. This is because it is resonating with your voice.
You can use resonance to do lots of curiously destructive things. For example, you know that stunt where the woman sings a note and the wineglass shatters? You can actually do it, and it is caused by resonance. The wineglass' natural frequency is the same as the opera singer's voice (you can work out the natural frequency by tapping the glass) and the vibrations caused by an opera singer's voice are violent enough to break the glass. There was a bridge made, called the Tacoma Narrows Bridge, whose natural frequency just happened to match the winds that used to strike it. This eventually caused the bridge to collapse, barely three months after it was completed. Finally, using infrasound, you can actually cause a person's organs to rupture and kill them if you cause them to vibrate at their natural frequency which is 3 to 7 Hz. This has happened.
When you walk, you create vibrations through the ground. These vibrations take the form of a wave or pulse, whose frequency is inversely proportional to the time it takes for you to take a single stride, and whose amplitude is proportional to your weight. Now, an army, as point of principle, marches. The ideal march is one whereby everyone's foot falls at the exact same time. So, each soldier is creating a wave with the same frequency as that of his comrades, and their footfalls reinforce one another.
Now, if the army is marching across a bridge, be it made of wood, concrete, or what-have-you, it sometimes happens that the frequency of their collective footfall is the same as that of the natural frequency of the bridge itself. Thanks to the combined power of reinforcement and resonance, they can tear the bridge apart simply by walking across it.
Hence, most squadrons of infantry will "break step" when walking across the bridge, specifically taking random steps, since no single soldier will be able to create the amplitude necessary to rip the bridge apart, even if they do accidentally hit upon the natural frequency.
once I thought we were born here with no clues no path, no means, no scent of home like a cellist without a bow, grappling with an arcane instrument before a vast audience of laughter
as if they knew better than me - "Tabula rasa", as if babies come into being with no brain or heart, no feeling, nothing that might have been carried from a lighter, timeless world
look at her fingers tremble on the strings - she's not afraid of the sound but of the audience, what they'll do when the sound wakes their hearts - one single note, to kiss, to destroy -
something to rise out of the brain into the early evening skyline they know the trees are shaking in the wind they saw the constellations appearing like diamonds sifted out of the sandy clouds
take care - they never asked to be reminded - "I'll know when I fall in love" - how are you so sure - except that you are a singing wineglass, a bell that hums when a voice speaks underneath, that knows the truth because you feel it making you true -
your mother will lead the tiger out of the house by its teeth, she'll put you to shame - while you wander through glaciers, mazes like endless Inca cities, stepped and geometric, unable to escape the memory of death
except that you hear the violinist - she doesn't know what she does, but the sound is not bound by her knowledge - if you cry when the crescendo takes hold of her hands, what is it in you that moves, that resonates,
what did you recognise, that you feel so ruined, devastated by happiness, reduced to nothing by love, like an empty evening sky for seeing comets, like wind for laughing, roads for the feeling of distance - an empty peace in your clearlight bedroom.
In the realm of electricity, a circuit is said to be in resonance if the inductive and capacitive reactances of the circuit cancel out, leaving only the resistance. This state only occurs at one frequency called the resonant frequency. This frequency can be determined by using the following formula:
Frequency = 1 / 2pi * sqrt (capacitance * inductance)
If the capacitance is given in farads, and the inductance in henrys, the frequency will come out as hertz. This frequency not only is the frequency that the circuit will pass with the least impedance, it is also the fundmental frequency the circuit will assume if the circuit is charged, then allowed to discharge through itself.
The basic building blocks of the universe seem to be either waves or vibrating strings, and most of the things they make up move in bigger waves and vibrations. If we hope to understand much about the physical workings of the universe, then, we need to have some idea about the way waves and vibrations work. The details of wave motion vary, but many of the principles are universal.
Among the most important concepts to grasp are resonance and standing waves; these are fundamental to countless phenomena in almost every branch of physics. They also underlie the production and perception of speech and music, and have countless applications in engineering. Resonance is what allows gentle pushes to propel a child ever higher on a swing, and it is what allows whipping winds or marching armies to tear asunder seemingly solid bridges.
Broadly speaking, resonance is the reinforcement or creation of an oscillation by an in-coming wave. The energy delivered by the wave will generally be strongest if the wave is at the same frequency as the oscillation, because this allows the two of them to maintain the same phase relationship, so that the direction of the push always matches that of the oscillatory motion. In cases where the vibration is caused by the wave in the first place, the 'natural' frequency is what is important - the frequency at which an object will naturally vibrate if it is excited, as discussed below. If the wave and the oscillation have different frequencies, then sooner or later they will drift out of phase and the motion of one will work against that of the other - however, if the wave is at a multiple of the frequency of the oscillation, a net reinforcement can still result.
The nature of standing waves is closely tied up with resonance, and it is not possible to fully understand one without grasping the other. Standing waves occur whenever a steady wave hits a reflecting barrier. The reflected wave travels at the same speed as the incoming wave, but in the opposite direction; this means that the peaks and troughs of each interfere with those of the other to make a pattern of 'nodes' and 'anti-nodes' - still points, and points which alternate between being crests and troughs. The strongest standing waves occur when the waves are reflected back again, and fit snugly inside a space which is just the right size and shape to allow incoming waves to be in phase with their own reflections and re-reflections; the frequencies at which this occurs are the resonant frequencies of the object the waves are in.
This effect, in which reflected waves are bounced back again after a whole number of wavelengths, is one of the most important kinds of resonance, and is the reason why tuning forks, for example, ring at a particular pitch. The fundamental or 'natural' frequency of anything which we ring or pluck to produce tones is generally the main pitch it makes. It amounts to the number of times a sound wave can travel from one end of the object to the other and back again in a second.
It is only waves of this frequency, or multiples thereof (harmonics), which consistently interfere constructively with their reflections and re-reflections. Anything else will soon be out of phase with the incoming wave, so the wave will actually reduce the energy of the system through destructive interference.
Conversely, an incoming sound matching one of the resonant frequencies of an object will cause larger and larger vibrations, limited only by damping - hence the supposed ability of some opera singers to shatter wine glasses, and also the possibility of tuning a guitar by watching the strings carefully.
There are many different types of resonance, and they are important in an endless variety of contexts. The following list covers many, but by no means all...
I would like to thank unperson, wrinkly, redbaker, Calast, tdent and quantumlemur for their helpful suggestions.
Resonances are the cornerstone of experimental high-energy particle physics. A resonance is the primary signature of a short-lived exotic particle, and they are relatively easy to detect and measure. Careful study of a resonance can yield a measurement of a particle's mass and lifetime.
Particle physics experiments, large or small, involve observing reactions between particles. Resonances are cleanest and easiest to see in simple reactions, and the simplest higher-energy reactions in particle physics come from lepton-antilepton collisions. In this writeup, I will primarily consider electron-positron collisions as they are simple but frequently used in particle physics experiments; the simplicity allows for relatively high precision. The mechanism for finding resonances is much the same for more complicated reactions, such as proton-antiproton annihilation.
For a particular choice of reaction, such as e+e- -> μ+μ-, the probability of occurence is quantified with a number called the cross-section, which is a function of the incoming particle energies. The variation of the cross-section contains vast amounts of information about the mechanism of the reaction.
Now in modern particle theory, a reaction like the above is not a direct conversion:
μ+ μ- ^ \ / / \ \ / | \ / | . | increasing time / \ | / \ | / \ | e+ e-
Rather, the particle interaction is mediated by virtual particles, in this case usually a photon. This reaction can then be written as e+e- -> γ -> μ+μ-, or shown schematically as:
μ+ μ- \ / \ / \ / . | | γ (virtual photon) | . / \ / \ / \ e+ e-
The cross-section for this reaction is relatively constant with energy, and can be calculated from theory to high precision.
However, this mechanism is not the only reaction of the form e+e- -> stuff -> μ+μ-. If the total energy of the two particles is close to the mass of a real particle, such as a J/ψ meson (whose double name is due to its near-simultaneous discovery by two groups each with their own ideas on naming), the e+e- collision can produce a real particle rather than a virtual photon that decays to two muons, i.e.
μ+ μ- \ / \ / \ / O | | J/ψ (real meson) | O / \ / \ / \ e+ e-
Resonances will appear in virtually any reaction, so long as the available quantum numbers match that of the produced particle. An electron-positron collision will never see the resonance of a (single) charged particle, since the total charge available is zero. Similar constraints apply to other particle characteristics ('quantum numbers') such as spin and parity, and so the appearance or non-appearance of resonances in the cross-sections of different reactions will reveal information about the quantum numbers of the corresponding particle.
The centre of a resonance peak will be found at the rest mass of the corresponding particle. This is the best way to measure the masses of the legions of short-lived, massive particles that exist. Furthermore, due to the energy-time uncertainty principle, δEδt ≥ h/4π, the width of a resonance peak is inversely proportional to the particle's lifetime. Thus, careful plotting of a resonance peak can be used to determing both the mass and lifetime of a particle.
Each distinct resonance appears to be a distinct particle. A particle will have the same mass as its antiparticle, but the two particles will have opposite quantum numbers; aside from this every resonance of the same central energy can be said to arise from the same particle. Thus, we classify every set of measured resonances with the same quantum numbers and energy as a particle and assign it a particle name.
In the early days of particle physics, each particle classified in this way was interpreted as its own fundamental particle. Soon, the bewildering array of new particles caused one particle physicist to remark, "Once, the discoverer of a new fundamental particle would earn a Nobel Prize; now, it seems that it should be punishable by a $10,000 fine."
With Murray Gell-Mann's work on the Eightfold Way and the ensuing development of the quark model, it became clear that the vast majority of observed particles are not fundamental particles, but rather various composites of mostly unobserved particles called quarks. The Standard Model of particle physics contains fewer than two dozen particles, plus their corresponding antiparticles, six of which are quarks. All of the composite particles fall into two classes: baryons, which are composites of three quarks or three antiquarks (an antibaryon), and mesons, which are composed of one quark and one antiquark.
Having chosen a compliment of quark and/or antiquark types (whimsically called 'flavours'), there are multiple ways in which they can be combined. The most basic difference that can be applied is different alignment of spin. Quarks all have a spin of 1/2, which can be set up to point in one of two directions. For a meson, the spins of the two particles can be aligned, in which case the spins add giving the meson a spin of 1, or the spins can be anti-aligned, in which case they subtract and the meson has a spin of 0. Baryons work much the same way: either all three are aligned giving a spin of 3/2, or one is opposite the other two giving spin 1/2.
These different spin states apppear, given the classification scheme above, as different particles, even though they have the same
