This is a spring system, designed to
demonstrate many of the universal features of waves. Have a play around!
This is how it works: A series of
weights are linked together, so that each is pulled towards its nearest
neighbours. This allows waves of motion to travel along the chain. A
driving force is applied to one weight, which produces such a wave.
Clicking in the display area pulls the nearest weight towards the
cursor. When you release the cursor, it twangs back.
Doubling the frequency of the driving
force reduces the wavelength by half, since they take half as long to
make.
Doubling the wave speed makes the waves twice as long, since they move
twice as far in the same time.
The wave speed is controlled by the tension, the strength of the
attraction between neighbouring weights;
the speed is proportional to the square root of the tension, so four
times the tension means double the wave speed.
When the crest of each wave matches the
crest of the next as its returns, resonance occurs.
This happens at the first harmonic, which is also known as the
fundamental frequency.
When the ends are looped, this corresponds to a wavelength equal to the
length of the chain.
Otherwise the ends reflect the waves, and each one needs to get to the
other end and back to meet the next wave,
so the first harmonic has a wavelength equal to twice the length of the
chain.
Resonance also occurs at multiples of the fundamental frequency - at
only the odd multiples when one end is fixed an the other free, but at
every multiple otherwise.
Resonata t-shirts are now
available!
This page was developed by Fergus
Ray-Murray with the help of funding
from Alt-W
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 that 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, and 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 whatever 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 a wide variety of contexts. Here
are a few...
Types of Resonance, and their
Applications
- Acoustic Resonance - the
sound of a musical instrument is always the result or more kind of
acoustic resonance; the types of resonance involved affect which
harmonics we hear, and hence the timbre of the note:
- Helmholtz Resonance - a cavity
with an opening resonates at a frequency which depends only on its
volume and the dimensions of the opening - in principle, the shape of
the hollow makes no difference. The classic example of Helmholtz
resonance is the sound made when you blow across the top of a bottle;
the effect is also significant in the string instruments.
- Resonating strings - string
instruments and pianos resonate simply when whole numbers of
wavelengths fit into their length.
- Tuning forks - like strings,
tuning forks and the like carry waves along their length. Since they
are fixed at one end, though, they only resonate with waves at odd
multiples of their length.
- Drum-skins and sounding-boards -
resonate in two dimensions, making more resonant frequencies possible.
The mathematics of this are more complex, but the principles are the
same.
- 3D acoustic resonance -
designers of concert halls and so on need to be very careful about
their acoustics, because resonance can reinforce certain frequencies at
the expense of others - sometimes this is desirable, but in many cases
great efforts are made to eliminate resonance as much as possible.
- The human vocal system uses a
combination of these effects to produce speech. The details of this
process are the subject of the branch of linguistics called
articulatory phonetics; understanding how we make speech-sounds helps
us to understand the ways that language can evolve.
- Atomic-level resonance
- One of the great advances made
possible by quantum mechanics was the ability of physical chemists to
explain the properties of the chemical elements in terms of standing
waves made by the electrons encircling their nuclei. Atoms only emit
and absorb radiation at particular frequencies, which depend on the
energies of different electron 'orbitals'. Electrons, like all
subatomic particles, act like waves in most circumstances; their
orbitals correspond to patterns of standing waves around the atom. The
absorption of light by atoms therefore fits under the definition of
resonance given above.
- Magnetic Resonance Imaging (MRI)
is a hugely important medical imaging technique, which works by
applying a magnetic field to a person's body and detecting the magnetic
resonance of molecules, chiefly hydrogen, in order to determine their
distribution.
- Electromagnetic
resonance
- Aerials work by resonating with
incoming electromagnetic waves (radio, TV, microwave, etc.) - typically
they are tuned to a particular frequency, and sensitive to a range of
frequencies around it. They may also pick up higher harmonics of that
frequency.
- Electrical resonance
- An electrical circuit including
an inductor and a capacitor will resonate at a frequency depending on
the inductance and capacitance involved, with energy oscillating
between the magnetic field of the inductor and the electric field of
the capacitor. Circuits like this are useful for generating waves
electronically, and for filtering unwanted frequencies in what is
called a band-pass filter. They are also the most important component
of the hugely entertaining Tesla coil, which creates artificial
lightning effects.
- Orbital resonance
- The orbit of a planet or a
satellite can be more stable when its period matches a simple ratio of
the orbit of another body nearby; for example, the orbits of Jupiter's
moons Ganymede, Europa and Io are stabilised by being in the ratio
1:2:4. A separate, but related phenomenon is tidal locking, the effect
which has caused Earth's Moon always to face towards the planet.
- Synthesisers
- Sophisticated synths
(electronic sound synthesisers) generally have a setting called
resonance, which gives a boost to sounds which are at frequencies close
to the cut-off point for band-pass filters.
- Psychological resonance
- People often talk of ideas,
stories, poems and so on resonating with them, or with other ideas. The
analogy is that just as a sound can set off sympathetic vibrations in
something with a matching resonant frequency, one idea can excite other
ideas with something in common, reinforcing the original idea rather
like a sounding-board reinforces the sound of a guitar string. While
this is not obviously the same kind of resonance as I have discussed
elsewhere, it is a hugely important concept in the arts, being one of
the key features which can make a work of art powerful, and as such it
deserves a mention.
Dangers of Resonance
- Machines
- Many of the physical limitations
of machines, including vehicles and manufacturing plants, are
determined by their susceptibility and resistance to vibrations. The
most destructive vibrations are often those at resonant frequencies of
some part of the machine, and avoiding these is crucial in high-powered
machinery.
- Buildings
- The buildings which are most
damaged by earthquakes are often those unfortunate enough to have a
resonant frequency matching the frequency of the quake. Tall buildings
in earthquake zones are often built with ingenious systems of dampers
to absorb the vibrations of the incoming earthquake waves, chiefly to
reduce the danger of this happening.
- Wind can also be a problem for
tall buildings, when their geometry causes the wind to buffet them at a
resonant frequency. Although it is rare for any building to get blown
right over, people always feel unsafe when the floor they are standing
on sways; for this reason, tall buildings in windy areas often employ
the same sort of dampers as those in earthquake zones.
- Other sources of vibration, such
as heavy machinery, walking or exercise, can cause floors to resonate
disconcertingly.
- Bridges
- Armies are trained to break step
when crossing bridges; if they all marched in time, and their pace
happened to match a resonant frequency of the bridge, there would be a
serious danger of collapse.
- The Tacoma
Narrows Bridge was ripped apart by a complicated resonance
effect, with the 40mph wind forming periodic vortices which mutually
reinforced the turning motion of the bridge. This is the classic
textbook example of forced resonance, but the full explanation is more
complicated than you may have been led to believe - and more
complicated than I have space to explain here.
- London's Millennium
Bridge was closed after a few days because it wobbled
alarmingly as 80,000 people walked across on its opening day. The
engineers had made allowances for the well-known danger of resonant
effects from the vertical motion of people stomping across, but they
had not realised the danger posed by people swaying from side to side
as they walk, with a frequency half that of their footfalls. Once the
bridge began to sway, people walking across sub-consciously fell into
step with it, swaying along with the bridge and amplifying its motion
in a sort of vicious circle. Expensive hydraulic dampers were put in
place to control the motion, and the bridge was finally re-opened more
than a year later.
- The Human Body
- Certain frequencies of vibration
can cause people to feel unwell, and sometimes do real damage, by
causing resonant vibrations of their abdominal cavity, head, eyes or
other parts. This is something which designers of heavy machinery and
vehicles - especially race cars - need to be aware of, in order to
minimise discomfort caused to their users.
- Possible military applications of
such sounds have long been talked about. Although these do appear to be
technically feasible, their actual military usefulness is questionable.
- Wolf notes
Unwanted resonance in musical
instruments can result in a wolf note - a note which causes the whole
instrument to resonate, much louder than other notes.
- Feedback
Microphones which are in
range of the speakers amplifying them can produce howling or screeching
sounds, rising in volume, as they reproduce the sound waves they picked
up just on the other side of the room, one or more wavelengths behind.
These can usually be avoided either by changing the distance between
the two, or reducing the amplification.
- Plumbing
- The strange sounds produced by
plumbing are often the result of resonance within the system, with
various sources of vibration causing humming, howling, whistling and
banging as they hit resonant frequencies of pipes, boilers and
radiators. The precise dynamics of this are largely mysterious.