here is a great in parallel bar
if you put a point of the waves in the flat grading which way we'll
the waves go
the shape of the spiking helmet is actually a clue more about later
we experimented with sound in microscopic grading
structures like this local phone only crystals was acoustic properties have been engineered to vary
periodically in space
in the experiment blue laser light of this create tiny time triples by deleting a
small ball
infrared light pulses detect the ripples
this time pitch is very high around one together with amplitude in the peak a
meter range
with down the detection one and change the timing of the latent vote is to
make movies of the ripples using interferometry
our grading is made of tiny colour and delay constraints on a silicon flat and
this is coded with goal
we've by i like the pulses repetitively at the center of a one and you
might want square area
this movie slowed down a thousand million times
let's analyze different frequencies
at low frequencies we see roughly circular ripples
actually this is reasonable because the sound wave length is about ten microns much larger
than the grading by a
so this time detective it doesn't see the grading
but at high frequencies we see this interesting shaped pattern
and the x shape close is at higher frequencies
the top row shows that we can get the same effect numerical simulations
but bottom row is experiment
now that and of life sound wavelength understand the in these images
there are two important space is called case phase and group velocity space
for a given frequency in case space we plot inverse of the wavelength or rather
the wave number in the x and y directions
in group a multi-space shown on the right we plot speed of a sound files
in this approximate analytical approach at low frequencies we get round shapes in both spaces
this means the ripples are roughly circular
as the frequency increases we hate of and got in the horizontal direction of direction
weights can travel visible through the opening so in case space
and this makes to the in group a two d space
these two circles position at higher frequencies
in case basis weights to vary strongly perpendicular to the turning points in the curves
in group a multi-space biz correspond to joining the times of the circles
this produces the shape with or
if we see all frequencies to get a group of l d space looks like
this
so now d the relation with the viking helmet
imagine a cross section three the helmet here
it is just the circle and that gives the round trip will happen
what is use like the helmet at higher frequencies that means higher you get too
small circles
so the way the channel in the direction of these two circles
this explains why exchange close is at higher frequencies
actually i should rotate the ice of this helmet to correspond to experiment like the
the spiky focusing buttons a cold costings
you can find them in coffee cups
and also when you generate sound waves on real crystals
so point so integrating produces an x pattern code by acoustics related to the band
is that they should also be seen in a variety of spatially periodic structures and
is not just confined to stand
it would with electromagnetic or what waves for example
i will conclude by saying
for that
which is the biking for thanks policemen