On Thursday, 12 March, 2015 13:11:10 Keller, Jacob wrote:
> >If projects a middle-C-tone into a piano, do all of the lower notes resonate
> >as well, according to the Kramers-Kronig relation?
> If you press the right pedal the harmonics of the note you play will
> resonate. My piano teachers never mentioned to me the Kramers-Kronig
> relation but that's a long time ago, perhaps they do these days.
>
> Right, I always understood that it was just the harmonics which would
> resonate. But according to Kramers-Kronig, wouldn't there be resonance on all
> strings, just as there's anomalous scattering at all higher energies above
> the edge? Each string of lower frequency would be analogous to an anomalous
> scatterer with an edge at a lower energy than the incident radiation. Hmm,
> maybe it really does happen?
The better-known example is the precaution of having
soldiers break step when crossing a bridge. The higher-frequency
input from march-tempo footsteps can excite a lower frequency
resonance in the bridge structure with possible bad consequence.
But yes, it works for pianos too.
Ethan
> A different question: do the real and imaginary components of anomalous
> scattering arise from different processes, or are they simply a way to
> represent the phase of the anomalous scattering?
>
> All the best,
>
> Jacob
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> ________________________________________
> From: CCP4 bulletin board [CCP4BB@JISCMAIL.AC.UK] on behalf of Keller, Jacob
> [kell...@janelia.hhmi.org]
> Sent: Wednesday, March 11, 2015 6:57 PM
> To: CCP4BB@JISCMAIL.AC.UK
> Subject: [ccp4bb] Basic Anomalous Scattering Theory
>
> Dear Crystallographers,
>
> I have had only a vague understanding of what specific things are happening
> with shell electrons at anomalous edges. Specifically, for example, to what
> energy of electron-transition does the x-ray k-edge correspond in terms of
> orbitals, and is that transition energy actually equal to the energy of the
> photon, suggesting that the photon is absorbed (or disappears?) in elevating
> the electron? I don't think we say it is absorbed, so how does the energy
> come back out, from the electron's falling back down, right? So then there's
> a new photon created, or the same one comes back out? Where was it?
>
> Further, I also have heard that the emerging anomalous/resonance photons are
> of the same wavelength as the incident radiation, but usually there is
> something lost in transitions (even non-fluorescence ones) I thought? Has it
> ever been definitively shown that the anomalous photons are of the same
> energy as the incident radiation?
>
> In the case of L-edges, why are there three separate edges? Further, if the
> resonance occurs when the energies are equal, why does resonance occur at
> energies greater than the edge? I don't think this happens in other resonance
> phenomena, or does it? If projects a middle-C-tone into a piano, do all of
> the lower notes resonate as well, according to the Kramers-Kronig relation? I
> think it may actually happen in the mammalian cochlea's travelling wave, but
> is it completely general to resonance phenomena?
>
> Just interested, and have wondered these things for a long time in the
> background of my mind...
>
> Jacob Keller
>
>
> *******************************************
> Jacob Pearson Keller, PhD
> Looger Lab/HHMI Janelia Research Campus
> 19700 Helix Dr, Ashburn, VA 20147
> email: kell...@janelia.hhmi.org
> *******************************************
--
Ethan A Merritt
Biomolecular Structure Center, K-428 Health Sciences Bldg
MS 357742, University of Washington, Seattle 98195-7742
