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 > > > > > > > > > > > ________________________________________ > 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