On Thursday, 12 March, 2015 10:41:46 Ethan A Merritt wrote: > 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.
Note that this can lead to "anomalous scattering" of the incident soldiers. Ethan > But yes, it works for pianos too. > > Ethan -- Ethan A Merritt Biomolecular Structure Center, K-428 Health Sciences Bldg MS 357742, University of Washington, Seattle 98195-7742