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This stems out of my personal curiosity and it's not related to any homework of sort.

Suppose I have a table made of some uniform substance (like plastic), and then I strike some point of the table with a hammer. Will the disturbance/wave I produce travel always the speed of sound in that medium, or will there be cases in which the wave travels at a different speeds?

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In any real material, there is dispersion, which means that the speed of the wave depends on its frequency. In that case, there are multiple speeds of sound (one for each frequency). In addition, the speed depends on the polarization of the wave (longitudinal and transverse waves will likely have different speeds). Finally, there are anistropic materials in which the speed of sound is different in different directions.

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  • $\begingroup$ Thanks. It's a bit more complex than I imagined. Would you please advise about a book that treats such matter in a mathematically sound but (relatively) simple way? P.S.: By "one for each frequency" you mean for each of the pure sine components that the FT would spit out from the composite wave generated by the hammer strike? $\endgroup$
    – MadHatter
    Commented Sep 8, 2023 at 15:42
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    $\begingroup$ @MadHatter. I mean, I learned this stuff not from a single source but from many sources that treat systems that support wave phenomena. So, basic introductory physics textbooks, optics textbooks, electromagnetism textbooks, solid state physics, quantum mechanics, and meth-methods-in-physics books. So I don't really have anything to recommend. And yes, by "one for each frequency", I mean "for each of the pure sine components", provided those are the normal modes of the system. $\endgroup$
    – march
    Commented Sep 8, 2023 at 17:16
  • $\begingroup$ Ok, thanks. I was wondering.. Since the various components of the wave travel at different speeds, why do we provide an exact value for the speed of sound in various materials? $\endgroup$
    – MadHatter
    Commented Sep 9, 2023 at 11:10
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    $\begingroup$ The speed of sound typically varies only weakly with the frequency over broad frequency ranges. For instance, for sound propagation in crystals, provided that the amplitude is small enough and that the wavelength is significantly longer than the interatomic spacing, the speed of sound is essentially constant with frequency. Again, you'll see these kinds of things in various contexts. I found that I understood a lot more after studying waves supported in a 1D chain of atoms, which treatment you'll find in any introductory solid state physics book. @MadHatter $\endgroup$
    – march
    Commented Sep 9, 2023 at 17:28
  • $\begingroup$ Again, thanks. I'll start from there. $\endgroup$
    – MadHatter
    Commented Sep 9, 2023 at 19:07

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