The violin supports a Helmholtz resonance, acting like a driven, damped harmonic oscillator. The amount of damping can be measured from the width of the response curve, and also from the decay of an undriven oscillator. The phase shift between driver and resonator is also consistent with theory. Shifts in resonant frequency due to changing the aspect ratio of the f hole are measured and found to be in qualitative agreement with a convenient formula for the resonant frequency associated with a long thin aperture.
The spreading of a one-dimensional wavepacket solution of Schrödinger’s equation is related to the diffraction of light, as can be verified by considering the three-dimensional spreading of a wavepacket for an arbitrary dispersion relation. This investigation uncovers a special property of Schrödinger’s equation for a free particle: A wavepacket with initial spherical symmetry will preserve this symmetry in all Galilean reference frames. This property leads to a derivation of de Broglie’s postulate that wave number is proportional to momentum (or velocity). The application to non-Gaussian wavepackets and to Fraunhoffer diffraction also is discussed.
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