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7: Longitudinal Oscillations and Sound

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    Transverse oscillations of a continuous system are easy to visualize because you can see directly the function that describes the displacement. The mathematics of longitudinal oscillations of a continuous linear space translation invariant system is the same. It must be, because it is completely determined by the space translation invariance. But the physics is different.


    In this chapter, we introduce two physical systems with longitudinal oscillations: massive springs and organ pipes.

    1. We describe the massive spring as the continuum limit of a system of masses connected by massless springs and study its normal modes for various boundary conditions.
    2. We discuss in some detail the system of a mass at the end of a massive spring. When the spring is “light,” this is an important example of physics with two different “scales.”
    3. We discuss the physics of sound waves in a tube, by analogy with the oscillations of the massive spring. We also introduce the “Helmholtz” approximation for the lowest mode of a bottle.

    This page titled 7: Longitudinal Oscillations and Sound is shared under a CC BY-NC-SA 4.0 license and was authored, remixed, and/or curated by Howard Georgi via source content that was edited to the style and standards of the LibreTexts platform; a detailed edit history is available upon request.