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Normal modes of a composite string

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Consider the normal modes of a vibration under uniform tension of a stretched string consisting of two sections of unequal mass density, so that the wave speed differs from one section to the next.

a. What conditions must be satisfied by the string displacement at the junction of the two sections?
b. Suppose that the mass density is higher (and the wave speed lower) in region A than in region B. The string is set vibrating in a high normal mode, so that there are several nodes in each region. Is the distance between notes in region A larger or smaller than that in region B? In which region is the amplitude of vibration larger?

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Solution Summary

In this solution we investigate properties of waves propagating on a composite string.

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(a) The two conditions that must be met at the boundary of regions A and B are that the displacements must match there and also that the spatial derivatives of ...

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