Let's use the above result to derive the *slope* of the ideal
vibrating string
From Eq.
(C.11), we have the string displacement given by

By linearity of differentiation, the

Consider only the right-going component, and define

with . By the

The left-going component is similar, but with . Thus, the string slope in terms of traveling velocity-wave components can be written as

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Center for Computer Research in Music and Acoustics (CCRMA), Stanford University