Arbitrary travelling wave on string (griffiths 9.5)

[DE7]

hi all,

i'm in need of a little help with griffiths 9.5 (EM). the problem concerns a traveling wave of arbitrary shape on a string. the string consists of two strings with different mass densities tied together at z=0. given the arbitrary incoming wave, what are the transmitted and reflected waves?

i know i must impose continuity conditions on the wave and its derivatives at z=0. however, are these two equations enough to determine the problem? or should i decompose the incoming wave using Fourier series? I'm not too sure how to go about doing that...any hints?

 

[mezarashi]

The problem of wave reflection and transmission is derived simply from the principle of continuity, so yes they are enough. Whether you decompose the wave or not into its fundamental harmonics is irrelevant to the reflected and transmitted wave magnitudes, which is usually the parameter of interest.

Reflection occurs when there is a change in propagating medium, such as air to glass, or string1 to string 2 for mechanical waves.