University Physics III · Mechanical waves and superposition
Amplitude reflection at a string junction
Problem
Two strings under the same tension are joined at $x=0$. A sinusoidal displacement wave travels from string 1, with density $\mu_1$, into string 2, with $\mu_2=4\mu_1$. Derive the reflected and transmitted displacement-amplitude ratios $r=A_r/A_i$ and $t=A_t/A_i$.
Hint
Impose continuity of displacement, giving $1+r=t$.
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