User:IssaRice/One-dimensional wave equation

why are people so bad at explaining this?

• stein and shakarchi just say "We further assume that the force (or tension) coming from the right of the $n$th particle is proportional to Failed to parse (syntax error): {\displaystyle (y_{n+1} − y_n)/h} " -- but... why? making the force proportional to the distance between the two adjacent particles makes sense, but why divide by h?
• this video by Christopher Lum doesn't explain why we get to say that $T_1\cos \alpha =T_2\cos \beta =T$, but not the same thing with sines. By analogy to his argument, we should be saying that $\sin \alpha =\sin \beta =0$ since the angles are small. (Seth Whittington points this out in comments, but the only response is "it's complicated so I'll explain it over a video call".) Also, tan(alpha) should be -slope instead of slope?