User:IssaRice/One-dimensional wave equation: Difference between revisions
(Created page with "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 <math>n</math>th particle...") |
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why are people so bad at explaining this? | 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 <math>n</math>th particle is proportional to <math>(y_{n+1} | * stein and shakarchi just say "We further assume that the force (or tension) coming from the right of the <math>n</math>th particle is proportional to <math>(y_{n+1} - y_n)/h</math>" -- but... why? making the force proportional to the distance between the two adjacent particles makes sense, but why divide by h? | ||
* [https://www.youtube.com/watch?v=IAut5Y-Ns7g this video] by Christopher Lum doesn't explain why we get to say that <math>T_1 \cos\alpha = T_2 \cos \beta = T</math>, but not the same thing with sines. By analogy to his argument, we should be saying that <math>\sin \alpha = \sin \beta = 0</math> 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? | * [https://www.youtube.com/watch?v=IAut5Y-Ns7g this video] by Christopher Lum doesn't explain why we get to say that <math>T_1 \cos\alpha = T_2 \cos \beta = T</math>, but not the same thing with sines. By analogy to his argument, we should be saying that <math>\sin \alpha = \sin \beta = 0</math> 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? | ||
Revision as of 04:17, 12 September 2021
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 th particle is proportional to " -- 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 , but not the same thing with sines. By analogy to his argument, we should be saying that 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?