User:IssaRice/One-dimensional wave equation - Revision history

IssaRice at 06:38, 13 September 2021

2021-09-13T06:38:44Z

← Older revision		Revision as of 06:38, 13 September 2021
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	* 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?		* 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? there's also this inconsistency in modeling where we only consider two points instead of three points (one point and its two adjacent points). Also, why is the tension in the string in the direction tangent to the string at each point? Tension T is a force, so it can be positive or negative; why do we get to write c^2?		* [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? there's also this inconsistency in modeling where we only consider two points instead of three points (one point and its two adjacent points). Also, why is the tension in the string in the direction tangent to the string at each point? Tension T is a force, so it can be positive or negative; why do we get to write c^2? also like, what even is tension?

IssaRice at 06:31, 13 September 2021

2021-09-13T06:31:59Z

← Older revision		Revision as of 06:31, 13 September 2021
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	* 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?		* 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? there's also this inconsistency in modeling where we only consider two points instead of three points (one point and its two adjacent points). Also, why is the tension in the string in the direction tangent to the string at each point?		* [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? there's also this inconsistency in modeling where we only consider two points instead of three points (one point and its two adjacent points). Also, why is the tension in the string in the direction tangent to the string at each point? Tension T is a force, so it can be positive or negative; why do we get to write c^2?

IssaRice at 06:20, 13 September 2021

2021-09-13T06:20:55Z

← Older revision		Revision as of 06:20, 13 September 2021
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	* 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?		* 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? there's also this inconsistency in modeling where we only consider two points instead of three points (one point and its two adjacent points).		* [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? there's also this inconsistency in modeling where we only consider two points instead of three points (one point and its two adjacent points). Also, why is the tension in the string in the direction tangent to the string at each point?

IssaRice at 04:19, 12 September 2021

2021-09-12T04:19:43Z

← Older revision		Revision as of 04:19, 12 September 2021
Line 2:		Line 2:

	* 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?		* 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? there's also this inconsistency in modeling where we only consider two points instead of three points (one point and its two adjacent points).

IssaRice at 04:17, 12 September 2021

2021-09-12T04:17:25Z

← Older revision		Revision as of 04:17, 12 September 2021
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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} − 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?		* 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?

IssaRice: 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 $n$ th particle..."

2021-09-12T04:16:59Z

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..."

New page

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} − 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?