- #1
kent davidge
- 931
- 56
Change in frequency with a small change in tension (guitar string)
AI Thread Summary
The discussion focuses on the relationship between frequency changes and tension adjustments in guitar strings. A participant confirms their solution by validating it with random numbers but struggles to express it as required by the problem. They reference the first terms of the series expansion of the square root function, specifically \(\sqrt{1+x} \approx 1 + x/2\) for small x. A mentor intervenes to clarify the thread title for better context. The conversation highlights the challenge of applying mathematical concepts to practical problems in music theory.
- #2
PietKuip
- 371
- 45
\sqrt{1+x} \approx 1 + x/2 when x \ll 1
- #3
kent davidge
- 931
- 56
ohhh thanks... I see that my answer was correct by checking my last formula with random numbers, but I'm still unable to solve it to get the expression as the problem asks. (sorry my english)
- #4
PietKuip
- 371
- 45
It is the first terms of the series expansion of \sqrt{1+x} close to 1.
- #5
gneill
Mentor
- 20,989
- 2,934
Mentor's note: Please note that I changed the thread title to make it more descriptive of the problem. The original title was entirely too vague.
In this question, I have a question. I am NOT trying to solve it, but it is just a conceptual question.
Consider the point on the rod, which connects the string and the rod. My question: just before and after the collision, is ANGULAR momentum CONSERVED about this point?
Lets call the point which connects the string and rod as P.
Why am I asking this? : it is clear from the scenario that the point of concern, which connects the string and the rod, moves in a circular path due to the string...
This problem is two parts. The first is to determine what effects are being provided by each of the elements - 1) the window panes; 2) the asphalt surface. My answer to that is
The second part of the problem is exactly why you get this affect.
And one more spoiler:
F1=(5000+200)g=5200*10=52000N --> F2=(5000+100)g=5100*10=51000N ?
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