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Topic: guitar string (Read 1744 times) |
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Larissa_Preedy
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guitar string
« on: Jun 8th, 2005, 12:11am » |
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A guitar string makes a higher note the tighter the tension in the string. Suppose
* the guitar has length L;
* the string tension is T; and
* the mass of the string is M kg per meter.
what is the order of magnitude of the expression for the frequency of vibration of the string?
i can get it down to 1/s2..but i need 1/s
L = metres
T = kgm/s2
M = kg/m
T/ML3
gives me 1/s2
how do i get that down to 1/s?
or am i going on the wrong tracK?
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Sir Col
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impudens simia et macrologus profundus fabulae
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Re: guitar string
« Reply #1 on: Jun 8th, 2005, 12:56am » |
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Don't forget that you're working with a sinusoidal wave, so when you derive the wave velocity you would obtain an expression involving a square root (v=sqrt(T/r), where r is mass per unit).
Then using the result that the fundamental frequency of a vibrating string is given by v/(2L), we get f=sqrt(T/r)/(2L), where T is tension (kgm/s2), r is mass per unit length (kg/m) and L is length of string (m).
U(T/r)=(kgm/s2)/(kg/m))=m2/s2
U(sqrt(T/r))=m/s
So U(f)=((m/s)/m)=1/s.
I hope that helps.
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Larissa_Preedy
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Re: guitar string
« Reply #2 on: Jun 8th, 2005, 1:35am » |
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hm, i dnt think it's meant to be so complex...
i think we're only meant to use the items given :S
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Sir Col
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Re: guitar string
« Reply #3 on: Jun 8th, 2005, 1:48am » |
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Sadly the word "fundamental" rarely means simple in mathematics and physics, rather it means of significant importance.
Simply put, the fundamental frequency of a vibrating string is of the order sqrt(T/M)/L, using the symbolic conventions you were given.
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Larissa_Preedy
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Re: guitar string
« Reply #4 on: Jun 8th, 2005, 2:00am » |
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that's my probelm though, i cannot have
sqrts
otherwise i would have put
sqrt (T/ML^3)
but i can't do that 
that's why i'm stuck
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towr
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Re: guitar string
« Reply #5 on: Jun 8th, 2005, 2:56am » |
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What is meant by "order of magnitude of the expression"?
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Larissa_Preedy
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Re: guitar string
« Reply #6 on: Jun 8th, 2005, 3:01am » |
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it's dimensional analysis.
i have to basically work out a formula from the given 3 identities, and get the answer in hertz..
L = m
T = kgm/s2
M = kg/m
i got to "cancel" the things down, to end up with 1/s or hertz
as i said, T/ML3 gives 1/s2
This is done by
kgm/s2*m/kg*m-2
the kg's cancel, the m's cancel, leaving 1/s2
however, i need to cancel down to get 1/s
the only method i can think off is square rooting the final answer, but that is not allowed
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| « Last Edit: Jun 8th, 2005, 3:01am by Larissa_Preedy » |
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towr
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Re: guitar string
« Reply #7 on: Jun 8th, 2005, 4:01am » |
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Is it alowed to use ^(1/2) (to the power 1/2) instead of sqrt? (Even though it's the same thing)
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Larissa_Preedy
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Re: guitar string
« Reply #8 on: Jun 8th, 2005, 6:48am » |
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omg, i'm such a fruitcake
i think i can do that..i'll try now
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Larissa_Preedy
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Re: guitar string
« Reply #9 on: Jun 8th, 2005, 6:55am » |
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yeh that worked 
so many silly mistakes i make
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towr
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Re: guitar string
« Reply #10 on: Jun 8th, 2005, 9:14am » |
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on Jun 8th, 2005, 6:55am, Larissa_Preedy wrote:| so many silly mistakes i make |
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Well, this is the best time to make them, better than during an exam. As long as you learn from them.
If you make every possible mistake now, you'll be able to recognize them when it counts 
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Icarus
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Re: guitar string
« Reply #11 on: Jun 8th, 2005, 6:29pm » |
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on Jun 8th, 2005, 2:56am, towr wrote:| What is meant by "order of magnitude of the expression"? |
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From Larissa's statements, I think what it really means is: determine the formula up to a multiplicative constant.
E.g., E = mv2 would be acceptable answer instead of the actual formula of E = (1/2)mv2.
I think the point of the questions is to show students that much of the information they need is available in the units (and hopefully instill in them the realization that carrying the units through the calculation can be helpful, instead of dropping the units at the start, then appending the expected units on the final answer as is their wont).
It is a bit risky determining formula by figuring out how to make the dimensions cancel out correctly. There may be contributors that you miss, or others that you included that should not have been included. (For instance, if their was some time quantity around with this problem, you might have been tempted to multiply your formula by it to get rid of one of the 1/sec factors, instead of taking the square root - thus resulting in an incorrect formula). However, this method does provide a good feel for what the actual formula should look like, which can be helpful in deriving it.
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