On Monday 22 September 2003 07:58, LGS-Europe wrote:
> Perhaps one of the rocket scientists (Arto, Taco?) on the list can help me
> with this.
> Mersenne and Galileo already found out that:
> - Frequency is inversely related to String Length.
> - Frequency is related to the square root of String Tension.
> - Fequency is inversely related to the square root of the String Mass per
> unit length.
> From this I can deduce a formula for calculating string length / frequency
> / material / diameter, much like Arto's Super String Calculator:
>
> T = constant * F^2 * L ^2 * Pi * (0.5 * d)^2 * D
>
> T = Tension
> F = Frequency
> L = String Length
> d = String diameter
> D = Density of String material
>
> The constant has to be 0,04
> My question is: why 0,04? Coincidence, some fixed constant in nature or
> just a
> stupid question because I am missing something obvious?
>
> David
>
hello david, some physics derivations:
The frequency of a vibrating string is derived from:
1
f = -- * sqrt (T / mu)
2l
mu is the mass per unit length of the string, i.e. m*l. The mass per unit
length is the same as the string density * cross section: r * pi * d/4
so this gives
1
f = -- sqrt ( T/r*pi)
2l
Which is your formula:
T = 4 * l^2 f^2 r pi (0.5 d)^2
It's 4 when you use SI units, so not the american/english pounds, feet, miles,
and other units from the middle ages.
The formula gives the same figures as Arto's calculator, but for some string
materials I get some unexplainable high tensions or very small diameters. I
still have to figure this out.
Taco
