A stretched wire vibrates in its first normal mode at a frequency of 369Hz. What would be the fundamental frequency if the wire were one third as long, its diameter were tripled, and its tension were increased two-fold?
f = 1/2L * squareroot(Ft/u)
The Attempt at a Solution
Can someone explain what I've done wrong?
369 = 1/2L * Sroot(Ft/u)
L is 1/3, so 1/2L becomes 3/(2L)
The Ft is doubled, but the u needs to be broken down further.
m/l = u
l is 1/3
m = dv
d stays the same, so v is the relevant one.
V = pi r2h
r is tripled, so the V increases by a factor of 9. However, since the h (aka l) also changes by a third. Total change of V is x3.
so, 3*m / (l/3)
Sroot ( 2Ft / (9u)
However, 369 * (3/2) * Sqroot (2/9) is wrong. ( = 260.922402258)