- #1

dantechiesa

## Homework Statement

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?

## Homework Equations

f = 1/2L * squareroot(Ft/u)

## The Attempt at a Solution

[/B]

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 r

^{2}h

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)

All together,

Sroot ( 2Ft / (9u)

However, 369 * (3/2) * Sqroot (2/9) is wrong. ( = 260.922402258)

Thanks.