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## Homework Statement

A stretched wire vibrates in its fundamental mode at a frequency of 375 Hz. What would be the fundamental frequency if the wire were one third as long, its diameter were tripled, and its tension were increased five-fold?

## Homework Equations

V = F*w = sqrt(T/u)

mass of cylinder = Volume x Density

m = πr

^{2}Lp

where

F = Frequency

w = wavelength,

T = tension

u = linear mass density

m = mass

L = length

p = density

## The Attempt at a Solution

m = πr

^{2}Lp

m/L = πr

^{2}p

1.

__u = πr__

^{2}pF*w = sqrt(T/u)

F*2L = sqrt(T/u)

F

^{2}4L

^{2}= T/u

2.

__F__

^{2}= T/(u4L^{2})sub in u from 1. into 2.

F

^{2}= T/(πr

^{2}p4L

^{2})

Question says..

T x 5

L x 1/3

D x 3 => r x 6

F2

^{2}/ F1

^{2}= [5T/(π(6r)

^{2}p4(1/3L)

^{2})] / [T/(πr

^{2}p4L

^{2})]

F2

^{2}/ F1

^{2}= 5 / 6

^{2}(1/3)

^{2}

F2 / F1 = sqrt(5/4)

F2 = sqrt(5/4)*F1

...This gave me the wrong answer,

Could someone please tell me where I went wrong? or where I missed something?

Thank you