Waves: fundamental frequency of taut cable

[Any Help]

1. Homework Statement

The wire cable supporting the mast of a sailboat has a length of 12 m and a linear mass density of 350 g/m. When pushed sideways at its midpoint with a force of 160 N, the cable deflects by 9.5 cm. What is the frequency of the fundamental mode of vibrations on this cable?

Homework Equations

λn.fn=v and velocity:v=sqrt(T/μ) , lemda λn=2L/n and L= length of string
fn=n/2L . sqrt(T/μ)
fundamental≡ the first mode ⇒ n=1

The Attempt at a Solution

for n=1
f=1/(2*12) .sqrt (160/0.35) =0.89 Hz
but it is incorrect why??

 

[Merlin3189]

In the equation you use, what are each of the terms? ( IE. what do the letters f, n, L, T and μ stand for?)
Which of these are given?
What other information are you given?
How will you work out the term, which is not given?

As a hint, you don't use one of the given values and you mis-use one of the given values.

 

[Any Help]

what do the letters f, n, L, T and μ stand for?)
Which of these are given?

velocity:v=sqrt(T/μ)

T=tension=160N
μ=linear mass=0.35kg/m

L= length of string

fundamental≡ the first mode ⇒ n=1

f is the frequence

 

[Merlin3189]

T=tension=160N

The tension should be the tension in the cable.
The value 160N is the force used to displace the cable sideways by 9.5cm.
The tension in the cable would be much greater. (A mast over 12m high would hardly be supported by a tension of 160N on each side.)

So you need to see how you can use the information given, to calculate the tension in the cable.