Waves: fundamental frequency of taut cable

• Any Help
In summary: Then you can use that value to calculate the frequency.In summary, we are given a problem involving a wire cable supporting a mast on a sailboat. The cable 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. Using the equations λn.fn=v and v=sqrt(T/μ), where λn=2L/n and fn=n/2L.sqrt(T/μ), we can determine the frequency of the fundamental mode of vibrations on the cable. However, the given value of 160 N is not the tension in the cable and must be solved for using the information given
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??

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.

Merlin3189 said:
what do the letters f, n, L, T and μ stand for?)
Which of these are given?
Any Help said:
velocity:v=sqrt(T/μ)
T=tension=160N
μ=linear mass=0.35kg/m
Any Help said:
L= length of string
Any Help said:
fundamental≡ the first mode ⇒ n=1
f is the frequence

Any Help said:
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.

1. What is the fundamental frequency of a taut cable?

The fundamental frequency of a taut cable refers to the lowest natural frequency at which the cable will vibrate when plucked or struck. It is determined by the tension, mass, and length of the cable.

2. How is the fundamental frequency of a taut cable calculated?

The fundamental frequency of a taut cable can be calculated using the equation f = 1/2L * √(T/μ), where L is the length of the cable, T is the tension, and μ is the mass per unit length of the cable.

3. What factors affect the fundamental frequency of a taut cable?

The fundamental frequency of a taut cable is affected by its tension, length, and mass per unit length. Additionally, the material and thickness of the cable can also impact its fundamental frequency.

4. Can the fundamental frequency of a taut cable be changed?

Yes, the fundamental frequency of a taut cable can be changed by altering the tension, length, or mass of the cable. For example, increasing the tension or reducing the length will result in a higher fundamental frequency.

5. What is the significance of the fundamental frequency of a taut cable?

The fundamental frequency of a taut cable is important in understanding the behavior of vibrating systems and in the design of musical instruments, as it determines the pitch or note that the cable will produce when vibrated.

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