Calculating Length of Stretched Wire from Frequency

In summary, the conversation discusses finding the length of a stretched wire with a tension of 50 N and a mass per unit length density of 0.025 kg m-1, based on a measured second harmonic frequency of 200 Hz. The formula L=λ/2 is considered, as well as the relationship between mass, frequency, tension, and length. The formula v=\lambda{f} is suggested for solving the problem.
  • #1
Travian
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0

Homework Statement



The second harmonic frequency on a stretched wire, with a tension of 50 N and a mass per unit length density of 0.025 kg m-1, is measured to be 200 Hz. What is the length of the wire?

Homework Equations


L=λ/2

The Attempt at a Solution


As far as I've discovered i must find L, but i am not sure if this is the correct formula:
L=λ/2

In case it is correct, then what is the relation between mass, frequency,tension and length.

If it is not, then what formula i should use in order to get length?

I searched throughout google, but i couldn't find any other formulas. Totally confused:/
 
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  • #2


someone?
 
  • #3


Hi. The velocity of the propagating wave [tex]v=\sqrt{\frac{T}{u}}[/tex] where [tex]{u}[/tex] is the mass per unit length.

In the second harmonic frequency, [tex]\lambda = L[/tex].

Use [tex]v=\lambda{f}[/tex] to solve the rest.
 
Last edited:

Related to Calculating Length of Stretched Wire from Frequency

1. How do I calculate the length of a stretched wire from its frequency?

To calculate the length of a stretched wire from its frequency, you will need to know the mass per unit length of the wire, the tension applied to the wire, and the frequency of the wire's vibration. Once you have this information, you can use the formula L = (m/4) * (T/f)^2, where L is the length of the wire, m is the mass per unit length, T is the tension, and f is the frequency.

2. What is the mass per unit length of a wire?

The mass per unit length of a wire is the mass of the wire divided by its length. This value is typically given in units of kilograms per meter (kg/m). It can be calculated by weighing a known length of the wire and dividing the weight by the length.

3. How do I measure the tension applied to a wire?

The tension applied to a wire can be measured using a tension meter or by hanging weights from the wire and measuring the resulting force. It is important to make sure the wire is under constant tension while measuring.

4. What is the relationship between frequency and length of a stretched wire?

The frequency of a stretched wire is directly proportional to its length. This means that as the length of the wire increases, the frequency of its vibration will also increase, and vice versa.

5. Can I use this formula for any type of wire?

This formula can be used for any wire as long as it is under constant tension and the mass per unit length is known. However, it is important to note that this formula is most accurate for thin, uniform wires. Thicker or non-uniform wires may require more complex calculations.

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