Calculating Length of Stretched Wire from Frequency

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SUMMARY

The discussion focuses on calculating the length of a stretched wire based on its second harmonic frequency. Given a tension of 50 N and a mass per unit length density of 0.025 kg/m, the second harmonic frequency is measured at 200 Hz. The correct formula to determine the length of the wire is L = λ/2, where λ represents the wavelength. The relationship between mass, frequency, tension, and length is established through the wave velocity formula v = √(T/u), where u is the mass per unit length.

PREREQUISITES
  • Understanding of wave mechanics, specifically harmonic frequencies
  • Familiarity with the relationship between tension, mass density, and wave velocity
  • Knowledge of basic physics formulas related to waves
  • Ability to manipulate equations to solve for unknown variables
NEXT STEPS
  • Study the derivation of the wave velocity formula v = √(T/u)
  • Learn how to apply the formula v = λf in various harmonic contexts
  • Explore the effects of tension and mass density on wave properties in stretched strings
  • Investigate the principles of standing waves and harmonics in different mediums
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Physics students, educators, and anyone interested in understanding wave mechanics and the properties of stretched wires in harmonic motion.

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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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someone?
 


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:

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