Calculating Fundamental Frequency and Overtone Frequency of a Stretched Wire

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SUMMARY

The discussion focuses on calculating the fundamental frequency and overtone frequency of a stretched wire using the formula f = (1/2L)√(T/(m/L)). The wire is 80 cm long, with a mass of 0.40 g, and is stretched across a sonometer with a length of 50 cm under a force of 500 N. The correct length to use in the equation is the length between the stops, which is 50 cm, as it represents the vibrating segment of the wire. The confusion regarding the two lengths in the equation is clarified, emphasizing that the length used in the frequency calculation should be the effective vibrating length.

PREREQUISITES
  • Understanding of wave mechanics and frequency calculations
  • Familiarity with the sonometer and its application in physics
  • Basic knowledge of tension, mass, and length relationships in vibrating strings
  • Proficiency in using the formula f = (1/2L)√(T/(m/L)) for frequency calculations
NEXT STEPS
  • Calculate the fundamental frequency of the wire using the provided parameters
  • Determine the frequency for the 2nd overtone using the same formula
  • Explore the impact of varying tension and mass on the frequency of a stretched wire
  • Investigate the principles of harmonics and overtones in string instruments
USEFUL FOR

Students studying physics, particularly those focusing on wave mechanics, as well as educators teaching concepts related to sound and vibrations in stretched strings.

i'mcheche
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Homework Statement


a flexible wire is 80 cm long has a mass of 0.40g. It is stretched across stops on a sonometer that are 50 cm apart by a force of 500N. Find the fundamental frequency with which the wire may vibrate. If it vibrates in 2 third overtone, what is it's frequency?

Homework Equations


f=\frac{1}{2L}\sqrt{\frac{T}{\frac{m}{L}}}

The Attempt at a Solution


I don't kno where to start. I substituted all the given data. And I'm not really sure about my answer.

I can't decide what length should be used in the equation. the problem states the total length of the wire and the length of the wire which is streched on the sonometer.
 
Last edited:
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welcome to PF :smile:

it is said that the sonometer stops are 50cm apart.So that should me the length. :smile:
 
There are two L's in the equation. Are they necessarily the same?
 

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