Finding fundamental frequency with length and successive frequencies

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SUMMARY

The fundamental frequency of a 1.3 m long string fixed at both ends, exhibiting successive frequencies of 24 Hz and 48 Hz, is determined to be 12 Hz. This conclusion is derived using the formula fo = nv/4L, where 'n' represents the harmonic number. The discussion clarifies that the term "successive frequencies" indicates that these frequencies correspond to different harmonics of the string, specifically the first and second harmonics.

PREREQUISITES
  • Understanding of standing wave principles
  • Familiarity with harmonic frequencies
  • Knowledge of wave equations, specifically fo = nv/4L
  • Basic concepts of string vibration and fixed boundary conditions
NEXT STEPS
  • Study the derivation of the wave equation fo = nv/4L
  • Explore the concept of harmonics in stringed instruments
  • Learn about the relationship between frequency and wavelength
  • Investigate the effects of string length on fundamental frequency
USEFUL FOR

Students studying physics, particularly those focusing on wave mechanics, as well as educators teaching concepts related to standing waves and harmonics.

cyclingnerd
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Homework Statement


Standing waves on a 1.3 m long string that is fixed at both ends are seen as successive frequencies of 24Hz and 48 Hz. What is the fundamental frequency?


Homework Equations


fo = nv/4L


The Attempt at a Solution


Okay, so I don't really know if that is the right equation, so I can't really see how I'm supposed to solve for this... Please help!
 
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What do they mean by "are seen as successive frequencies"?
 
klawlor419 said:
What do they mean by "are seen as successive frequencies"?
They mean that standing waves can exist on the string at those two frequencies, but at no frequency in between.
cyclingnerd (I could say, fellow cyclingnerd :approve:) how many wavelengths would there be on a string vibrating at its fundamental frequency? How many at successive harmonics?
 

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