Fundamental Frequency of Stretched Strings & Closed Pipes

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SUMMARY

The fundamental frequency of a stretched string is calculated using the formula f = v/2L, while for a closed pipe, it is f = v/4L. Both frequencies can be equal when the relationship v1/2L1 = v2/4L2 holds true, where v represents the speed of sound in the respective medium. Factors affecting these frequencies include the lengths of the string and pipe, as well as any variables that influence the speed of sound, such as temperature and medium density.

PREREQUISITES
  • Understanding of wave mechanics
  • Familiarity with the speed of sound in different media
  • Knowledge of fundamental frequency calculations
  • Basic concepts of string and pipe acoustics
NEXT STEPS
  • Research the effects of temperature on the speed of sound in air
  • Study the relationship between string tension and frequency
  • Explore the acoustic properties of closed pipes
  • Learn about harmonics in string instruments and their mathematical representation
USEFUL FOR

Physics students, acoustics engineers, musicians, and educators interested in the principles of sound and vibration in strings and pipes.

cutesoqq
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HI
As we know, the fundametal freq of a stretched string is f=v/2L
while the fundametal freq. of a closed pipe is f=v/4L
then,
how can the fundametal freq. of both can be the same?!

and, what factors would affect their freq.?!
 
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The frequencies will be the same when [itex]\frac{v_1}{2L_1} = \frac{v_2}{4L_2}[/itex], of course. The speed is the speed of sound: in the string and in air. The fundamental frequencies will be affected by their lengths and whatever affects the speed of sound--look it up! :smile:
 
thank you very much
 

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