Fundamental Frequency of Open and Closed Tube

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SUMMARY

The fundamental frequency of a tube closed at one end and open at the other is calculated using the formula f (open and closed) = v/4L, yielding a frequency of 242 Hz. For a tube that is open at both ends, the fundamental frequency is determined using the formula f (open) = v/2L. Given the speed of sound as 343 m/s and a calculated length of 0.354 m, the fundamental frequency for the open tube is 484 Hz. The calculations and conclusions presented are accurate and validated by peer feedback.

PREREQUISITES
  • Understanding of wave mechanics and sound propagation
  • Familiarity with the speed of sound in air (343 m/s)
  • Knowledge of fundamental frequency calculations for open and closed tubes
  • Basic algebra for manipulating equations
NEXT STEPS
  • Study the effects of tube length on fundamental frequency
  • Explore harmonic frequencies in open and closed tubes
  • Learn about the impact of temperature on the speed of sound
  • Investigate applications of tube resonances in musical instruments
USEFUL FOR

Physics students, acoustics researchers, and anyone interested in the principles of sound waves and their applications in real-world scenarios.

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Homework Statement



A tube closed at one end and open at the other has a fundamental frequency of 242 Hz. What is the fundamental whenboth are open?

Homework Equations



f (open and closed) = v/4L
f (open) = v/2L
v sound = 343 m/s

The Attempt at a Solution



f1 (open and closed) = v/4L = 242Hz = 343/4L

L = .354 m

f (open) = v /2L = 343/ 2(.354m) = 484 Hz

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