Organ Pipe and Fundamental Frequency

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SUMMARY

The discussion focuses on an organ pipe that is 2.0 m long and open at both ends, originally tuned to a fundamental frequency of 128 Hz. The wavelength of the fundamental frequency is calculated using the formula λ = 2L, resulting in a wavelength of 4.0 m. When the frequency changes to 262 Hz, the relationship v = fλ is applied, using a speed of sound of 330 m/s to determine the new length of the pipe with respect to the blockage position.

PREREQUISITES
  • Understanding of wave properties, specifically wavelength and frequency
  • Knowledge of the speed of sound in air (330 m/s)
  • Familiarity with the equations for standing waves in open pipes
  • Basic algebra skills for solving equations
NEXT STEPS
  • Learn how to calculate the fundamental frequency of different pipe lengths
  • Explore the effects of temperature on the speed of sound in air
  • Investigate the harmonics produced by pipes open at both ends
  • Study the relationship between frequency, wavelength, and pipe length in musical acoustics
USEFUL FOR

Students studying physics, particularly those focusing on acoustics and wave mechanics, as well as musicians and sound engineers interested in understanding the principles of organ pipe tuning.

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Homework Statement


The organ pipe is 2.0 m long, was open at both ends, and was originally tuned to a fundamental frequency of 128 Hz (C below middle C).
a) what is the wavelength of the fundamental?
b)if the note you now hear is closer to 262 Hz (middle C), where is the blockage with respect to the opening at the bottom of the pipe?


Homework Equations


for a pipe open on both ends: lambda=2L


The Attempt at a Solution


a) lambda=2L= 4.0 m
b) I know the pipe will have a displacement antinode at each end, and a pressure node at each end. I don't understand how to find L given only the frequency 262 Hz; I looked at all my equations, but couldn't find one that seemed to work.
Help please!
 
Physics news on Phys.org
v=f\lambda

Using that relationship you can change the frequency in wavelength (speed\ of\ sound=330 ms^{-1} if not specified.) So from there it's should be pretty straight forward to solve for L
 

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