Calculate open pipe length given resonance.

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To calculate the length of an open pipe needed for resonance at 384 Hz, the speed of sound is given as 343 m/s. The relevant formula is f = nv/2l, where f is frequency, n is the harmonic number (1 for the fundamental frequency), v is the speed of sound, and l is the length of the pipe. The calculation shows that the length of the pipe should be approximately 9.45 meters. Understanding the formula's components, particularly the factor of 2 in the denominator, is crucial for solving similar problems in exams. This approach effectively demonstrates how to derive the required length for resonance in an open pipe.
seker
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Homework Statement



What length of open pipe is needed to give resonance to a 384 Hz sound? Assume the speed of sound to 343 m/s.

Homework Equations



f=\frac{nv}{2l}

The Attempt at a Solution



I am lost as to how to even start this problem.
 
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welcome to pf!

hi seker! welcome to pf! :smile:

what is the (shortest) length (of an open pipe) needed to give a particular wavelength? :wink:
 
This is what I have come up with so far.

(384)(l)=\frac{(1)(343)}{2}

l=9.45m
 
looks ok! :smile:

(btw, do you understand why there's a "2" on the bottom, and would you be able to work it out for yourself in an exam if you couldn't remember the exact formula? :wink:)
 

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