Answered: Two successive frequencies of harmonic…

College Physics

11th Edition

ISBN:9781305952300

Author:Raymond A. Serway, Chris Vuille

Publisher:Raymond A. Serway, Chris Vuille

Chapter1: Units, Trigonometry. And Vectors

Section: Chapter Questions

Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...

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Two successive frequencies of harmonic vibration (reasonance) in a pipe are 532HZ and 684Hz. Is the pipe open at both ends or closed at one end?

I'm just trying to conceptually understand this. Thank you for your help.

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Step 1: Frequencies of harmonic vibration in the pipe open at both ends and closed at one end

The frequencies of harmonic vibration (resonance) in a pipe open at both ends are:

$f subscript n equals fraction numerator n v over denominator 2 L end fraction equals space n f subscript 1$ , where $n$ is a natural number ( $n space equals space 1 comma space 2 comma space 3 comma space...$ )

The frequencies of harmonic vibration (resonance) in a pipe closed at one end:

$f subscript n equals fraction numerator n v over denominator 4 L end fraction equals space n f subscript 1$ , where $n$ is an odd natural number ( $space n equals space 1 comma space 3 comma space 5 comma space...$ )

Where:

$f subscript 1$ is fundamental frequency,

$v$ is velocity of the wave

$L$ is length of the pipe.

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