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What is the length of a tube that has a fundamental frequency of 176 Hz and a first overtone of 352 Hz if the speed of sound is 343 m/s?
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Final Answer

$0.974 \textrm{ m}$

Solution Video

OpenStax College Physics Solution, Chapter 17, Problem 47 (Problems & Exercises) (1:23)

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Video Transcript

This is College Physics Answers with Shaun Dychko. We are told that a tube has a fundamental frequency of 176 hertz and the first overtone is 352 hertz and the speed of sound on this day is 343 meter per second and we need to figure out what is the length of the tube. So, we will take a ratio of two frequencies, 352 hertz divided by 176 and notice that this is two and even multiples are possible only for tubes that are open at both ends and so we can draw this way and we can say that half of the fundamental wavelength fits in this length <i>L</i> in this case fundamental wavelength <i>Lambda one</i> is two times <i>L</i> and knowing that the wave speed formula <i>v</i> equals <i>f lambda</i>, we can solve for <i>f</i> in term of <i>v</i> and <i>lambda</i> by dividing both sides by <i>lambda</i> and so the fundamental frequency is speed of sound divided by fundamental wavelength and that’s gonna be <i>v</i> divided by two <i>L</i> and then solving for <i>L</i>, multiply both sides by <i>L</i> over <i>f one</i> and we get <i>L</i> is <i>v</i> over two times <i>f one</i> and so that’s 343 meter per second divided by two times the fundamental frequency of 176 hertz which is 0.974 meters.