Answer to Question #123103 in Physics for Katie

Question #123103
In an experiment, a glass tube is submerged into a larger graduated cylinder full of water. A tuning fork is vibrating above the tube at a frequency of 659 Hz. If the 1st resonant frequency is heard at 14.2 cm, what is the speed of sound? Round your answer to the nearest meter.
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Expert's answer
2020-06-22T11:13:03-0400

The resonant frequency ff , the lenght of the tube LL and the speed of the sound vv are connected with the following expression (see https://en.wikipedia.org/wiki/Acoustic_resonance#Open_at_both_ends):


f=nv2Lf = \dfrac{nv}{2L}

Expressing vv from this equation and setting n=1n=1 (for the 1st resonant frequency), obtain:


v=2fLv = 2fL

Substituting numerical values, get:


v=2659Hz0.142m=187.156m/s187m/sv = 2\cdot 659Hz\cdot 0.142m = 187.156 m/s\approx187m/s

Answer. v = 187 m/s.


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