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(a) What resonant frequency would you expect from blowing across the top of an empty soda bottle that is 18 cm deep, if you assumed it was a closed tube? (b) How would that change if it was one-third full of soda?

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boffeemadrid

Answer:

476.387 Hz

714.583 Hz

Explanation:

L = Length of tube

v = Speed of sound in air = 343 m/s

Frequency for a closed tube is given by

[tex]f=\dfrac{v}{4L}\\\Rightarrow f=\dfrac{343}{4\times 0.18}\\\Rightarrow f=476.389\ Hz[/tex]

The frequency is 476.387 Hz

If it was one third full [tex]L=0.18-\dfrac{1}{3}0.18[/tex]

[tex]f=\dfrac{v}{4L}\\\Rightarrow f=\dfrac{343}{4\times (0.18-\dfrac{1}{3}0.18)}\\\Rightarrow f=714.583\ Hz[/tex]

The frequency is 714.583 Hz

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