Question

(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?

Answer 1

476.387 Hz

714.583 Hz

Step-by-step explanation:

L = Length of tube

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

Frequency for a closed tube is given by

`f=(v)/(4L)\\\Rightarrow f=(343)/(4* 0.18)\\\Rightarrow f=476.389\ Hz`

The frequency is 476.387 Hz

If it was one third full
`L=0.18-(1)/(3)0.18`

`f=(v)/(4L)\\\Rightarrow f=(343)/(4* (0.18-(1)/(3)0.18))\\\Rightarrow f=714.583\ Hz`

The frequency is 714.583 Hz