Question

(a) What resonant frequency would you expect from blowing across the top of an empty soda bottle that is 24 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

Answer:

a) 357.29 Hz

b) 535.9375 Hz

Step-by-step explanation:

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

l = length = 24 cm

a)

$l=\frac{1}{4}\lambda \\\Rightarrow \lambda=4l$

$f=\frac{v}{\lambda}\\\Rightarrow f=\frac{v}{4l}\\\Rightarrow f=\frac{343}{4\times 0.24}\\\Rightarrow f=357.29\ Hz$

∴ Resonant frequency is 357.29 Hz

b) Here one third is filled with soda

So, length becomes $l=24-\frac{24}{3}=16\ cm$

$f=\frac{v}{4l}\\\Rightarrow f=\frac{343}{4\times 0.16}\\\Rightarrow f=535.9375\ Hz$

∴ Resonant frequency is 535.9375 Hz