The Resonant Wine Bottle · AI Generator #GEN-BC940070

Physics

Problem

A musician discovers that when she blows across the top of an empty wine bottle, it produces a clear tone at frequency

f_0 = 220\;\text{Hz}

. Curious about the physics, she partially fills the bottle with water and finds that the frequency increases to

f_1 = 330\;\text{Hz}

. The wine bottle can be modeled as a cylindrical tube of length

L = 30\;\text{cm}

that is closed at the bottom. When partially filled, the effective length of the air column is reduced. The speed of sound in air is

v = 343\;\text{m/s}

. What height of water did she add to the bottle?