One cold and windy winter day, Zach notices a humming sound coming from his chimney when the chimney is open at the top and closed at the bottom. He opens the chimney at the bottom and notices that the sound changes. He goes over to the piano to try to match the chimney is producing with the bottom open.
He finds that the "C" three octaves below middle "C" matches the chimney's fundamental frequency. Zach knows that the frequency of middle "C" is 261.6 Hz, and each lower octave is 1/2 of the frequency of the octave above. From this information, Zach finds the height of the chimney and the fundamental frequency of the note that was produced when the chimney was closed at the bottom. Assuming that the speed of sound in the cold air is 330 m/s, reproduce Zach's calculations to find
(a) The height of the chimney
(b) The fundamental frequency of the chimney when it is closed at the bottom?