One cold and windy winter day, Zach notices a humming sound coming from his chim

Question

One cold and windy winter day, Zach notices a humming sound coming from his chimney, which 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 note that the chimney is producing with the bottom open. He findes that the "C" three octabes below middle "C" matches the chimney's fundamental frequency. Xach knows that the frequencey of middle "C" is 261.6Hz, and each lower octave is 1/2 of the frequencyof the octave above. from this information, Zach finds the height of the chimney and the fundamental frequency of the note that was producen the chimney was closed at the bottom. Assuming that the speed of sound in cold air 330m/s, reproduce Zach's calculations to find:
a) the heigt of the chimney
b) the fundamental frequency of the chimney when it is closed at the bottom.

Explanation / Answer

Frequency at 3 octaves below middle c= 261.6/23=32.7 hz.

For an open chimney, fundamental frequency= v/2L= 32.7

v=330 for sound waves in air.

therefore, L=330/(2*32.7)= 5.046 m5 m

If the chimney is closed at the bottom, fundamental frequency= v/4L= 330/(4*5)= 16.5 hz.

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