Round your answer to three significant figures. One cold and windy winter day, Z
ID: 1468655 • Letter: R
Question
Round your answer to three significant figures.
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 note that the chimney is producing with the bottom open. He finds that the "G#' two octaves below the "G#" above middle "C" matches the chimney's fundamental frequency. Zach knows that the frequency of the "G#" above middle "C" is 415.305 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 the speed of sound in the cold air is 332 m/s, reporduce Zach's calculations to find
(a) the height of the chimeny
h=______ m
and
(b) the fundamental frquency of the chimney when it is closed at the bottom.
=________ Hz
Explanation / Answer
1. for the open chimney the frequency that was observed is:
f= 415.305 /2/2/2 for ocatve
f = 415.305 /8
f = 51.9 Hz
so this is a fundamental frequency of the chimney with open end.
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2. Now we may find what is the fundamental frequency of the same chimney with closed end.
It will be an ocatve (half) lower than that of open ends.
therefore we have fundamental frequency = 51.9/2 = 25.95 Hz
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3. Now we may found the lenght f=n*v/4L,
n=1, v=332,
L=nv/4f=
L = 332/(4*25.95)
L = 3.2 m
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