You have a nice fire going in the fireplace on a cold, wintery evening. The damp

Question

You have a nice fire going in the fireplace on a cold, wintery evening. The damper, of course, is open and the chimney is a tube open at both ends. Your chimney has length L. As the wind passes over the upper opening of the chimney it causes the air in the chimney to vibrate giving a moaning sound that makes you feel happy to be indoors and out of the cold. You may assume that the temperature in the chimney is between that of the hot air in the fire, and the cold air outdoors averages to T.

a) What is the speed of sound v in the air of the chimney?

b) What is the fundamental frequency f of moaning the chimney?

L=6.7m

T= 72 degrees C

Explanation / Answer

Speed of sound in air at a particular temp is given by:

v = 331m/s + 0.6m/s/C * T

So at T=72

a) v= 331 +0.6*72=374.2 m/s

b) Fundamental frequency is given by fo=v/4L

=> fo=374.2/4*6.7=13.96 Hz

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