You have a nice fire going in the fireplace on a cold, wintry evening. The dampe

Question

You have a nice fire going in the fireplace on a cold, wintry evening. The damper, of course, is open and the chimney is a tube open at both ends. Your chimney has a length 5.4m(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 74 degree C (T). What is the speed of sound v in the air of the chimney What is the fundamental frequency f_1 of moaning the chimney v = ________ f_0 = ________

Explanation / Answer

Given that

@=2 $=5

The pipe is opened then the length becomes L =lamda/2

Then the fundamnetal frequency is given by

f =v/2L

Given that

L =3+$/2+@/5 =3+5/2+2/5 =5.9m

T =30+2@+5@ =30+2*5+5*5 =65oC

The speed of the sound at the 650C is given by

v =331+0.6*T =331m/s+0.6*65 =370m/s

b)

The fundamental frequency of the chimney is given by

f0 =v/2L =370m/s/2*5.9m =31.356Hz

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