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A certain pipe (not a musical instrument) produces the following consecutive harmonics: 209.1 Hz, and 348.5 Hz. (a) Is the pipe open or closed. (b) Taking the temperature of the surrounding to be 22.5°C, find the length of the pipe.
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Answer #1

for closed pipe, the harmonics are

f1, 3f1, 5f1, 7f1, ......

for open pipe pipe

f1, 2f1, 3f1, 4 f1, .......

the given frequency is

209.1 Hz = 3f1

f1 = 69.7 Hz

the net harmonic frequency is 5f1 = 5 (69.7) = 348.5 Hz

the consecutive harmonics are belong to closed pipe.

(b)

the speed of sound at temperature T is

v= 331 + 0.6 T = 331+0.6(22.5) = 344.5 m/s

length of closed pipe is

f= n*v/ 4L

L = v/4f = 5* 344.5/4 ( 348.5) = 1.23 m

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