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Question

Find the number of possible natural frequencies of an air column in an open pipe frequencies of which lie below 1250 Hz. The length of the pipe is 85 cm. The speed of sound is 340 ms1

A
3
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B
4
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C
5
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D
6
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Solution

The correct option is D 6
For open organ pipe, length of the pipe will be multiple of all possible λ/2 (even and odd).mλ/2=L,

λ=2L/m, here m=1,2,3....
therefor from the formula,
v=fλ
fm=v/λ=v/(2L/m)
fm=mv/2L
now,
f1=340/1.7=200Hz
f2=2340/1.7=400Hz
f3=600Hz, f4=800Hz, f5=1000Hz, f6=1200Hz
therefore option "D" is correct.

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