Question

Find the number of possible natural frequencies of an air column in an open pipe frequencies of which lie below $1250Hz$. The length of the pipe is $85cm$. The speed of sound is $340m{s}^{-1}$

• A. $3$
• B. $4$
• C. $5$
• D. $6$

Answer 1

The correct option is D $6$

For open organ pipe, length of the pipe will be multiple of all possible $\lambda /2$ (even and odd).$m\lambda /2=L$,

$\lambda =2L/m$, here $m=1,2,3....$

therefor from the formula,

$v=f\lambda$

$f_m=v/\lambda =v/\left(2L/m\right)$

$f_m=mv/2L$

now,

$f_1=340/1.7=200Hz$

$f_2=2\ast 340/1.7=400Hz$

$f_3=600Hz$, $f_4=800Hz$, $f_5=1000Hz$, $f_6=1200Hz$

therefore option "D" is correct.