Question

How many frequencies below $1kHz$ of natural oscillations of air column will be produced if a pipe of length $1m$ is closed at one end? [velocity of sound in air $340m/s$]

• A. $3$
• B. $6$
• C. $4$
• D. $8$

Answer 1

The correct option is B $6$

Given, frequency limit of $1KHz=1000Hz,L=1m\&v=340m/s$.

We have to find how many harmonics have frequency lower than $1KHz$.

The frequency of a closed organ pipe is denoted by $f=\frac{v(2N-1)}{4L}$ where, $N=1,2,3\dots$

$f\le 1000Hz$

$f=\frac{v(2N-1)}{4L}\le 1000$

$f=340(2N-1)\le 1000\times 4$

$f=(2N-1)\le 11.76$

$N<=6.38$

So, 6 harmonics have frequency less than $1000Hz$.

Hence, B is the correct answer.