Question

The frequency of an open organ pipe is $n$. If one end is closed then its fundamental frequency will be

• A. $n/2$
• B. $3n/4$
• C. $n$
• D. $2n$

Answer 1

The correct option is A $n/2$

Let velocity of sound in air be $v.$

Open organ pipe:

Let Length of the pipe be $L$.

Fundamental frequency i.e $m=1$, ${\nu }_1=n=\frac{v}{2L}$

Closed organ pipe:

Frequency of different modes , ${\nu }_p^{\prime }=\frac{(2p-1)v}{4L}$

Fundamental frequency i.e $p=1$ , ${\nu }_1^{\prime }=\frac{v}{4L}=\frac{n}{2}$