Question

The fundamental frequency of an open organ pipe is $300Hz$. The first overtone of this pipe has same frequency as first overtone of a closed organ pipe. If speed of sound is $330m/s$, then the length of closed organ pipe is

• A. 41 cm
• B. 37 cm
• C. 45 cm
• D. 35 cm

Answer 1

Answer: (A)

For open pipe, $n=\frac{v}{21}$,
where $n_0$ is the fundamental frequency of the open pipe.
$\therefore 1=\frac{v}{2n}=\frac{330}{2\times 300}=\frac{11}{20}$
As frequency of first overtone of open pipe $=$ frequency of first overtone of closed pipe.
$\therefore 2\frac{v}{21}=3\frac{v}{41^{\prime }}$
$\Rightarrow 1^{\prime }=\frac{31}{4}=\frac{3}{4}\times \frac{11}{20}$
$=41.25cm$