Question

The fundamental frequency of an open organ pipe is $300\, Hz$. The first overtone of this pipe has same frequency as first overtone of a closed organ pipe. If speed of sound is $330\, m/s$, 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.
$\therefore 1=\frac{ v }{2 n }=\frac{330}{2 \times 300}=\frac{11}{20}$
As frequency of first overtone of open pipe $=$ frequency of first overtone of closed pipe.
$\therefore 2 \frac{ v }{21}=3 \frac{ v }{41'}$
$\Rightarrow 1'=\frac{31}{4}=\frac{3}{4} \times \frac{11}{20}$
$=41.25\, cm$