Question

The fundamental frequency of a closed organ pipe of length $20\,cm$ is equal to the second overtone of an organ pipe open at both the ends. The length of organ pipe open at both the ends is

• A. 120 cm
• B. 140 cm
• C. 80 cm
• D. 100 cm

Answer 1

Answer: (A)

For closed organ pipe, fundamental frequency is given by $v_{c}=\frac{v}{4 l}$
For open organ pipe, fundamental frequency is given by $v_{o}=\frac{v}{2 l^{\prime}}$
$2^{\text {nd }}$ overtone of open organ pipe
$v^{\prime}=3 v_{o} ; v^{\prime}=\frac{3 v}{2 l^{\prime}}$
According to question, $v_{c}=v^{\prime}$
$\frac{v}{4 l}=\frac{3 v}{2 l^{\prime}} $
$l^{\prime}=6 l$
Here, $l=20 \,cm , l^{\prime}=$ ?
$\therefore l^{\prime}=6 \times 20=120 \,cm$