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)

120 cm

Answer 2

For closed organ pipe, fundamental frequency is given by $\upsilon_c=\frac{v}{4l}$ For open organ pipe, fundamental frequency is given by $\upsilon_0=\frac{v}{2l'}$ $2^{nd}$ overtone of open organ pipe $\upsilon'=3\upsilon_a ; \upsilon'=\frac{3v}{2l'}$ According to question, $\upsilon_c=\upsilon'$ $\frac{v}{4l}=\frac{3v}{2l'}$ $l'=6l$ Here, $l$ = 20 cm, $l' = ?$ $\therefore l'=6\times 20=120\, cm$