Question

If the fundamental frequency of a closed organ pipe is the same as the first overtone frequency of an open pipe and the length of the open pipe is 50 cm, the length of the closed pipe is

• A. 25 cm
• B. 15 m
• C. 100 cm
• D. 200 cm

Answer 1

The correct option is B 15 m

For a closed organ pipe, frequency is given by

${\nu }_n=\frac{\nu }{4l}$

For the fundamental frequency $(n=0)$

${\nu }_0=\frac{\nu }{4l_c}\to \left(1\right)$

For open organ pipe,

${\nu }^{\prime }=\frac{n\nu }{2l_0}$

For overtone frequency, $(n=2)$

${\nu }_1^{\prime }=\frac{\nu }{l_0}\to \left(2\right)$

${\nu }_0={\nu }_1^{\prime }$

$\frac{\nu }{4l_c}=\frac{\nu }{l_0}$

$⟹l_c=\frac{l_0}{4}=\frac{60}{4}=15cm$