Question

The second overtone of an open organ pipe has the same frequency as the first overtone of a closed pipe `L` metre long. The length of the open pipe will be
A. `(L)/(2)`
B. `4L`
C. `L`
D. `2L`

Answer 1

Correct Answer - D
For second overtone (3rd harmonic) in open organ pipe,
`(3lamda)/(2)=l_0implieslamda=(2l_0)/(3)`
For first overtone (3rd harmonic) in closed organ pipe,
`(3lamda)/(4)=l_Cimplieslamda=(4l_C)/(3)=(4L)/(3)`
so, `(2l_0)/(3)=(4L)/(3)impliesl_0=2L`