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

Options

A. `(L)/(2)`
B. 4 L
C. L
D. 2 L

Answer

D

Explanation

For second overtone (`3^(rd)` harmonic) in open organ pipe,
`(3lambda)/(2)=l_(0)implieslambda=(2l_(0))/(3)`
For first overtone (`3^(rd)` harmonic) in closed organ pipe,
`(3lambda)/(4)=l_(C)implieslambda=(4l_(C))/(3)=(4L)/(3)`
So, `(2l_(0))/(3)=(4L)/(3)impliesl_(0)=2L`.