The frequency of the third overtone of a closed pipe
of length `L_(c)` is the same as the frequency of the sixth
overtone of an open pipe of the length `L_(o).` Then

Options

A. `L_(o)/L_(c) = 4`
B. `L_(o)/L_(c) = 2/1`
C. `L_(o)/L_(c) = 1/4`
D. `L_(o)/L_(c) = 1/2`

Answer

B

Explanation

For third overtone of closed pipe, the frequency
`= 7n = (7V)/(4Lc) `
and for sixth overtone of the open pipe (Lo) , `7n' = (7V)/(2Lo) `
` :. (7V)/(4Lc) = (7V)/(2Lo) :. (Lo)/(Lc) = 2/1`