First overtone frequency of a closed pipe of length `l_1` is equal to the `2^(nd)` harmonic frequency of an `l_2` open pipe of length. The ratio `l_1/l_2` =

Options

A. `3/4`
B. `4/3`
C. `3/2`
D. `2/3`

Answer

A

Explanation

First overtone frequency (i.e `3^(rd)` harmonic ) of the closed pipe of length `l_1` is
`upsilon_c=(3v)/(4l_1)` (where v is the speed of sound in air) and `2^(nd)` harmonic frequency of the open pipe of length `l_2` is
`upsilon_0=(2v)/(2l_2)=v/l_2`
As per question `upsilon_c=upsilon_o`
`:.(3v)/(4l_1)=v/l_2" or "l_1/l_2=3/4`