The second overtone of an open pipe A and closed pipe B have the same frequencies at a given temperature. Both pipes contain air. The ratio of fundamental frequency of a to the fundamental frequency of B is

Options

A. `3:5`
B. `5:3`
C. `5:6`
D. `6:5`

Answer

B

Explanation

Second overtone of open pipe `= (3V)/(2l_1)`
Second overtone of closed pipe = `(5V)/(4l_2)`
Since these frequency are same
`implies (3V)/(2l_1) = (5V)/(4l_2) implies (l_1)/(l_2) = (4 xx 3)/(2 xx 5) = 6/5`
Now, the ratio of fundamental frequencies :
`(f_1)/(f_2) = ((V)/(2l_2))/((V)/(4l_2))`
`= (2l_2)/(f_1)`
`= 10 : 6 = 5 :3`