Two narrow organ pipes, one open (length `l_(1)`) and the other cloed (length `l_(2)`) are sounded in their respective fundamental modes. The beat frequency heard is `5 Hz`. If now the pipes are sounded in their first overtones, then also the beat frequency heard is `5 Hz`. Then:

Options

A. `(l_(1))/(l_(2)) = (1)/(2)`
B. `(l_(1))/(l_(2)) = (1)/(1)`
C. `(l_(1))/(l_(2)) = (3)/(2)`
D. `(l_(1))/(l_(2)) = (2)/(3)`

Answer

B, C

Explanation

fundamental frequency of
open pipe, `n_(0) = (V)/(2l_(1))` , closed pipe, `n_(C) = (V)/(4l_(2))`
`(V)/(2l_(1)) - (V)/(4l_(2)) = 5`
For first overtone , `n_(0) = (V)/(l_(1)) , n_(0) = (3V)/(4l_(2))`
`(V)/(l_(1)) - (3V)/(4l_(2)) = 5` .......(2)
on solving `(1)` and `(2) l_(1) = l_(2) rArr (l_(1))/(l_(2)) = (1)/(1)`