A closed organ pipe of length `L` and an open organ pipe contain gasses of densities `rho_(1)` and `rho_(2)`, respectively. The compressibility of gasses are equal in both the pipes. Both the pipes are vibrating in their first overtone with same frequency . The length of the open organ pipe is
(a) `(L)/(3)`
`(4l) / (3)`
(c ) `(4l)/(3)sqrt((rho_(1))/(rho_(2)))`
(d) `(4l)/(3)sqrt((rho_(2))/(rho_(1)))`

Explanation

To solve the problem, we need to analyze the relationship between the lengths of the closed organ pipe and the open organ pipe when both are vibrating in their first overtone with the same frequency.

### Step-by-Step Solution:

1. **Understanding the Properties of the Pipes**:
- A closed organ pipe has one closed end and one open end. The fundamental frequency (first harmonic) for a closed pipe is given by:
\[
f_c = \frac{3V_c}{4L_c}
...