The `4^(th)` overtone of an open organ pipe resonates with the first overtone of semi-open organ pipe. The ration of the length of the open pipe to the semi-open pipe is

Options

A. `5 : 3`
B. `4 : 1`
C. `10 : 3`
D. none of thses

Explanation

To solve the problem, we need to find the ratio of the lengths of an open organ pipe to a semi-open organ pipe, given that the fourth overtone of the open pipe resonates with the first overtone of the semi-open pipe.

### Step-by-Step Solution:

1. **Understanding Overtones**:
- For an open organ pipe, the frequency of the nth overtone is given by:
\[
F_n = \frac{nV}{2L_1}
...