Find the number of possible natural oscillations of air column in a pipe frequencies of which lie below ` v_(0) = 1250 Hz`. The length of the pipe is `l = 85 cm`. The velocity of sound is `v = 340 m//s`. Consider two cases
i. the pipe is closed from the end ,
ii. the pipe is open from both ends.

Explanation

To solve the problem, we will analyze the two cases separately: one where the pipe is closed at one end and the other where the pipe is open at both ends.

### Case 1: Pipe Closed at One End

1. **Understanding the Fundamental Frequency**:
For a pipe closed at one end, the natural frequencies can be expressed as:
\[
f_n = \frac{(2n - 1) v}{4L}
...