An organ pipe of length L open at both ends is found to vibrate in its harmonic when sounded with a tuning fork of 480Hz. What should be the length of a pipe closed at one end, so that it also vibrates in its first harmonic with the same tuning fork?

Explanation

To solve the problem, we need to find the length of a pipe closed at one end that vibrates in its first harmonic with the same frequency as an open pipe of length L vibrating in its first harmonic.

### Step-by-Step Solution:

1. **Understand the Harmonics of Open and Closed Pipes:**
- An open pipe (open at both ends) supports standing waves with nodes at both ends. The fundamental frequency (first harmonic) for an open pipe is given by:
\[
f = \frac{v}{2L}
...