An organ pipe of length L open at both ends is found to vibrate in its first harmonic when sounded with a tuning fork of 480 Hz. 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?

Hint: Use the concept of standing waves.
Step 1: Find the frequency of the open pipe.
Consider the situation in the diagram.
As the organ pipe is open at both ends. Hence, for the first harmonic,
where c is the speed of the sound wave in the air.
Step 2: Find the frequency of the closed pipe.
For pipe closed at one end, ν'=c4L'
For the first harmonic,
L'L=24=12L'=L2                                                      [ for resonance with same tuning fork]
[ speed remains constant]