Question

the fundamental note produced by a closed organ pipe is of frequency f the fundamental note produced by an organ open pipe of same length will be of frequency​

Answer 1

Explanation:

The note produced by an open organ pie consists of both odd and even hapmonics but the note produced by a closed organ pipe consists of only odd harmonics. Due to the presence of larger number of overtones or harmonics, the note produced by an open organ pipe is is sweeter."

I disagree with the answer. If we assume two organ pipes of the same length l the first one open and the second one closed, the harmonics of both the organ pipes are:

Open: v2l, 2v2l,3v2l, etc with a difference of v2l between successive harmonics

Closed: v4l, 3v4l,5v4l, etc with a difference of v2l between successive harmonics.

In both cases the harmonics form an AP with the same common difference. Just the first term is different. Then how can we say that the open organ pipe would have larger no. of overtones? According to this logic the very statement that the note produced by an open organ pipe is sweeter then that produced by a closed organ pipe seems false. Where am I going wrong?