Final answer:
The fundamental difference between harmonics produced by open and closed organ pipes is the presence of even multiples of the fundamental frequency in open pipes and odd multiples in closed pipes. Open-pipe resonators have more overtones than closed-pipe resonators. If two tubes with the same fundamental frequency but different open or closed ends are played, they will sound different due to their different overtones.
Step-by-step explanation:
The fundamental difference between harmonics produced by open and closed organ pipes is the presence of even multiples of the fundamental frequency in open pipes and odd multiples in closed pipes.
An open-pipe resonator, such as an open tube, has more overtones than a closed-pipe resonator, like a closed tube. This is because open pipes allow for the presence of both odd and even multiples of the fundamental frequency, while closed pipes only have odd multiples.
For example, if you have two tubes with the same fundamental frequency, but one is open at both ends and the other is closed at one end, they will sound different when played because they have different overtones. The open tube will sound richer because it has even multiples of the fundamental as well as odd, while the closed tube only has odd multiples.