Final answer:
Harmonics in organ pipes are the frequencies at which the pipe naturally resonates, with open pipes supporting integer multiples of the fundamental frequency as harmonics. The pattern for harmonics depends on whether the pipe is open or closed at one or both ends, affecting the standing wave pattern within the pipe.
Step-by-step explanation:
The concept of harmonics in organ pipes refers to the series of frequencies that the pipe can produce when it resonates. An organ pipe that is open at both ends can support harmonics that are integer multiples of the fundamental frequency. The fundamental frequency is the lowest frequency and is associated with the longest wavelength that fits the length of the pipe, with antinodes (points of maximum amplitude) at both ends and a node (point of zero amplitude) at the center. To find a higher harmonic, such as the next one above a known harmonic, you would look for the next integer multiple. For example, if a pipe has a known harmonic of 448 Hz, and the next higher harmonic is 504 Hz, this suggests that these harmonics may be the so-called n-th and (n+1)-th harmonics of the pipe's fundamental frequency.
In a pipe that is open at both ends, the resonance modes are such that the distance between the two antinodes at the ends is a whole number of half-wavelengths (½λ, 1λ, 1½λ, etc.). For closed-end pipes, only odd harmonics are present, with a node at the closed end and an antinode at the open end, meaning the standing wave fits ¼λ, ¾λ, 5¼λ, and so on.