An organ pipe open at both ends is tuned so that its fundamental frequency is a G.

Question:

An organ pipe open at both ends is tuned so that its fundamental frequency is a G. How long is the pipe?

A. \(43 \mathrm{~cm}\)

B. \(87 \mathrm{~cm}\)

C. \(130 \mathrm{~cm}\)

D. \(173 \mathrm{~cm}\)

You know that certain musical notes sound good togetherharmonious-whereas others do not. This harmony is related to the various harmonics of the notes.
The musical notes \(\mathrm{C}(262 \mathrm{~Hz})\) and G (392 Hz) make a pleasant sound when played together; we call this consonance. As Figure P16.70 shows, the harmonics of the two notes are either far from each other or very close to each other (within a few \(\mathrm{Hz}\) ). This is the key to consonance: harmonics that are spaced either far apart or very close. The close harmonics have a beat frequency of a few Hz that is perceived as pleasant. If the harmonics of two notes are close but not too close, the rather high beat frequency between the two is quite unpleasant. This is what we hear as dissonance. Exactly how much a difference is maximally dissonant is a matter of opinion, but harmonic separations of 30 or \(40 \mathrm{~Hz}\) seem to be quite unpleasant for most people. image text in transcribed