Domande onde stazionarie en
From "Physics, Waves, Music": a website about the physics of waves and sound, acoustics of musical instruments, musical scales, harmony and music.
| AI-translated from Italian. Original page: Domande_onde_stazionarie |
Seeing that a stationary wave does not propagate, how is it a wave?
A standing (stationary) wave is still a wave because it is a particular solution of the wave equation. Moreover, it can be shown that every standing wave can be broken down into a sum of travelling waves. So, even if we stick to the less mathematical definition of a wave (wave = a disturbance that propagates), we could say that standing waves are nothing but particular combinations (or rather superpositions) of travelling waves.
- If you are interested in finding out more, see the pages
and related links.
- For a more formal treatment see also
and related links.
The frequencies of a string are integer multiples of the fundamental, with no frequencies in between: is this a "quantum" phenomenon?
No. It is true that a vibrating string emits only certain frequencies, integer multiples of the fundamental (at least for an ideal string), but this has nothing to do with quantum physics. It depends only on the boundary conditions: the string is fixed at its ends, so only standing waves with a node at both ends can exist on it, that is those in which the string contains a whole number of half wavelengths (see normal modes of a string).
The similarity with quantum mechanics is not accidental: in the atom, too, energy levels are discrete because the "matter waves" of the electrons must satisfy boundary conditions. But the string is a classical system, like that of the air in an organ pipe.
For this reason the expression "quantum spectroscopy" is not suitable for musical acoustics: in physics it refers to observing lines in the electromagnetic spectrum emitted or absorbed by atoms and molecules. For sounds one speaks of a harmonic spectrum. Note finally that in real strings the partials are not exactly harmonic: the stiffness of the string makes them slightly higher than exact multiples, the more so the thicker and shorter the string.
