New answers tagged dispersion
Good theoretical answer is that it results from linear acoustical wave equation and its presuppositions. It is therefore good approximation whenever linear acoustics still can describe the wave propagation (that would by e.g. 90% of room acoustics practical examples). Typical examples of problematic models are large-amplitude events (e.g. a shockwave after ...
The spectrum of various resonant tube arrangements (half-open, fully-open fully closed) is something that can be measured in a very basic laboratory and gives solid evidence that the claim is true over the kinds of frequencies that are accessible in such a lab. Say a few hundred to a few thousand hertz.
It's a bit pat maybe, but if the wavelength-dependence were detectable over human distance scales, the (quality of) sound (not just the volume) of music, speech etc. would depend noticeably on how far one were from the source.
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