As an exercise, I pose this question. A cymbal has no definite pitch, but it rings for a long time. So it does not follow the rules below. Why?
On Sat, 29 Nov 2014, Herbert Ward wrote: >> But I invite all you proper physicists out there to explain why! > > I have a PhD in experimental physics. > > The term "resonant frequency" is a bit complicated. > > A string has a "resonant frequency" (its pitch). > But a string's resonant frequency is obviously different from > a lute's "resonant frequency". For when I tap my lute, it does not > ring at a specific pitch like (F# or Bb or 413.7 Hz). > > A lute's resonant frequency is very broad (I guess several octaves). > A string's resonant frequency is very narrow (I guess 0.5 Hz). > > As the math works out: > lute haves a broad resonant frequency = short ring time > string haves a narrow resonant frequency = long ring time > > The physical difference is how much "damping" there here. > You can google "damped harmonic oscillater" for more info. > > Many factors apply to both lutes and strings: > 1. lighter = higher pitch > 2. stiffer = higher pitch > 3. heavier = lower pitch > 4. looser = lower pitch > > As to why a smaller rosette makes a lower pitch, I'm not sure. It > might be simply because the is more mass in the soundboard (#3 above). > Or it might have be related to how wooodwind sound holes work. Or maybe > both. An experiment to resolve the question would, I'm afraid, involve > the destruction/degradation of the soundboard on a good lute. > > > > To get on or off this list see list information at > http://www.cs.dartmouth.edu/~wbc/lute-admin/index.html >
