On Tue, 6 Jan 2009, Herbert Ward wrote: > Thanks for the note. I did indeed observe that the peaks in the spectrum > broadened as the observation region was decreased. However, I made the > assumption that the peak centroids remained unmoved despite the broadening, > and thus I thought my results unaffected. > > It seems the validity of my assumption can be easily checked by using > a tone from an electronic device and doing the Fourier integral over > many different observation times, varying both in length and start > time. I'll do this in the next few days.
I calculated the spectral density of a cosine over a finite interval. The width of the central peak does indeed do what it must, i.e., it increases as the interval decreases, but I could not come up with any simple mechanism that would shift the maximum of the curve noticeably. In other words, my calculation seems to confirm your assumption, and the shift needs some explanation other than the being the result of an arbitrary, ill-defined window function (see e.g. http://en.wikipedia.org/wiki/Window_function). Maybe the following qualitative argument explains your observed shift to lower frequencies. Initially, all the vibrational energy is in the vibrating string. Then other parts of the lute start to vibrate too, which means that the the body of the lute drains energy out of the string, which provides an effective damping mechanism. If we can consider the vibrating string as a damped harmonic oscillator, it would indeed vibrate at a lower frequency than an undamped string. After a while the whole object, body and string, approaches a semblance of equilibrium and in the process the frequency increases as the fast initial damping ceases. It would make sense that this whole process happens much faster than the ultimate damping of the sound. Unfortunately, I do not know how verify all of this in a couple of minutes, but it should not be too difficult to come up with a simple model consisting of a bunch of coupled oscillators. Peter. > > > > To get on or off this list see list information at > http://www.cs.dartmouth.edu/~wbc/lute-admin/index.html > the next auto-quote is: When people learn no tools of judgment and merely follow their hopes, the seeds of political manipulation are sown. (Stephen Jay Gould) /\/\ Peter Nightingale Telephone (401) 874-5882 Department of Physics, East Hall Fax (401) 874-2380 University of Rhode Island Kingston, RI 02881
