When looking at the FFT spectrum of a sonometer, I noticed that the harmonics decayed faster than the fundamental. Why is this?
Joella Kait said:When looking at the FFT spectrum of a sonometer, I noticed that the harmonics decayed faster than the fundamental. Why is this?
Do you mean they decay faster in time? Looking at a FFT will not show you that, so your question confuses me.
anorlunda said:Do you mean they decay faster in time? Looking at a FFT will not show you that, so your question confuses me.
Joella Kait said:Yes, I mean decaying faster in time. We kept the FFT spectrum running while we plucked the string and watched peaks form then decay, and the harmonics decayed faster. If this is still confusing (probably due to my inability to explain it well), then don't worry about the FFT part. The point of my question is that I want to know why the harmonics decay faster than the fundamental mode in vibrating string.
boneh3ad said:Sure it would, if you had the FFT at various points in time. This is sometimes called a short-time Fourier transform (STFT).
Out of curiosity here, did you actually measure the decay rates of the fundamental and harmonic and the decay rates were actually different, or did you just notice that the harmonic disappears first?
Do you understand where the harmonics come from on a guitar string?Joella Kait said:I just eyeballed it, and noticed that the harmonics seem to decay faster. I then googled it, and read that this is usually the case, but I'm not sure why.
The energy in a simple free oscillator will decay exponentially and the Q factor is the number of cycles for the energy to drop to 1/e of an initial value.Joella Kait said:and read that this is usually the case, but I'm not sure why.
sophiecentaur said:The energy in a simple free oscillator will decay exponentially and the Q factor is the number of cycles for the energy to drop to 1/e of an initial value.
If the various modes on the string all have the same Q factor (a bit of an assumption perhaps but go with it) then the energy in the modes will all take the same number of cycles of oscillationto fall to 1/e of the original value. That would take half as long for a second harmonic and one third as long for a third harmonic.
anorlunda said:I'm old fashioned, when I think of an FFT, I think of it printed on paper.
A general answer is that most physical systems are low pass filters. They attenuate high frequencies more than low frequencies. There are exceptions, but most things are like that.
marcusl said:Can you explain how energy is exchanged between modes in a string? Modes are, by definition, orthogonal.
rcgldr said:Link to an article with graphs. Figure 3 shows an unusual case where the fundamental harmonic decayed first, but the rest of the harmonics decayed quicker for higher harmonics.
Note it's also possible to place a finger on the node of a harmonic to prevent the fundamental frequency from being generated (or at least greatly reduce it).
I made a broad assumption - true. But the modes would be orthogonal on an ideal string. A guitar has a complex set of resonances and the ends of the strings are not well defined or constant throughout the ranger of angles made by the string. This can result in frequency / mode length modulation of one mode by another mode. In fact, the fact that your effect is observed actually implies that there must be some non linearity. Also, of course, the overtones are not perfect harmonics of the fundamental and you could perhaps expect some beating between modal frequencies and harmonics of the fundamental due to non linearity. Quite a can of worms, in fact.Dr. Courtney said:It is an errant assumption that the different modes all start with a peak energy and decay independently. In reality, energy is traded back and forth between modes and amplitudes of a given spectral peak will both rise and fall over time. Sure, in the long term, they are all decreasing, but the decrease of some modes is not even monotonic, much less exponential.
Joella Kait said:I just eyeballed it, and noticed that the harmonics seem to decay faster.
Mister T said:What did you see that led you to this conclusion? When I pluck a string and look at the FFT what I usually notice is that the higher harmonics have a smaller amplitude. This is not always the case, as it depends to some extent on how the string is plucked. In any case, the information I get about the relative amplitude of the harmonics doesn't necessarily tell me which of them are decaying faster.
If we're going into details it might be interesting to ask how the sonometer string was excited - for instance was it plucked and where. Also, how was the string tensioned and were there any other strings on the apparatus at the same time?boneh3ad said:This is why I asked my original question about how OP was reaching this conclusion, and whether he or she actually measured the decay rate or simply based it on which peak disappeared first.