How do wood panels resonate, and why do my graphs appear as they do?

[abray]

Homework Statement

I have this Physics coursework, where I have been investigating how the resonant frequency of wood changes as I increase the length of the wood and the width, by using increasingly long and increasingly wide panels of thin MDF.

What I would expect to see would be a decrease in resonant frequency as both length and width increase.

The problem is that I am slightly unsure about how resonance occurs in wood panels. I have attached a Vibration generator to the wood in the center of the panel, and then increased the frequency to see when the amplitude of oscillation increases largely (when the wood resonates). The problem is that I have produced some graphs, which show that as the length and width of wing increase, the first resonant frequencies both decrease as I have increased the length, but the data showing the second resonant frequency against an increase in length does show a decrease, but the gradient of my best fit line is not constant. I tried to see if the graph was logarithmic, as the graph did look logarithmic, but it is not, but just a smooth curve. The second resonant frequency of the shortest length (30cm) was just less than 80Hz, whilst the first resonant frequency was just over 20Hz, so it does seem to be a multiple of the first resonant frequency, which seems to make sense, but I am unsure as to why I have not got resonance occurring at e.g. 40Hz.

For the graphs of first and second resonant frequency against width, I have got results which show that for the first resonant frequency - as the width increases, the first resonant frequency decreases (with a constant gradient for the line of best fit), but for the second resonant frequency, the gradient is positive, i.e. as width increases, so does the second resonant frequency. I do not understand why this has occurred.

Homework Equations

V = F*Wavelength

The Attempt at a Solution

I have tried to think about how the wood resonates, and I do sort of understand it, i.e. when resonant frequency = driving frequency, the resonance occurs due to the upwards movement of the driving pin attached to the wing coinciding with the upwards movement of the wing at this point, but I am unsure about how vibrations travel through the wood, i.e is it one whole wavelength either side of the driving pin, with a whole wavelength for the outwards vibration? It does make sense that as the length increases, the first resonant frequency decreases, due to the larger amplitude of oscillation and the longer time taken for the vibrations to travel through the wood, but I do not understand how this fits in when considering waves traveling through the wood, which is partly where I have the problem in even beginning to understand why I have the graphs I do have for the second resonant frequencies for the wood panels.

Any assistance would be greatly appreciated! Thanks

 

[abray]

Please do no bother replying to this. I realize I haven't done enough research and I am aware that the idea about waves traveling through the wood is incorrect. I will research further online.