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AAS Chromaphone Manual

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4.2 General Notions of Acoustics 21
As an example, the vibration motion associated with two normal modes of a rectangular plate
is illustrated in Figures 7 and 8. In the first figure, one can see the vibration motion associated with
two different normal modes of the plate (modes [1,1] and [3,2]). Over one period of oscillation,
all the points go up and down in phase. The principle remains the same for all mode, the motion
pattern only becoming more and more complex as the order of the mode increases. The full motion
of a plate, however complicated, will always correspond to a combination of all its normal modes.
Figure 8 is a top view of the plate and shows contour lines corresponding to the same normal modes.
A contour line groups points that oscillate with the same amplitude. In particular, the straight lines
in the second graph of this figure, corresponds to so-called nodal lines where the amplitude of the
motion is zero and therefore where the plate is still.
The relative frequencies or ratio of the frequency of the overtones to the fundamental frequency
is specific to the type of the object and its boundary conditions (whether its boundaries are free to
vibrate or are fixed). In other words this distribution of partials is characteristic of the type of object
and could be viewed as its tonal signature; it allows us to distinguish, for example, a vibrating
plate from a drumhead. The specific frequency of the partials, related to the sensation of pitch, is
determined by the dimensions of the object, for example a small plate will have a higher pitch than
an larger one.
Figure 7: Motion corresponding to normal mode [1,1] and [3,2] of a plate.
But this is not all, we can distinguish different types of objects, such as a vibrating plate and a
beam, but also two objects of the same type but made out of different material. For example a metal
plate will sound brighter and have a longer decay than a wooden plate. This is due to the fact that
the physical properties of an object depend on its material which determine the relative amplitude
and phase of the different partials as well as their damping, a measure of how fast they will decay
once excited. The specific amplitude, phase and damping of each partial therefore determine the
specific tone of the object as well as how it evolves with time.
There is finally one more parameter which affects how an object sounds, it is the point of
excitation. Indeed, a drumhead does not sound the same if it is hit in the middle or near the rim
of the drum. This can be understood by the fact that exciting an object on a point located on a
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